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class="vector-toc-list"> </ul> </li> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Types</span> </div> </a> <button aria-controls="toc-Types-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Types subsection</span> </button> <ul id="toc-Types-sublist" class="vector-toc-list"> <li id="toc-Diamagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diamagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Diamagnetism</span> </div> </a> <ul id="toc-Diamagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Paramagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Paramagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Paramagnetism</span> </div> </a> <ul id="toc-Paramagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferromagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferromagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Ferromagnetism</span> </div> </a> <ul id="toc-Ferromagnetism-sublist" class="vector-toc-list"> <li id="toc-Magnetic_domains" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Magnetic_domains"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.1</span> <span>Magnetic domains</span> </div> </a> <ul id="toc-Magnetic_domains-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Antiferromagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Antiferromagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Antiferromagnetism</span> </div> </a> <ul id="toc-Antiferromagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferrimagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferrimagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Ferrimagnetism</span> </div> </a> <ul id="toc-Ferrimagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Superparamagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Superparamagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Superparamagnetism</span> </div> </a> <ul id="toc-Superparamagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nagaoka_magnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nagaoka_magnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Nagaoka magnetism</span> </div> </a> <ul id="toc-Nagaoka_magnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_types_of_magnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_types_of_magnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Other types of magnetism</span> </div> </a> <ul id="toc-Other_types_of_magnetism-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Electromagnet" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Electromagnet"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Electromagnet</span> </div> </a> <ul id="toc-Electromagnet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetism,_electricity,_and_special_relativity" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Magnetism,_electricity,_and_special_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Magnetism, electricity, and special relativity</span> </div> </a> <ul id="toc-Magnetism,_electricity,_and_special_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetic_fields_in_a_material" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Magnetic_fields_in_a_material"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Magnetic fields in a material</span> </div> </a> <ul id="toc-Magnetic_fields_in_a_material-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetic_force" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Magnetic_force"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Magnetic force</span> </div> </a> <ul id="toc-Magnetic_force-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetic_dipoles" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Magnetic_dipoles"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Magnetic dipoles</span> </div> </a> <button aria-controls="toc-Magnetic_dipoles-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Magnetic dipoles subsection</span> </button> <ul id="toc-Magnetic_dipoles-sublist" class="vector-toc-list"> <li id="toc-Magnetic_monopoles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Magnetic_monopoles"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Magnetic monopoles</span> </div> </a> <ul id="toc-Magnetic_monopoles-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Units" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Units"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Units</span> </div> </a> <button aria-controls="toc-Units-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Units subsection</span> </button> <ul id="toc-Units-sublist" class="vector-toc-list"> <li id="toc-SI" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SI"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>SI</span> </div> </a> <ul id="toc-SI-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Other</span> </div> </a> <ul id="toc-Other-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Living_things" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Living_things"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Living things</span> </div> </a> <ul id="toc-Living_things-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interpretation_of_magnetism_by_means_of_relative_velocities" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Interpretation_of_magnetism_by_means_of_relative_velocities"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Interpretation of magnetism by means of relative velocities</span> </div> </a> <ul id="toc-Interpretation_of_magnetism_by_means_of_relative_velocities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum-mechanical_origin_of_magnetism" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Quantum-mechanical_origin_of_magnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Quantum-mechanical origin of magnetism</span> </div> </a> <ul id="toc-Quantum-mechanical_origin_of_magnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Magnetism</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 92 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-92" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">92 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Afrikaans" lang="af" hreflang="af" data-title="Magnetisme" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%82%E0%A4%AC%E0%A4%95%E0%A4%A4%E0%A5%8D%E0%A4%B5" title="चुंबकत्व – Angika" lang="anp" hreflang="anp" data-title="चुंबकत्व" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%BA%D9%86%D8%A7%D8%B7%D9%8A%D8%B3%D9%8A%D8%A9" title="مغناطيسية – Arabic" lang="ar" hreflang="ar" data-title="مغناطيسية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%84%D5%A1%D5%A3%D5%B6%D5%AB%D5%BD%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%AB%D6%82%D5%B6" title="Մագնիսականութիւն – Western Armenian" lang="hyw" hreflang="hyw" data-title="Մագնիսականութիւն" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Magnetismu" title="Magnetismu – Asturian" lang="ast" hreflang="ast" data-title="Magnetismu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Maqnetizm" title="Maqnetizm – Azerbaijani" lang="az" hreflang="az" data-title="Maqnetizm" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A7%81%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%95%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="চুম্বকত্ব – Bangla" lang="bn" hreflang="bn" data-title="চুম্বকত্ব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ch%C3%BB-kh%C3%AC" title="Chû-khì – Minnan" lang="nan" hreflang="nan" data-title="Chû-khì" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D1%8B%D0%B7%D0%BC" title="Магнетызм – Belarusian" lang="be" hreflang="be" data-title="Магнетызм" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D1%8D%D1%82%D1%8B%D0%B7%D0%BC" title="Магнэтызм – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Магнэтызм" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Central Bikol" lang="bcl" hreflang="bcl" data-title="Magnetismo" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D1%8A%D0%BC" title="Магнетизъм – Bulgarian" lang="bg" hreflang="bg" data-title="Магнетизъм" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Magnetismus" title="Magnetismus – Bavarian" lang="bar" hreflang="bar" data-title="Magnetismus" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%81%E0%BD%96%E0%BC%8B%E0%BD%A3%E0%BD%BA%E0%BD%93%E0%BC%8B" title="ཁབ་ལེན་ – Tibetan" lang="bo" hreflang="bo" data-title="ཁབ་ལེན་" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Magnetizam" title="Magnetizam – Bosnian" lang="bs" hreflang="bs" data-title="Magnetizam" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Gwarellegezh" title="Gwarellegezh – Breton" lang="br" hreflang="br" data-title="Gwarellegezh" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Catalan" lang="ca" hreflang="ca" data-title="Magnetisme" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Магнетизм – Chuvash" lang="cv" hreflang="cv" data-title="Магнетизм" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Magnetismus" title="Magnetismus – Czech" lang="cs" hreflang="cs" data-title="Magnetismus" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Danish" lang="da" hreflang="da" data-title="Magnetisme" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Magnetismus" title="Magnetismus – German" lang="de" hreflang="de" data-title="Magnetismus" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Magnetism" title="Magnetism – Estonian" lang="et" hreflang="et" data-title="Magnetism" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B3%CE%BD%CE%B7%CF%84%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Μαγνητισμός – Greek" lang="el" hreflang="el" data-title="Μαγνητισμός" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Spanish" lang="es" hreflang="es" data-title="Magnetismo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Esperanto" lang="eo" hreflang="eo" data-title="Magnetismo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Basque" lang="eu" hreflang="eu" data-title="Magnetismo" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%BA%D9%86%D8%A7%D8%B7%DB%8C%D8%B3" title="مغناطیس – Persian" lang="fa" hreflang="fa" data-title="مغناطیس" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Magn%C3%A9tisme" title="Magnétisme – French" lang="fr" hreflang="fr" data-title="Magnétisme" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Maighn%C3%A9adas" title="Maighnéadas – Irish" lang="ga" hreflang="ga" data-title="Maighnéadas" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Galician" lang="gl" hreflang="gl" data-title="Magnetismo" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9E%90%EA%B8%B0" title="자기 – Korean" lang="ko" hreflang="ko" data-title="자기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A3%D5%B6%D5%AB%D5%BD%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Մագնիսականություն – Armenian" lang="hy" hreflang="hy" data-title="Մագնիսականություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95%E0%A4%A4%E0%A5%8D%E0%A4%B5" title="चुम्बकत्व – Hindi" lang="hi" hreflang="hi" data-title="चुम्बकत्व" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Magnetizam" title="Magnetizam – Croatian" lang="hr" hreflang="hr" data-title="Magnetizam" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Ido" lang="io" hreflang="io" data-title="Magnetismo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Indonesian" lang="id" hreflang="id" data-title="Magnetisme" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ubuwonga" title="Ubuwonga – Zulu" lang="zu" hreflang="zu" data-title="Ubuwonga" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Segulmagn" title="Segulmagn – Icelandic" lang="is" hreflang="is" data-title="Segulmagn" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Italian" lang="it" hreflang="it" data-title="Magnetismo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%92%D7%A0%D7%98%D7%99%D7%95%D7%AA" title="מגנטיות – Hebrew" lang="he" hreflang="he" data-title="מגנטיות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%C9%A9%C9%A3t%CA%8B_h%C9%94m_%C9%96o%C5%8B_(magn%C3%A9tisme)" title="Ñɩɣtʋ hɔm ɖoŋ (magnétisme) – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñɩɣtʋ hɔm ɖoŋ (magnétisme)" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B2%BE%E0%B2%82%E0%B2%A4%E0%B2%A4%E0%B3%86" title="ಕಾಂತತೆ – Kannada" lang="kn" hreflang="kn" data-title="ಕಾಂತತೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%92%E1%83%9C%E1%83%94%E1%83%A2%E1%83%98%E1%83%96%E1%83%9B%E1%83%98" title="მაგნეტიზმი – Georgian" lang="ka" hreflang="ka" data-title="მაგნეტიზმი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Магнетизм – Kazakh" lang="kk" hreflang="kk" data-title="Магнетизм" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Usumaku" title="Usumaku – Swahili" lang="sw" hreflang="sw" data-title="Usumaku" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Магнетизм – Kyrgyz" lang="ky" hreflang="ky" data-title="Магнетизм" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Magn%C4%93tisms" title="Magnētisms – Latvian" lang="lv" hreflang="lv" data-title="Magnētisms" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Magnetismus" title="Magnetismus – Luxembourgish" lang="lb" hreflang="lb" data-title="Magnetismus" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Magnetizmas" title="Magnetizmas – Lithuanian" lang="lt" hreflang="lt" data-title="Magnetizmas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Limburgish" lang="li" hreflang="li" data-title="Magnetisme" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/makykai" title="makykai – Lojban" lang="jbo" hreflang="jbo" data-title="makykai" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/M%C3%A1gness%C3%A9g" title="Mágnesség – Hungarian" lang="hu" hreflang="hu" data-title="Mágnesség" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%B0%D0%BC" title="Магнетизам – Macedonian" lang="mk" hreflang="mk" data-title="Магнетизам" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B4%A4" title="കാന്തികത – Malayalam" lang="ml" hreflang="ml" data-title="കാന്തികത" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kemagnetan" title="Kemagnetan – Malay" lang="ms" hreflang="ms" data-title="Kemagnetan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%B6%E1%80%9C%E1%80%AD%E1%80%AF%E1%80%80%E1%80%BA%E1%80%93%E1%80%AC%E1%80%90%E1%80%BA" title="သံလိုက်ဓာတ် – Burmese" lang="my" hreflang="my" data-title="သံလိုက်ဓာတ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Dutch" lang="nl" hreflang="nl" data-title="Magnetisme" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%A3%81%E6%80%A7" title="磁性 – Japanese" lang="ja" hreflang="ja" data-title="磁性" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Magnetisme" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Magnetisme" title="Magnetisme – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Magnetisme" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Magnetizm" title="Magnetizm – Uzbek" lang="uz" hreflang="uz" data-title="Magnetizm" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9A%E0%A9%81%E0%A9%B0%E0%A8%AC%E0%A8%95%E0%A8%A4%E0%A8%BE" title="ਚੁੰਬਕਤਾ – Punjabi" lang="pa" hreflang="pa" data-title="ਚੁੰਬਕਤਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D9%82%D9%86%D8%A7%D8%B7%DB%8C%D8%B3%DB%8C%D8%AA" title="مقناطیسیت – Pashto" lang="ps" hreflang="ps" data-title="مقناطیسیت" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Magnetyzm" title="Magnetyzm – Polish" lang="pl" hreflang="pl" data-title="Magnetyzm" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Portuguese" lang="pt" hreflang="pt" data-title="Magnetismo" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Magnetism" title="Magnetism – Romanian" lang="ro" hreflang="ro" data-title="Magnetism" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Llut%27ariy" title="Llut'ariy – Quechua" lang="qu" hreflang="qu" data-title="Llut'ariy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Магнетизм – Russian" lang="ru" hreflang="ru" data-title="Магнетизм" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Magnetizmi" title="Magnetizmi – Albanian" lang="sq" hreflang="sq" data-title="Magnetizmi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Magnitismu" title="Magnitismu – Sicilian" lang="scn" hreflang="scn" data-title="Magnitismu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Magnetism" title="Magnetism – Simple English" lang="en-simple" hreflang="en-simple" data-title="Magnetism" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%85%D9%82%D9%86%D8%A7%D8%B7%D9%8A%D8%B3%D9%8A%D8%AA" title="مقناطيسيت – Sindhi" lang="sd" hreflang="sd" data-title="مقناطيسيت" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Magnetizmus" title="Magnetizmus – Slovak" lang="sk" hreflang="sk" data-title="Magnetizmus" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Magnetizem" title="Magnetizem – Slovenian" lang="sl" hreflang="sl" data-title="Magnetizem" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%B0%D0%BC" title="Магнетизам – Serbian" lang="sr" hreflang="sr" data-title="Магнетизам" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Magnetizam" title="Magnetizam – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Magnetizam" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Magn%C3%A9tisme" title="Magnétisme – Sundanese" lang="su" hreflang="su" data-title="Magnétisme" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Magnetismi" title="Magnetismi – Finnish" lang="fi" hreflang="fi" data-title="Magnetismi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Magnetism" title="Magnetism – Swedish" lang="sv" hreflang="sv" data-title="Magnetism" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Tagalog" lang="tl" hreflang="tl" data-title="Magnetismo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%BE%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="காந்தவியல் – Tamil" lang="ta" hreflang="ta" data-title="காந்தவியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%85%E0%B0%AF%E0%B0%B8%E0%B1%8D%E0%B0%95%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B0%A4%E0%B1%8D%E0%B0%B5%E0%B0%82" title="అయస్కాంతత్వం – Telugu" lang="te" hreflang="te" data-title="అయస్కాంతత్వం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B9%87%E0%B8%81" title="ความเป็นแม่เหล็ก – Thai" lang="th" hreflang="th" data-title="ความเป็นแม่เหล็ก" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Manyetizma" title="Manyetizma – Turkish" lang="tr" hreflang="tr" data-title="Manyetizma" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Магнетизм – Ukrainian" lang="uk" hreflang="uk" data-title="Магнетизм" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%82%D9%86%D8%A7%D8%B7%DB%8C%D8%B3%DB%8C%D8%AA" title="مقناطیسیت – Urdu" lang="ur" hreflang="ur" data-title="مقناطیسیت" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%AB_h%E1%BB%8Dc" title="Từ học – Vietnamese" lang="vi" hreflang="vi" data-title="Từ học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Magn%C3%B5tism" title="Magnõtism – Võro" lang="vro" hreflang="vro" data-title="Magnõtism" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Magnetismo" title="Magnetismo – Waray" lang="war" hreflang="war" data-title="Magnetismo" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%A3%81" title="磁 – Wu" lang="wuu" hreflang="wuu" data-title="磁" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%A3%81" title="磁 – Cantonese" lang="yue" hreflang="yue" data-title="磁" data-language-autonym="粵語" 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Class of physical phenomena</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Magnetic" and "Magnetized" redirect here. For other uses, see <a href="/wiki/Magnetic_(disambiguation)" class="mw-disambig" title="Magnetic (disambiguation)">Magnetic (disambiguation)</a>, <a href="/wiki/Magnetism_(disambiguation)" class="mw-disambig" title="Magnetism (disambiguation)">Magnetism (disambiguation)</a>, and <a href="/wiki/Magnetized_(disambiguation)" class="mw-disambig" title="Magnetized (disambiguation)">Magnetized (disambiguation)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Metal_shavings_around_bar_magnet_(close-up).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Metal_shavings_around_bar_magnet_%28close-up%29.jpg/300px-Metal_shavings_around_bar_magnet_%28close-up%29.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Metal_shavings_around_bar_magnet_%28close-up%29.jpg/450px-Metal_shavings_around_bar_magnet_%28close-up%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Metal_shavings_around_bar_magnet_%28close-up%29.jpg/600px-Metal_shavings_around_bar_magnet_%28close-up%29.jpg 2x" data-file-width="3078" data-file-height="2052" /></a><figcaption>The shape of a bar <a href="/wiki/Magnet" title="Magnet">magnet</a>'s <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> is revealed by the orientation of <a href="/wiki/Iron_filings" title="Iron filings">iron filings</a> sprinkled on the table around it.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl 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0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a></th></tr><tr><td class="sidebar-image"><span class="skin-invert-image" typeof="mw:File/Frameless"><a href="/wiki/File:VFPt_Solenoid_correct2.svg" class="mw-file-description" title="Solenoid"><img alt="Solenoid" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/190px-VFPt_Solenoid_correct2.svg.png" decoding="async" width="190" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/285px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/380px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electricity" title="Electricity">Electricity</a></li> <li><a class="mw-selflink selflink">Magnetism</a></li> <li><a href="/wiki/Optics" title="Optics">Optics</a></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks</a></li> <li><a href="/wiki/List_of_electrical_phenomena" title="List of electrical phenomena">Phenomena</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a href="/wiki/Magnetic_scalar_potential" title="Magnetic scalar potential">Magnetic scalar potential</a></li> <li><a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">Magnetic vector potential</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">Permeability</a></li> <li><a href="/wiki/Right-hand_rule#Electromagnetism" title="Right-hand rule">Right-hand rule</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Electrodynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrical_network" title="Electrical network">Electrical network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a></li> <li><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></li> <li><a href="/wiki/Current_density" title="Current density">Current density</a></li> <li><a href="/wiki/Direct_current" title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Magnetism</b> is the class of physical attributes that occur through a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>, which allows objects to attract or repel each other. Because both <a href="/wiki/Electric_current" title="Electric current">electric currents</a> and <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moments</a> of <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a> give rise to a magnetic field, magnetism is one of two aspects of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>. </p><p>The most familiar effects occur in <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> materials, which are strongly attracted by magnetic fields and can be <a href="/wiki/Magnetization" title="Magnetization">magnetized</a> to become permanent <a href="/wiki/Magnet" title="Magnet">magnets</a>, producing magnetic fields themselves. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones are <a href="/wiki/Iron" title="Iron">iron</a>, <a href="/wiki/Cobalt" title="Cobalt">cobalt</a>, <a href="/wiki/Nickel" title="Nickel">nickel</a>, and their alloys. </p><p>All substances exhibit some type of magnetism. Magnetic materials are classified according to their bulk susceptibility.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, but there are actually several types of magnetism. <a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnetic</a> substances, such as <a href="/wiki/Aluminium" title="Aluminium">aluminium</a> and <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, are weakly attracted to an applied magnetic field; <a href="/wiki/Diamagnetism" title="Diamagnetism">diamagnetic</a> substances, such as <a href="/wiki/Copper" title="Copper">copper</a> and <a href="/wiki/Carbon" title="Carbon">carbon</a>, are weakly repelled; while <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">antiferromagnetic</a> materials, such as <a href="/wiki/Chromium" title="Chromium">chromium</a>, have a more complex relationship with a magnetic field.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness"><span title="This information is too vague. (October 2024)">vague</span></a></i>]</sup> The force of a magnet on paramagnetic, diamagnetic, and antiferromagnetic materials is usually too weak to be felt and can be detected only by laboratory instruments, so in everyday life, these substances are often described as non-magnetic. </p><p>The strength of a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> always decreases with distance from the magnetic source,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> though the exact mathematical relationship between strength and distance varies. Many factors can influence the magnetic field of an object including the magnetic moment of the material, the physical shape of the object, both the magnitude and direction of any electric current present within the object, and the temperature of the object. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History of electromagnetic theory</a></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Magnetism" title="Special:EditPage/Magnetism">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">October 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lodestone_attracting_nails.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Lodestone_attracting_nails.png/170px-Lodestone_attracting_nails.png" decoding="async" width="170" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Lodestone_attracting_nails.png/255px-Lodestone_attracting_nails.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Lodestone_attracting_nails.png/340px-Lodestone_attracting_nails.png 2x" data-file-width="532" data-file-height="668" /></a><figcaption><a href="/wiki/Lodestone" title="Lodestone">Lodestone</a>, a natural <a href="/wiki/Magnet" title="Magnet">magnet</a>, attracting iron nails. Ancient humans discovered the property of magnetism from lodestone.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Blacksmith_at_the_anvil._Wellcome_L0005875.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Blacksmith_at_the_anvil._Wellcome_L0005875.jpg/220px-Blacksmith_at_the_anvil._Wellcome_L0005875.jpg" decoding="async" width="220" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Blacksmith_at_the_anvil._Wellcome_L0005875.jpg/330px-Blacksmith_at_the_anvil._Wellcome_L0005875.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Blacksmith_at_the_anvil._Wellcome_L0005875.jpg/440px-Blacksmith_at_the_anvil._Wellcome_L0005875.jpg 2x" data-file-width="1479" data-file-height="1206" /></a><figcaption>An illustration from Gilbert's 1600 <i>De Magnete</i> showing one of the earliest methods of making a magnet. A blacksmith holds a piece of red-hot iron in a north–south direction and hammers it as it cools. The magnetic field of the Earth aligns the domains, leaving the iron a weak magnet.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg/170px-A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg" decoding="async" width="170" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg/255px-A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg/340px-A_man_is_violently_rubbed_with_magnets._Coloured_lithograph_Wellcome_V0011767.jpg 2x" data-file-width="2526" data-file-height="3124" /></a><figcaption>Drawing of a medical treatment using magnetic brushes. <a href="/wiki/Charles_Jacque" title="Charles Jacque">Charles Jacque</a> 1843, France.</figcaption></figure> <p>Magnetism was first discovered in the ancient world when people noticed that <a href="/wiki/Lodestone" title="Lodestone">lodestones</a>, naturally magnetized pieces of the mineral <a href="/wiki/Magnetite" title="Magnetite">magnetite</a>, could attract iron.<sup id="cite_ref-Tremolet_3-0" class="reference"><a href="#cite_note-Tremolet-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The word <i>magnet</i> comes from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Greek</a> term μαγνῆτις λίθος <i>magnētis lithos</i>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> "the Magnesian stone, lodestone".<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In ancient Greece, <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> attributed the first of what could be called a scientific discussion of magnetism to the philosopher <a href="/wiki/Thales" class="mw-redirect" title="Thales">Thales</a> of <a href="/wiki/Miletus" title="Miletus">Miletus</a>, who lived from about 625 BC to about 545 BC.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/History_of_India" title="History of India">ancient Indian</a> medical text <i><a href="/wiki/Sushruta_Samhita" title="Sushruta Samhita">Sushruta Samhita</a></i> describes using magnetite to remove arrows embedded in a person's body.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/History_of_China#Ancient_China" title="History of China">ancient China</a>, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, <i><a href="/wiki/Guiguzi" title="Guiguzi">Guiguzi</a></i>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The 2nd-century BC annals, <i><a href="/wiki/L%C3%BCshi_Chunqiu" title="Lüshi Chunqiu">Lüshi Chunqiu</a></i>, also notes: "The <a href="/wiki/Lodestone" title="Lodestone">lodestone</a> makes iron approach; some (force) is attracting it."<sup id="cite_ref-Li54_9-0" class="reference"><a href="#cite_note-Li54-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The earliest mention of the attraction of a needle is in a 1st-century work <i><a href="/wiki/Lunheng" title="Lunheng">Lunheng</a></i> (<i>Balanced Inquiries</i>): "A lodestone attracts a needle."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The 11th-century <a href="/wiki/History_of_science_and_technology_in_China" title="History of science and technology in China">Chinese scientist</a> <a href="/wiki/Shen_Kuo" title="Shen Kuo">Shen Kuo</a> was the first person to write—in the <i><a href="/wiki/Dream_Pool_Essays" title="Dream Pool Essays">Dream Pool Essays</a></i>—of the magnetic needle compass and that it improved the accuracy of navigation by employing the <a href="/wiki/Astronomical" class="mw-redirect" title="Astronomical">astronomical</a> concept of <a href="/wiki/True_north" title="True north">true north</a>. By the 12th century, the Chinese were known to use the lodestone <a href="/wiki/Compass#China" title="Compass">compass</a> for navigation. They sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south. </p><p><a href="/wiki/Alexander_Neckam" title="Alexander Neckam">Alexander Neckam</a>, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, <a href="/wiki/Peter_of_Maricourt" class="mw-redirect" title="Peter of Maricourt">Peter Peregrinus de Maricourt</a> wrote the <i>Epistola de magnete</i>, the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compasses were discussed by <a href="/wiki/Al-Ashraf_Umar_II" title="Al-Ashraf Umar II">Al-Ashraf Umar II</a>, a <a href="/wiki/Islamic_physics" class="mw-redirect" title="Islamic physics">Yemeni physicist</a>, <a href="/wiki/Islamic_astronomy" class="mw-redirect" title="Islamic astronomy">astronomer</a>, and <a href="/wiki/Islamic_geography" class="mw-redirect" title="Islamic geography">geographer</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Leonardo_Garzoni" title="Leonardo Garzoni">Leonardo Garzoni</a>'s only extant work, the <i>Due trattati sopra la natura, e le qualità della calamita</i> (<i>Two treatises on the nature and qualities of the magnet</i>), is the first known example of a modern treatment of magnetic phenomena. Written in years near 1580 and never published, the treatise had a wide diffusion. In particular, Garzoni is referred to as an expert in magnetism by Niccolò Cabeo, whose Philosophia Magnetica (1629) is just a re-adjustment of Garzoni's work. Garzoni's treatise was known also to <a href="/wiki/Giovanni_Battista_Della_Porta" class="mw-redirect" title="Giovanni Battista Della Porta">Giovanni Battista Della Porta</a>. </p><p>In 1600, <a href="/wiki/William_Gilbert_(astronomer)" class="mw-redirect" title="William Gilbert (astronomer)">William Gilbert</a> published his <i><a href="/wiki/De_Magnete" title="De Magnete">De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure</a></i> (<i>On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth</i>). In this work he describes many of his experiments with his model earth called the <a href="/wiki/Terrella" title="Terrella">terrella</a>. From his experiments, he concluded that the <a href="/wiki/Earth%27s_magnetic_field" title="Earth's magnetic field">Earth</a> was itself magnetic and that this was the reason compasses pointed north whereas, previously, some believed that it was the pole star <a href="/wiki/Polaris" title="Polaris">Polaris</a> or a large magnetic island on the north pole that attracted the compass. </p><p>An understanding of the relationship between <a href="/wiki/Electricity" title="Electricity">electricity</a> and magnetism began in 1819 with work by <a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Hans Christian Ørsted</a>, a professor at the University of Copenhagen, who discovered, by the accidental twitching of a compass needle near a wire, that an electric current could create a magnetic field. This landmark experiment is known as Ørsted's Experiment. <a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Jean-Baptiste Biot</a> and <a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Félix Savart</a>, both of whom in 1820 came up with the <a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a> giving an equation for the magnetic field from a current-carrying wire. Around the same time, <a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">André-Marie Ampère</a> carried out numerous systematic experiments and discovered that the magnetic force between two DC current loops of any shape is equal to the sum of the individual forces that each current element of one circuit exerts on each other current element of the other circuit. </p><p>In 1831, <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> discovered that a time-varying magnetic flux induces a voltage through a wire loop. In 1835, <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> hypothesized, based on <a href="/wiki/Amp%C3%A8re%27s_force_law" title="Ampère's force law">Ampère's force law</a> in its original form, that all forms of magnetism arise as a result of elementary point charges moving relative to each other.<sup id="cite_ref-Gauss1835_12-0" class="reference"><a href="#cite_note-Gauss1835-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Wilhelm Eduard Weber</a> advanced Gauss's theory to <a href="/wiki/Weber_electrodynamics" title="Weber electrodynamics">Weber electrodynamics</a>. </p><p>From around 1861, <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> synthesized and expanded many of these insights into <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>, unifying electricity, magnetism, and <a href="/wiki/Optics" title="Optics">optics</a> into the field of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>. However, Gauss's interpretation of magnetism is not fully compatible with Maxwell's electrodynamics. In 1905, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> used Maxwell's equations in motivating his theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>,<sup id="cite_ref-Moving_13-0" class="reference"><a href="#cite_note-Moving-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> requiring that the laws held true in all <a href="/wiki/Inertial_reference_frame" class="mw-redirect" title="Inertial reference frame">inertial reference frames</a>. Gauss's approach of interpreting the magnetic force as a mere effect of relative velocities thus found its way back into electrodynamics to some extent. </p><p>Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a>, <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>, <a href="/wiki/Electroweak_theory" class="mw-redirect" title="Electroweak theory">electroweak theory</a>, and finally the <a href="/wiki/Standard_model" class="mw-redirect" title="Standard model">standard model</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=2" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic moment</a></div> <p>Magnetism, at its root, arises from three sources: </p> <ol><li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Spin_magnetic_moment" class="mw-redirect" title="Spin magnetic moment">Spin magnetic moments</a> of <a href="/wiki/Elementary_particles" class="mw-redirect" title="Elementary particles">elementary particles</a></li> <li>Changing electric fields</li></ol> <p>The magnetic properties of materials are mainly due to the magnetic moments of their <a href="/wiki/Atom" title="Atom">atoms</a>' orbiting <a href="/wiki/Electron" title="Electron">electrons</a>. The magnetic moments of the nuclei of atoms are typically thousands of times smaller than the electrons' magnetic moments, so they are negligible in the context of the magnetization of materials. Nuclear magnetic moments are nevertheless very important in other contexts, particularly in <a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">nuclear magnetic resonance</a> (NMR) and <a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">magnetic resonance imaging</a> (MRI). </p><p>Ordinarily, the enormous number of electrons in a material are arranged such that their magnetic moments (both orbital and intrinsic) cancel out. This is due, to some extent, to electrons combining into pairs with opposite intrinsic magnetic moments as a result of the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> (see <i><a href="/wiki/Electron_configuration" title="Electron configuration">electron configuration</a></i>), and combining into filled <a href="/wiki/Electron_subshell" class="mw-redirect" title="Electron subshell">subshells</a> with zero net orbital motion. In both cases, the electrons preferentially adopt arrangements in which the magnetic moment of each electron is canceled by the opposite moment of another electron. Moreover, even when the <a href="/wiki/Electron_configuration" title="Electron configuration">electron configuration</a> <i>is</i> such that there are unpaired electrons and/or non-filled subshells, it is often the case that the various electrons in the solid will contribute magnetic moments that point in different, random directions so that the material will not be magnetic. </p><p>Sometimes—either spontaneously, or owing to an applied external magnetic field—each of the electron magnetic moments will be, on average, lined up. A suitable material can then produce a strong net magnetic field. </p><p>The magnetic behavior of a material depends on its structure, particularly its <a href="/wiki/Electron_configuration" title="Electron configuration">electron configuration</a>, for the reasons mentioned above, and also on the temperature. At high temperatures, random <a href="/wiki/Thermal_motion" class="mw-redirect" title="Thermal motion">thermal motion</a> makes it more difficult for the electrons to maintain alignment. </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=3" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Magnetism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Magnetism.svg/660px-Magnetism.svg.png" decoding="async" width="660" height="430" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Magnetism.svg/990px-Magnetism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Magnetism.svg/1320px-Magnetism.svg.png 2x" data-file-width="780" data-file-height="508" /></a><figcaption>Hierarchy of types of magnetism.<sup id="cite_ref-Meyers1_14-0" class="reference"><a href="#cite_note-Meyers1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Diamagnetism">Diamagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=4" title="Edit section: Diamagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Diamagnetism" title="Diamagnetism">Diamagnetism</a></div> <p>Diamagnetism appears in all materials and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates.<sup id="cite_ref-Westbrook_15-0" class="reference"><a href="#cite_note-Westbrook-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood <a href="/wiki/Classical_physics" title="Classical physics">classically</a> as follows: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to their <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb</a> attraction to the nucleus, a <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> from the magnetic field. Depending on which direction the electron is orbiting, this force may increase the <a href="/wiki/Centripetal_force" title="Centripetal force">centripetal force</a> on the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect systematically increases the orbital magnetic moments that were aligned opposite the field and decreases the ones aligned parallel to the field (in accordance with <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>). This results in a small bulk magnetic moment, with an opposite direction to the applied field.</p></blockquote> <p>This description is meant only as a <a href="/wiki/Heuristic" title="Heuristic">heuristic</a>; the <a href="/wiki/Bohr%E2%80%93Van_Leeuwen_theorem" title="Bohr–Van Leeuwen theorem">Bohr–Van Leeuwen theorem</a> shows that diamagnetism is impossible according to classical physics, and that a proper understanding requires a <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum-mechanical</a> description. </p><p>All materials undergo this orbital response. However, in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effects caused by the unpaired electrons. </p> <div class="mw-heading mw-heading3"><h3 id="Paramagnetism">Paramagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=5" title="Edit section: Paramagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnetism</a></div> <p>In a paramagnetic material there are unpaired electrons; i.e., <a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic</a> or <a href="/wiki/Molecular_orbital" title="Molecular orbital">molecular orbitals</a> with exactly one electron in them. While paired electrons are required by the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it. </p> <div class="mw-heading mw-heading3"><h3 id="Ferromagnetism">Ferromagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=6" title="Edit section: Ferromagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnetism</a></div> <p>A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered-energy state. Thus, even in the absence of an applied field, the magnetic moments of the electrons in the material spontaneously line up parallel to one another. </p><p>Every ferromagnetic substance has its own individual temperature, called the <a href="/wiki/Curie_temperature" title="Curie temperature">Curie temperature</a>, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy-lowering due to ferromagnetic order. </p><p>Ferromagnetism only occurs in a few substances; common ones are <a href="/wiki/Iron" title="Iron">iron</a>, <a href="/wiki/Nickel" title="Nickel">nickel</a>, <a href="/wiki/Cobalt" title="Cobalt">cobalt</a>, their <a href="/wiki/Alloy" title="Alloy">alloys</a>, and some alloys of <a href="/wiki/Rare-earth" class="mw-redirect" title="Rare-earth">rare-earth</a> metals. </p> <div class="mw-heading mw-heading4"><h4 id="Magnetic_domains">Magnetic domains</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=7" title="Edit section: Magnetic domains"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Magnetic_domains" class="mw-redirect" title="Magnetic domains">Magnetic domains</a></div> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:392px;max-width:392px"><div class="trow"><div class="tsingle" style="width:194px;max-width:194px"><div class="thumbimage" style="height:192px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Magnetic_Domains_2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Magnetic_Domains_2.svg/192px-Magnetic_Domains_2.svg.png" decoding="async" width="192" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Magnetic_Domains_2.svg/288px-Magnetic_Domains_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Magnetic_Domains_2.svg/384px-Magnetic_Domains_2.svg.png 2x" data-file-width="498" data-file-height="504" /></a></span></div><div class="thumbcaption">Magnetic domains boundaries (white lines) in ferromagnetic material (black rectangle)</div></div><div class="tsingle" style="width:194px;max-width:194px"><div class="thumbimage" style="height:192px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Magnetic_Domains_3.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Magnetic_Domains_3.svg/192px-Magnetic_Domains_3.svg.png" decoding="async" width="192" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Magnetic_Domains_3.svg/288px-Magnetic_Domains_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Magnetic_Domains_3.svg/384px-Magnetic_Domains_3.svg.png 2x" data-file-width="498" data-file-height="504" /></a></span></div><div class="thumbcaption">Effect of a magnet on the domains</div></div></div></div></div> <p>The magnetic moments of atoms in a <a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetic</a> material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called <a href="/wiki/Magnetic_domains" class="mw-redirect" title="Magnetic domains">magnetic domains</a> or <a href="/wiki/Weiss_domains" class="mw-redirect" title="Weiss domains">Weiss domains</a>. Magnetic domains can be observed with a <a href="/wiki/Magnetic_force_microscope" title="Magnetic force microscope">magnetic force microscope</a> to reveal magnetic domain boundaries that resemble white lines in the sketch. There are many scientific experiments that can physically show magnetic fields. </p><p>When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably. </p><p>When exposed to a magnetic field, the domain boundaries move, so that the domains aligned with the magnetic field grow and dominate the structure (dotted yellow area), as shown at the left. When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet. </p><p>When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is <a href="/wiki/Saturation_(magnetic)" title="Saturation (magnetic)">magnetically saturated</a>. When a magnetized ferromagnetic material is heated to the <a href="/wiki/Curie_point" class="mw-redirect" title="Curie point">Curie point</a> temperature, the molecules are agitated to the point that the magnetic domains lose the organization, and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns, in a manner roughly analogous to how a liquid can <a href="/wiki/Freezing" title="Freezing">freeze</a> into a crystalline solid. </p> <div class="mw-heading mw-heading3"><h3 id="Antiferromagnetism">Antiferromagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=8" title="Edit section: Antiferromagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Antiferromagnetic_ordering.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Antiferromagnetic_ordering.svg/220px-Antiferromagnetic_ordering.svg.png" decoding="async" width="220" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Antiferromagnetic_ordering.svg/330px-Antiferromagnetic_ordering.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Antiferromagnetic_ordering.svg/440px-Antiferromagnetic_ordering.svg.png 2x" data-file-width="443" data-file-height="213" /></a><figcaption>Antiferromagnetic ordering</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnetism</a></div> <p>In an <a href="/wiki/Antiferromagnet" class="mw-redirect" title="Antiferromagnet">antiferromagnet</a>, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in <i>opposite</i> directions. When all atoms are arranged in a substance so that each neighbor is anti-parallel, the substance is <b>antiferromagnetic</b>. Antiferromagnets have a zero net magnetic moment because adjacent opposite moment cancels out, meaning that no field is produced by them. Antiferromagnets are less common compared to the other types of behaviors and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferromagnetic properties. </p><p>In some materials, neighboring electrons prefer to point in opposite directions, but there is no geometrical arrangement in which <i>each</i> pair of neighbors is anti-aligned. This is called a <a href="/wiki/Spin_canting" title="Spin canting">canted antiferromagnet</a> or <a href="/wiki/Spin_ice" title="Spin ice">spin ice</a> and is an example of <a href="/wiki/Geometrical_frustration" title="Geometrical frustration">geometrical frustration</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Ferrimagnetism">Ferrimagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=9" title="Edit section: Ferrimagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ferrimagnetic_ordering.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ferrimagnetic_ordering.svg/220px-Ferrimagnetic_ordering.svg.png" decoding="async" width="220" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ferrimagnetic_ordering.svg/330px-Ferrimagnetic_ordering.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ferrimagnetic_ordering.svg/440px-Ferrimagnetic_ordering.svg.png 2x" data-file-width="443" data-file-height="213" /></a><figcaption><a href="/wiki/Ferrimagnetic" class="mw-redirect" title="Ferrimagnetic">Ferrimagnetic</a> ordering</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnetism</a></div> <p>Like ferromagnetism, <b>ferrimagnets</b> retain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins tend to point in opposite directions. These two properties are not contradictory, because in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons that point in one direction, than from the sublattice that points in the opposite direction. </p><p>Most <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrites</a> are ferrimagnetic. The first discovered magnetic substance, <a href="/wiki/Magnetite" title="Magnetite">magnetite</a>, is a ferrite and was originally believed to be a ferromagnet; <a href="/wiki/Louis_N%C3%A9el" title="Louis Néel">Louis Néel</a> disproved this, however, after discovering ferrimagnetism. </p> <div class="mw-heading mw-heading3"><h3 id="Superparamagnetism">Superparamagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=10" title="Edit section: Superparamagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnetic_orders.webm/220px--Magnetic_orders.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="132" data-mwtitle="Magnetic_orders.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Magnetic_orders.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/5/57/Magnetic_orders.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/57/Magnetic_orders.webm/Magnetic_orders.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AMagnetic_orders.webm&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AMagnetic_orders.webm&lang=it&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="it" label="italiano ‪(it)‬" data-dir="ltr" /></video></span><figcaption>Magnetic orders: comparison between ferro, antiferro and ferrimagnetism</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Superparamagnetism" title="Superparamagnetism">Superparamagnetism</a></div> <p>When a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is subject to <a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a>. Its response to a magnetic field is qualitatively similar to the response of a paramagnet, but much larger. </p> <div class="mw-heading mw-heading3"><h3 id="Nagaoka_magnetism">Nagaoka magnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=11" title="Edit section: Nagaoka magnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Japanese physicist Yosuke Nagaoka conceived of a type of magnetism in a square, two-dimensional lattice where every lattice node had one electron. If one electron was removed under specific conditions, the lattice's energy would be minimal only when all electrons' spins were parallel. </p><p>A variation on this was achieved experimentally by arranging the atoms in a triangular <a href="/wiki/Moir%C3%A9_pattern" title="Moiré pattern">moiré</a> lattice of <a href="/wiki/Molybdenum_diselenide" title="Molybdenum diselenide">molybdenum diselenide</a> and <a href="/wiki/Tungsten_disulfide" title="Tungsten disulfide">tungsten disulfide</a> monolayers. Applying a weak magnetic field and a voltage led to ferromagnetic behavior when 100–150% more electrons than lattice nodes were present. The extra electrons delocalized and paired with lattice electrons to form doublons. Delocalization was prevented unless the lattice electrons had aligned spins. The doublons thus created localized ferromagnetic regions. The phenomenon took place at 140 millikelvins.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_types_of_magnetism">Other types of magnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=12" title="Edit section: Other types of magnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Metamagnetism" title="Metamagnetism">Metamagnetism</a></li> <li><a href="/wiki/Molecule-based_magnets" title="Molecule-based magnets">Molecule-based magnets</a></li> <li><a href="/wiki/Single-molecule_magnet" title="Single-molecule magnet">Single-molecule magnet</a></li> <li><a href="/wiki/Amorphous_magnet" title="Amorphous magnet">Amorphous magnet</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Electromagnet">Electromagnet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=13" title="Edit section: Electromagnet"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Electromagnet.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Electromagnet.gif/260px-Electromagnet.gif" decoding="async" width="260" height="193" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Electromagnet.gif/390px-Electromagnet.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Electromagnet.gif/520px-Electromagnet.gif 2x" data-file-width="656" data-file-height="488" /></a><figcaption>An electromagnet attracts paper clips when current is applied, creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.</figcaption></figure> <p>An <a href="/wiki/Electromagnet" title="Electromagnet">electromagnet</a> is a type of <a href="/wiki/Magnet" title="Magnet">magnet</a> in which the <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> is produced by an <a href="/wiki/Electric_current" title="Electric current">electric current</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The magnetic field disappears when the current is turned off. Electromagnets usually consist of a large number of closely spaced turns of wire that create the magnetic field. The wire turns are often wound around a <a href="/wiki/Magnetic_core" title="Magnetic core">magnetic core</a> made from a <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> or <a href="/wiki/Ferrimagnetic" class="mw-redirect" title="Ferrimagnetic">ferrimagnetic</a> material such as <a href="/wiki/Iron" title="Iron">iron</a>; the magnetic core concentrates the <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> and makes a more powerful magnet. </p><p>The main advantage of an electromagnet over a <a href="/wiki/Permanent_magnet" class="mw-redirect" title="Permanent magnet">permanent magnet</a> is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field. </p><p>Electromagnets are widely used as components of other electrical devices, such as <a href="/wiki/Electric_motor" title="Electric motor">motors</a>, <a href="/wiki/Electric_generator" title="Electric generator">generators</a>, <a href="/wiki/Relay" title="Relay">relays</a>, solenoids, <a href="/wiki/Loudspeaker" title="Loudspeaker">loudspeakers</a>, <a href="/wiki/Hard_disk" class="mw-redirect" title="Hard disk">hard disks</a>, <a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">MRI machines</a>, scientific instruments, and <a href="/wiki/Magnetic_separation" title="Magnetic separation">magnetic separation</a> equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel.<sup id="cite_ref-Merzouki_18-0" class="reference"><a href="#cite_note-Merzouki-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Electromagnetism was discovered in 1820.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Magnetism,_electricity,_and_special_relativity"><span id="Magnetism.2C_electricity.2C_and_special_relativity"></span>Magnetism, electricity, and special relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=14" title="Edit section: Magnetism, electricity, and special relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Classical electromagnetism and special relativity</a></div> <p>As a consequence of Einstein's theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as <a href="/wiki/Length_contraction" title="Length contraction">length contraction</a>, <a href="/wiki/Time_dilation" title="Time dilation">time dilation</a>, and the fact that the <a href="/wiki/Magnetic_force" class="mw-redirect" title="Magnetic force">magnetic force</a> is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (<a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>) is fully consistent with special relativity.<sup id="cite_ref-Moving_13-1" class="reference"><a href="#cite_note-Moving-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In particular, a phenomenon that appears purely electric or purely magnetic to one observer may be a mix of both to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>, analogous to how general relativity "mixes" space and time into <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. </p><p>All observations on <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> apply to what might be considered to be primarily magnetism, e.g. perturbations in the magnetic field are necessarily accompanied by a nonzero electric field, and propagate at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Magnetic_fields_in_a_material">Magnetic fields in a material</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=15" title="Edit section: Magnetic fields in a material"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Magnetic_field#H_and_B_inside_and_outside_of_magnetic_materials" title="Magnetic field">Magnetic field § H and B inside and outside of magnetic materials</a></div> <p>In vacuum, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} \ =\ \mu _{0}\mathbf {H} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} \ =\ \mu _{0}\mathbf {H} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2afaaeaf4dacfb733b7d54c54995eba08924414" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.355ex; height:2.676ex;" alt="{\displaystyle \mathbf {B} \ =\ \mu _{0}\mathbf {H} ,}"></span></dd></dl> <p>where <span class="texhtml"><i>μ</i><sub>0</sub></span> is the <a href="/wiki/Vacuum_permeability" title="Vacuum permeability">vacuum permeability</a>. </p><p>In a material, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} \ =\ \mu _{0}(\mathbf {H} +\mathbf {M} ).\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mo stretchy="false">)</mo> <mo>.</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} \ =\ \mu _{0}(\mathbf {H} +\mathbf {M} ).\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16eca715d215eaf4534928b54dc243338f3b1314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.51ex; height:2.843ex;" alt="{\displaystyle \mathbf {B} \ =\ \mu _{0}(\mathbf {H} +\mathbf {M} ).\ }"></span></dd></dl> <p>The quantity <span class="texhtml"><i>μ</i><sub>0</sub><b>M</b></span> is called <i>magnetic polarization</i>. </p><p>If the field <span class="texhtml"><b>H</b></span> is small, the response of the magnetization <span class="texhtml"><b>M</b></span> in a <a href="/wiki/Diamagnet" class="mw-redirect" title="Diamagnet">diamagnet</a> or <a href="/wiki/Paramagnet" class="mw-redirect" title="Paramagnet">paramagnet</a> is approximately linear: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {M} =\chi \mathbf {H} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mo>=</mo> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {M} =\chi \mathbf {H} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b409b9800aed8b1b65eb8bae442a7b78c9642adc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.829ex; height:2.509ex;" alt="{\displaystyle \mathbf {M} =\chi \mathbf {H} ,}"></span></dd></dl> <p>the constant of proportionality being called the magnetic susceptibility. If so, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{0}(\mathbf {H} +\mathbf {M} )\ =\ \mu _{0}(1+\chi )\mathbf {H} \ =\ \mu _{r}\mu _{0}\mathbf {H} \ =\ \mu \mathbf {H} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mo stretchy="false">)</mo> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{0}(\mathbf {H} +\mathbf {M} )\ =\ \mu _{0}(1+\chi )\mathbf {H} \ =\ \mu _{r}\mu _{0}\mathbf {H} \ =\ \mu \mathbf {H} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1af7084722518dd84cf4029e2c69bf6b826d9dad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:47.391ex; height:2.843ex;" alt="{\displaystyle \mu _{0}(\mathbf {H} +\mathbf {M} )\ =\ \mu _{0}(1+\chi )\mathbf {H} \ =\ \mu _{r}\mu _{0}\mathbf {H} \ =\ \mu \mathbf {H} .}"></span></dd></dl> <p>In a hard magnet such as a ferromagnet, <span class="texhtml"><b>M</b></span> is not proportional to the field and is generally nonzero even when <span class="texhtml"><b>H</b></span> is zero (see <a href="/wiki/Remanence" title="Remanence">Remanence</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Magnetic_force">Magnetic force</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=16" title="Edit section: Magnetic force"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Magnet0873.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/220px-Magnet0873.png" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/330px-Magnet0873.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/440px-Magnet0873.png 2x" data-file-width="444" data-file-height="298" /></a><figcaption>Magnetic lines of force of a bar magnet shown by iron filings on paper</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Magnet_bar.ogv/220px-seek%3D35-Magnet_bar.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="85" data-mwtitle="Magnet_bar.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Magnet_bar.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/a/a2/Magnet_bar.ogv" type="video/ogg; codecs="theora"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a2/Magnet_bar.ogv/Magnet_bar.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AMagnet_bar.ogv&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr" /></video></span><figcaption>Detecting magnetic field with compass and with iron filings</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></div> <p>The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields. </p><p>Maxwell's equations, which simplify to the <a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a> in the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore, magnetism is seen whenever electrically <a href="/wiki/Electric_charge" title="Electric charge">charged particles</a> are in <a href="/wiki/Motion_(physics)" class="mw-redirect" title="Motion (physics)">motion</a>—for example, from movement of electrons in an <a href="/wiki/Electric_current" title="Electric current">electric current</a>, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" <a href="/wiki/Magnetic_dipole" title="Magnetic dipole">magnetic dipoles</a> arising from quantum-mechanical <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>. </p><p>The same situations that create magnetic fields—charge moving in a current or in an atom, and intrinsic magnetic dipoles—are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole. </p><p>When a charged particle moves through a <a href="/wiki/Magnetic_field#B_and_H" title="Magnetic field">magnetic field</a> <b>B</b>, it feels a <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> <b>F</b> given by the <a href="/wiki/Cross_product" title="Cross product">cross product</a>:<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =q(\mathbf {v} \times \mathbf {B} ),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =q(\mathbf {v} \times \mathbf {B} ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a23bf9e6d23ed1be74d2bd719487299db4eb5aa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.459ex; height:2.843ex;" alt="{\displaystyle \mathbf {F} =q(\mathbf {v} \times \mathbf {B} ),}"></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> is the electric charge of the particle, and</dd> <dd><b>v</b> is the <a href="/wiki/Velocity" title="Velocity">velocity</a> <a href="/wiki/Vector_(geometric)" class="mw-redirect" title="Vector (geometric)">vector</a> of the particle</dd></dl> <p>Because this is a <a href="/wiki/Cross_product" title="Cross product">cross product</a>, the force is <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> to both the motion of the particle and the magnetic field. The magnitude of the force is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=qvB\sin \theta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>q</mi> <mi>v</mi> <mi>B</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=qvB\sin \theta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d26bd32e7816b59c759307a929b2a29ad7c3b01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.908ex; height:2.509ex;" alt="{\displaystyle F=qvB\sin \theta \,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is the angle between <b>v</b> and <b>B</b>. </p><p>One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the <a href="/wiki/Index_finger" title="Index finger">index finger</a> "V"<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="wrong if q is negative. "V" should be "qv". (July 2021)">dubious</span></a> – <a href="/wiki/Talk:Magnetism#Dubious" title="Talk:Magnetism">discuss</a></i>]</sup>, the <a href="/wiki/Middle_finger" title="Middle finger">middle finger</a> "B", and the <a href="/wiki/Thumb" title="Thumb">thumb</a> "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also <a href="/wiki/Right-hand_rule" title="Right-hand rule">right-hand rule</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Magnetic_dipoles">Magnetic dipoles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=17" title="Edit section: Magnetic dipoles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Magnetic_dipole" title="Magnetic dipole">Magnetic dipole</a></div> <p>A very common source of magnetic field found in nature is a <a href="/wiki/Dipole" title="Dipole">dipole</a>, with a "<a href="/wiki/South_pole" class="mw-redirect" title="South pole">South pole</a>" and a "<a href="/wiki/North_pole" class="mw-redirect" title="North pole">North pole</a>", terms dating back to the use of magnets as compasses, interacting with the <a href="/wiki/Earth%27s_magnetic_field" title="Earth's magnetic field">Earth's magnetic field</a> to indicate North and South on the <a href="/wiki/Globe" title="Globe">globe</a>. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south pole of another magnet. The Earth's <a href="/wiki/North_Magnetic_Pole" class="mw-redirect" title="North Magnetic Pole">North Magnetic Pole</a> (currently in the Arctic Ocean, north of Canada) is physically a south pole, as it attracts the north pole of a compass. A magnetic field contains <a href="/wiki/Energy" title="Energy">energy</a>, and physical systems move toward configurations with lower energy. When diamagnetic material is placed in a magnetic field, a <i>magnetic dipole</i> tends to align itself in opposed polarity to that field, thereby lowering the net field strength. When ferromagnetic material is placed within a magnetic field, the magnetic dipoles align to the applied field, thus expanding the domain walls of the magnetic domains. </p> <div class="mw-heading mw-heading3"><h3 id="Magnetic_monopoles">Magnetic monopoles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=18" title="Edit section: Magnetic monopoles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Magnetic_monopole" title="Magnetic monopole">Magnetic monopole</a></div> <p>Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole—if such a thing exists—would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, as of 2010<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Magnetism&action=edit">[update]</a></sup>, they have never been observed, and could very well not exist.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>Nevertheless, some <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a> models predict the existence of these <a href="/wiki/Magnetic_monopoles" class="mw-redirect" title="Magnetic monopoles">magnetic monopoles</a>. <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> observed in 1931 that, because electricity and magnetism show a certain <a href="/wiki/Symmetry" title="Symmetry">symmetry</a>, just as <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum theory</a> predicts that individual <a href="/wiki/Positive_charge" class="mw-redirect" title="Positive charge">positive</a> or <a href="/wiki/Negative_charge" class="mw-redirect" title="Negative charge">negative</a> electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge—that is, why the observed <a href="/wiki/Elementary_particles" class="mw-redirect" title="Elementary particles">elementary particles</a> carry charges that are multiples of the charge of the electron. </p><p>Certain <a href="/wiki/Grand_unified_theories" class="mw-redirect" title="Grand unified theories">grand unified theories</a> predict the existence of monopoles which, unlike elementary particles, are <a href="/wiki/Solitons" class="mw-redirect" title="Solitons">solitons</a> (localized energy packets). The initial results of using these models to estimate the number of monopoles created in the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> contradicted cosmological observations—the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of <a href="/wiki/Cosmic_inflation" title="Cosmic inflation">inflation</a> (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Units">Units</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=19" title="Edit section: Units"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="SI">SI</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=20" title="Edit section: SI"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable plainrowheaders"> <caption><style data-mw-deduplicate="TemplateStyles:r1045256916">.mw-parser-output .navbar-header{text-align:center;position:relative;white-space:nowrap}.mw-parser-output .navbar-header .navbar{position:absolute;right:0;top:0;margin:0 5px}</style><div class="navbar-header"><a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> units<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:SI_electromagnetism_units" title="Template:SI electromagnetism units"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:SI_electromagnetism_units" title="Template talk:SI electromagnetism units"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:SI_electromagnetism_units" title="Special:EditPage/Template:SI electromagnetism units"><abbr title="Edit this template">e</abbr></a></li></ul></div></div> </caption> <tbody><tr> <th scope="col">Symbol<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </th> <th scope="col">Name of quantity </th> <th scope="col">Unit name </th> <th scope="col">Symbol </th> <th scope="col">Base units </th></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">E</span> </th> <th scope="row"><a href="/wiki/Energy" title="Energy">energy</a> </th> <td><a href="/wiki/Joule_(unit)" class="mw-redirect" title="Joule (unit)">joule</a> </td> <td>J = C⋅V = W⋅s </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">Q</span> </th> <th scope="row"><a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> </th> <td><a href="/wiki/Coulomb" title="Coulomb">coulomb</a> </td> <td>C </td> <td>A⋅s </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">I</span> </th> <th scope="row"><a href="/wiki/Electric_current" title="Electric current">electric current</a> </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> </td> <td>A = C/s = W/V </td> <td>A </td></tr> <tr> <th scope="row"><span class="texhtml"><b>J</b></span> </th> <th scope="row"><a href="/wiki/Current_density" title="Current density">electric current density</a> </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> per square metre </td> <td>A/m<sup>2</sup> </td> <td>A⋅m<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">U</span>, <span class="texhtml">Δ<i>V</i></span>; <span class="texhtml">Δ<i>ϕ</i></span>; <span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', 'Tex Gyre Chorus', cursive, serif;">E</span>, <span class="texhtml mvar" style="font-style:italic;">ξ</span> </th> <th scope="row"><a href="/wiki/Potential_difference" class="mw-redirect" title="Potential difference">potential difference</a>; <a href="/wiki/Voltage" title="Voltage">voltage</a>; <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a> </th> <td><a href="/wiki/Volt" title="Volt">volt</a> </td> <td>V = J/C </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−1</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">R</span>; <span class="texhtml mvar" style="font-style:italic;">Z</span>; <span class="texhtml mvar" style="font-style:italic;">X</span> </th> <th scope="row"><a href="/wiki/Electric_resistance" class="mw-redirect" title="Electric resistance">electric resistance</a>; <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a>; <a href="/wiki/Reactance_(electronics)" class="mw-redirect" title="Reactance (electronics)">reactance</a> </th> <td><a href="/wiki/Ohm_(unit)" class="mw-redirect" title="Ohm (unit)">ohm</a> </td> <td>Ω = V/A </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">ρ</span> </th> <th scope="row"><a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a> </th> <td><a href="/wiki/Ohm_(unit)" class="mw-redirect" title="Ohm (unit)">ohm</a> <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>Ω⋅m </td> <td>kg⋅m<sup>3</sup>⋅s<sup>−3</sup>⋅A<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">P</span> </th> <th scope="row"><a href="/wiki/Electric_power" title="Electric power">electric power</a> </th> <td><a href="/wiki/Watt" title="Watt">watt</a> </td> <td>W = V⋅A </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−3</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">C</span> </th> <th scope="row"><a href="/wiki/Capacitance" title="Capacitance">capacitance</a> </th> <td><a href="/wiki/Farad" title="Farad">farad</a> </td> <td>F = C/V </td> <td>kg<sup>−1</sup>⋅m<sup>−2</sup>⋅A<sup>2</sup>⋅s<sup>4</sup> </td></tr> <tr> <th scope="row"><span class="texhtml">Φ<sub>E</sub></span> </th> <th scope="row"><a href="/wiki/Electric_flux" title="Electric flux">electric flux</a> </th> <td><a href="/wiki/Volt" title="Volt">volt</a> <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>V⋅m </td> <td>kg⋅m<sup>3</sup>⋅s<sup>−3</sup>⋅A<sup>−1</sup> </td></tr> <tr> <th scope="row"><span class="texhtml"><b>E</b></span> </th> <th scope="row"><a href="/wiki/Electric_field" title="Electric field">electric field</a> strength </th> <td><a href="/wiki/Volt" title="Volt">volt</a> per <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>V/m = N/C </td> <td>kg⋅m⋅A<sup>−1</sup>⋅s<sup>−3</sup> </td></tr> <tr> <th scope="row"><span class="texhtml"><b>D</b></span> </th> <th scope="row"><a href="/wiki/Electric_displacement_field" title="Electric displacement field">electric displacement field</a> </th> <td><a href="/wiki/Coulomb" title="Coulomb">coulomb</a> per <a href="/wiki/Square_metre" title="Square metre">square metre</a> </td> <td>C/m<sup>2</sup> </td> <td>A⋅s⋅m<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">ε</span> </th> <th scope="row"><a href="/wiki/Permittivity" title="Permittivity">permittivity</a> </th> <td><a href="/wiki/Farad" title="Farad">farad</a> per <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>F/m </td> <td>kg<sup>−1</sup>⋅m<sup>−3</sup>⋅A<sup>2</sup>⋅s<sup>4</sup> </td></tr> <tr> <th scope="row"><span class="texhtml"><i>χ</i><sub>e</sub></span> </th> <th scope="row"><a href="/wiki/Electric_susceptibility" title="Electric susceptibility">electric susceptibility</a> </th> <td>(<a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless</a>) </td> <td>1 </td> <td>1 </td></tr> <tr> <th scope="row"><span class="texhtml"><b>p</b></span> </th> <th scope="row"><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">electric dipole moment</a> </th> <td><a href="/wiki/Coulomb" title="Coulomb">coulomb</a> <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>C⋅m </td> <td>A⋅s⋅m </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">G</span>; <span class="texhtml mvar" style="font-style:italic;">Y</span>; <span class="texhtml mvar" style="font-style:italic;">B</span> </th> <th scope="row"><a href="/wiki/Electrical_conductance" class="mw-redirect" title="Electrical conductance">conductance</a>; <a href="/wiki/Admittance" title="Admittance">admittance</a>; <a href="/wiki/Susceptance" class="mw-redirect" title="Susceptance">susceptance</a> </th> <td><a href="/wiki/Siemens_(unit)" title="Siemens (unit)">siemens</a> </td> <td>S = Ω<sup>−1</sup> </td> <td>kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>3</sup>⋅A<sup>2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">κ</span>, <span class="texhtml mvar" style="font-style:italic;">γ</span>, <span class="texhtml mvar" style="font-style:italic;">σ</span> </th> <th scope="row"><a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">conductivity</a> </th> <td><a href="/wiki/Siemens_(unit)" title="Siemens (unit)">siemens</a> per <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>S/m </td> <td>kg<sup>−1</sup>⋅m<sup>−3</sup>⋅s<sup>3</sup>⋅A<sup>2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml"><b>B</b></span> </th> <th scope="row"><a href="/wiki/Magnetic_field" title="Magnetic field">magnetic flux density, magnetic induction</a> </th> <td><a href="/wiki/Tesla_(unit)" title="Tesla (unit)">tesla</a> </td> <td>T = Wb/m<sup>2</sup> = N⋅A<sup>−1</sup>⋅m<sup>−1</sup> </td> <td>kg⋅s<sup>−2</sup>⋅A<sup>−1</sup> </td></tr> <tr> <th scope="row"><span class="texhtml">Φ</span>, <span class="texhtml">Φ<sub>M</sub></span>, <span class="texhtml">Φ<sub>B</sub></span> </th> <th scope="row"><a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> </th> <td><a href="/wiki/Weber_(unit)" title="Weber (unit)"> weber</a> </td> <td>Wb = V⋅s </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−1</sup> </td></tr> <tr> <th scope="row"><span class="texhtml"><b>H</b></span> </th> <th scope="row"><a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> strength </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> per <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>A/m </td> <td>A⋅m<sup>−1</sup> </td></tr> <tr> <th scope="row"><span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', 'Tex Gyre Chorus', cursive, serif;">F</span> </th> <th scope="row"><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">magnetomotive force</a> </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> </td> <td>A = Wb/H </td> <td>A </td></tr> <tr> <th scope="row"><span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', 'Tex Gyre Chorus', cursive, serif;">R</span> </th> <th scope="row"><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">magnetic reluctance</a> </th> <td>inverse <a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> </td> <td>H<sup>−1</sup> = A/Wb </td> <td>kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>2</sup>⋅A<sup>2</sup> </td></tr> <tr> <th scope="row"><span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', 'Tex Gyre Chorus', cursive, serif;">P</span> </th> <th scope="row"><a href="/wiki/Magnetic_permeance" class="mw-redirect" title="Magnetic permeance">magnetic permeance</a> </th> <td><a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> </td> <td>H = Wb/A </td> <td>kg⋅m<sup>2</sup>⋅s<sup>–2</sup>⋅A<sup>–2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">L</span>, <span class="texhtml mvar" style="font-style:italic;">M</span> </th> <th scope="row"><a href="/wiki/Inductance" title="Inductance">inductance</a> </th> <td><a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> </td> <td>H = Wb/A = V⋅s/A </td> <td>kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">μ</span> </th> <th scope="row"><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> </th> <td><a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> per <a href="/wiki/Metre" title="Metre">metre</a> </td> <td>H/m </td> <td>kg⋅m<sup></sup>⋅s<sup>−2</sup>⋅A<sup>−2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">χ</span> </th> <th scope="row"><a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a> </th> <td>(<a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless</a>) </td> <td>1 </td> <td>1 </td></tr> <tr> <th scope="row"><span class="texhtml"><b>m</b></span> </th> <th scope="row"><a href="/wiki/Magnetic_dipole_moment" class="mw-redirect" title="Magnetic dipole moment">magnetic dipole moment</a> </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> <a href="/wiki/Square_meter" class="mw-redirect" title="Square meter">square meter</a> </td> <td>A⋅m<sup>2</sup> = J⋅T<sup>−1</sup> </td> <td>A⋅m<sup>2</sup> </td></tr> <tr> <th scope="row"><span class="texhtml mvar" style="font-style:italic;">σ</span> </th> <th scope="row">mass <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> </th> <td><a href="/wiki/Ampere" title="Ampere">ampere</a> <a href="/wiki/Square_meter" class="mw-redirect" title="Square meter">square meter</a> per <a href="/wiki/Kilogram" title="Kilogram">kilogram</a> </td> <td>A⋅m<sup>2</sup>/kg </td> <td>A⋅m<sup>2</sup>⋅kg<sup>−1</sup> </td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Other">Other</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=21" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gauss_(unit)" title="Gauss (unit)">gauss</a> – the <a href="/wiki/Centimeter-gram-second" class="mw-redirect" title="Centimeter-gram-second">centimeter-gram-second</a> (CGS) <a href="/wiki/Units_of_measurement" class="mw-redirect" title="Units of measurement">unit</a> of magnetic field (denoted <b>B</b>).</li> <li><a href="/wiki/Oersted" title="Oersted">oersted</a> – the CGS unit of <a href="/wiki/Magnetic_field#B_and_H" title="Magnetic field">magnetizing field</a> (denoted <b>H</b>)</li> <li><a href="/wiki/Maxwell_(unit)" title="Maxwell (unit)">maxwell</a> – the CGS unit for <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a></li> <li>gamma – a unit of <i>magnetic flux density</i> that was commonly used before the <a href="/wiki/Tesla_(unit)" title="Tesla (unit)">tesla</a> came into use (1.0 gamma = 1.0 nanotesla)</li> <li><i>μ</i><sub>0</sub> – common symbol for the <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> of free space (<span class="nowrap">4π × 10<sup>−7</sup></span> <a href="/wiki/Newton_(unit)" title="Newton (unit)">newton</a>/(<a href="/wiki/Ampere-turn" title="Ampere-turn">ampere-turn</a>)<sup>2</sup>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Living_things">Living things</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=22" title="Edit section: Living things"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Frog_diamagnetic_levitation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/220px-Frog_diamagnetic_levitation.jpg" decoding="async" width="220" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/330px-Frog_diamagnetic_levitation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/440px-Frog_diamagnetic_levitation.jpg 2x" data-file-width="607" data-file-height="574" /></a><figcaption>A live frog levitates inside a 32 <a href="/wiki/Millimetre" title="Millimetre">mm</a> <a href="/wiki/Diameter" title="Diameter">diameter</a> vertical bore of a <a href="/wiki/Bitter_solenoid" class="mw-redirect" title="Bitter solenoid">Bitter solenoid</a> in a very strong magnetic field—about 16 <a href="/wiki/Tesla_(unit)" title="Tesla (unit)">teslas</a></figcaption></figure> <p>Some <a href="/wiki/Organisms" class="mw-redirect" title="Organisms">organisms</a> can detect magnetic fields, a phenomenon known as <a href="/wiki/Magnetoception" class="mw-redirect" title="Magnetoception">magnetoception</a>. Some materials in living things are ferromagnetic, though it is unclear if the magnetic properties serve a special function or are merely a byproduct of containing iron. For instance, <a href="/wiki/Chitons" class="mw-redirect" title="Chitons">chitons</a>, a type of marine mollusk, produce magnetite to harden their teeth, and even humans produce <a href="/wiki/Magnetite" title="Magnetite">magnetite</a> in bodily tissue.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Magnetobiology" title="Magnetobiology">Magnetobiology</a> studies the effects of magnetic fields on living organisms; fields naturally produced by an organism are known as <a href="/wiki/Biomagnetism" title="Biomagnetism">biomagnetism</a>. Many biological organisms are mostly made of water, and because water is <a href="/wiki/Diamagnetic" class="mw-redirect" title="Diamagnetic">diamagnetic</a>, extremely strong magnetic fields can repel these living things. </p> <div class="mw-heading mw-heading2"><h2 id="Interpretation_of_magnetism_by_means_of_relative_velocities">Interpretation of magnetism by means of relative velocities</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=23" title="Edit section: Interpretation of magnetism by means of relative velocities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the years after 1820, <a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">André-Marie Ampère</a> carried out numerous experiments in which he measured the forces between direct currents. In particular, he also studied the magnetic forces between non-parallel wires.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> The final result of his work was a force law that is now named after him. In 1835, <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> realized <sup id="cite_ref-Gauss1835_12-1" class="reference"><a href="#cite_note-Gauss1835-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> that <a href="/wiki/Ampere%27s_force_law" class="mw-redirect" title="Ampere's force law">Ampere's force law</a> in its original form can be explained by a generalization of <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a>. </p><p>Gauss's force law states that the electromagnetic force <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \mathbf {F} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mathbf {F} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db19e06dea24dd9c99fd7f93d7432360a98ef762" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.737ex; height:2.509ex;" alt="{\textstyle \mathbf {F} _{1}}"></span> experienced by a point charge, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9daa41f6e8f78ea6bb5711d7ac97901ce564b94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{1}}"></span> with trajectory <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} _{1}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{1}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c1ddc11df9399f87a55873b0dc3c7434cdd2dc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.805ex; height:2.843ex;" alt="{\displaystyle \mathbf {r} _{1}(t)}"></span>, in the vicinity of another point charge, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd2d05084feb02b8ba29b0673440fb673b102589" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{2}}"></span> with trajectory <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} _{2}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{2}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/942952f0fd27871a61e29c4a70a9329041bba8fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.805ex; height:2.843ex;" alt="{\displaystyle \mathbf {r} _{2}(t)}"></span>, in a vacuum is equal to the <a href="/wiki/Central_force" title="Central force">central force</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{1}={\frac {q_{1}\,q_{2}}{4\,\pi \,\epsilon _{0}}}\,{\frac {\mathbf {r} }{|\mathbf {r} |^{3}}}\,\left(1+{\frac {|\mathbf {v} |^{2}}{c^{2}}}-{\frac {3}{2}}\,\left({\frac {\mathbf {r} }{|\mathbf {r} |}}\cdot {\frac {\mathbf {v} }{c}}\right)^{2}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mspace width="thinmathspace" /> <mi>π</mi> <mspace width="thinmathspace" /> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} _{1}={\frac {q_{1}\,q_{2}}{4\,\pi \,\epsilon _{0}}}\,{\frac {\mathbf {r} }{|\mathbf {r} |^{3}}}\,\left(1+{\frac {|\mathbf {v} |^{2}}{c^{2}}}-{\frac {3}{2}}\,\left({\frac {\mathbf {r} }{|\mathbf {r} |}}\cdot {\frac {\mathbf {v} }{c}}\right)^{2}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e78254eebe017f6c55b0310565f67b6bccad2db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:46.525ex; height:7.509ex;" alt="{\displaystyle \mathbf {F} _{1}={\frac {q_{1}\,q_{2}}{4\,\pi \,\epsilon _{0}}}\,{\frac {\mathbf {r} }{|\mathbf {r} |^{3}}}\,\left(1+{\frac {|\mathbf {v} |^{2}}{c^{2}}}-{\frac {3}{2}}\,\left({\frac {\mathbf {r} }{|\mathbf {r} |}}\cdot {\frac {\mathbf {v} }{c}}\right)^{2}\right)}"></span>,</dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \mathbf {r} =\mathbf {r} _{1}(t)-\mathbf {r} _{2}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mathbf {r} =\mathbf {r} _{1}(t)-\mathbf {r} _{2}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5e75350c63060759ca1c86e923ad933b6567d99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.651ex; height:2.843ex;" alt="{\textstyle \mathbf {r} =\mathbf {r} _{1}(t)-\mathbf {r} _{2}(t)}"></span> is the distance between the charges and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \mathbf {v} ={\dot {\mathbf {r} }}_{1}(t)-{\dot {\mathbf {r} }}_{2}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mathbf {v} ={\dot {\mathbf {r} }}_{1}(t)-{\dot {\mathbf {r} }}_{2}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef1276c1d38a0144d2ffe5d3961413d62f824c3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.081ex; height:2.843ex;" alt="{\textstyle \mathbf {v} ={\dot {\mathbf {r} }}_{1}(t)-{\dot {\mathbf {r} }}_{2}(t)}"></span> is the relative velocity. <a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Wilhelm Eduard Weber</a> confirmed Gauss's hypothesis in numerous experiments.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> By means of <a href="/wiki/Weber_electrodynamics" title="Weber electrodynamics">Weber electrodynamics</a> it is possible to explain the static and quasi-static effects in the non-relativistic regime of classical electrodynamics without <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> and <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a>. </p><p>Since 1870, <a href="/wiki/Maxwell_electrodynamics" class="mw-redirect" title="Maxwell electrodynamics">Maxwell electrodynamics</a> has been developed, which postulates that electric and magnetic fields exist. In Maxwell's electrodynamics, the actual electromagnetic force can be calculated using the Lorentz force, which, like the Weber force, is speed-dependent. However, Maxwell's electrodynamics is not fully compatible with the work of Ampère, Gauss and Weber in the quasi-static regime. In particular, Ampère's original force law and the <a href="/wiki/Biot-Savart_law" class="mw-redirect" title="Biot-Savart law">Biot-Savart law</a> are only equivalent if the field-generating conductor loop is closed.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Maxwell's electrodynamics therefore represents a break with the interpretation of magnetism by Gauss and Weber, since in Maxwell's electrodynamics it is no longer possible to deduce the magnetic force from a central force. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum-mechanical_origin_of_magnetism">Quantum-mechanical origin of magnetism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=24" title="Edit section: Quantum-mechanical origin of magnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While heuristic explanations based on classical physics can be formulated, diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A successful model was developed already in 1927, by <a href="/wiki/Walter_Heitler" title="Walter Heitler">Walter Heitler</a> and <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a>, who derived, quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/569afa745dd477cdb1c357e9c6ddf9bafa5b7835" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.795ex; height:2.009ex;" alt="{\displaystyle u_{A}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d62e72a2182506f3bad6d8d29fc65b3e67bab262" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.809ex; height:2.009ex;" alt="{\displaystyle u_{B}}"></span> centered at the nuclei <i>A</i> and <i>B</i>, see below. That this leads to magnetism is not at all obvious, but will be explained in the following. </p><p>According to the Heitler–London theory, so-called two-body molecular <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span>-orbitals are formed, namely the resulting orbital is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (\mathbf {r} _{1},\,\,\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}\,\,\left(u_{A}(\mathbf {r} _{1})u_{B}(\mathbf {r} _{2})+u_{B}(\mathbf {r} _{1})u_{A}(\mathbf {r} _{2})\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <mrow> <mo>(</mo> <mrow> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (\mathbf {r} _{1},\,\,\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}\,\,\left(u_{A}(\mathbf {r} _{1})u_{B}(\mathbf {r} _{2})+u_{B}(\mathbf {r} _{1})u_{A}(\mathbf {r} _{2})\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b11bb60d870ef476a7ab4454713d5c9a6ccca168" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:49.357ex; height:6.176ex;" alt="{\displaystyle \psi (\mathbf {r} _{1},\,\,\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}\,\,\left(u_{A}(\mathbf {r} _{1})u_{B}(\mathbf {r} _{2})+u_{B}(\mathbf {r} _{1})u_{A}(\mathbf {r} _{2})\right)}"></span></dd></dl> <p>Here the last product means that a first electron, <b>r</b><sub>1</sub>, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus. This "exchange" phenomenon is an expression for the quantum-mechanical property that particles with identical properties cannot be distinguished. It is specific not only for the formation of <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bonds</a>, but also for magnetism. That is, in this connection the term <a href="/wiki/Exchange_interaction" title="Exchange interaction">exchange interaction</a> arises, a term which is essential for the origin of magnetism, and which is stronger, roughly by factors 100 and even by 1000, than the energies arising from the electrodynamic dipole-dipole interaction. </p><p>As for the <i>spin function</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi (s_{1},s_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi (s_{1},s_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e38e9202f14d21f2a81105367c0fa7659af74089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.588ex; height:2.843ex;" alt="{\displaystyle \chi (s_{1},s_{2})}"></span>, which is responsible for the magnetism, we have the already mentioned Pauli's principle, namely that a symmetric orbital (i.e. with the + sign as above) must be multiplied with an antisymmetric spin function (i.e. with a − sign), and <i>vice versa</i>. Thus: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi (s_{1},\,\,s_{2})={\frac {1}{\sqrt {2}}}\,\,\left(\alpha (s_{1})\beta (s_{2})-\beta (s_{1})\alpha (s_{2})\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>β</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>β</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>α</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi (s_{1},\,\,s_{2})={\frac {1}{\sqrt {2}}}\,\,\left(\alpha (s_{1})\beta (s_{2})-\beta (s_{1})\alpha (s_{2})\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddfb2c2dcd74a0812a4f925e0203f9429b9bf94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:43.661ex; height:6.176ex;" alt="{\displaystyle \chi (s_{1},\,\,s_{2})={\frac {1}{\sqrt {2}}}\,\,\left(\alpha (s_{1})\beta (s_{2})-\beta (s_{1})\alpha (s_{2})\right)}"></span>,</dd></dl> <p>I.e., not only <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/569afa745dd477cdb1c357e9c6ddf9bafa5b7835" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.795ex; height:2.009ex;" alt="{\displaystyle u_{A}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d62e72a2182506f3bad6d8d29fc65b3e67bab262" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.809ex; height:2.009ex;" alt="{\displaystyle u_{B}}"></span> must be substituted by <i>α</i> and <i>β</i>, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally <b>r</b><sub>i</sub> by the discrete values <i>s</i><sub>i</sub> (= ±<style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>); thereby we have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (+1/2)=\beta (-1/2)=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>β</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (+1/2)=\beta (-1/2)=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65c3f5416a6d484f1e6709fc237827f852201774" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.389ex; height:2.843ex;" alt="{\displaystyle \alpha (+1/2)=\beta (-1/2)=1}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (-1/2)=\beta (+1/2)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>β</mi> <mo stretchy="false">(</mo> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (-1/2)=\beta (+1/2)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a17a0a8516eab03d034e301d2ca461e2d125f480" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.389ex; height:2.843ex;" alt="{\displaystyle \alpha (-1/2)=\beta (+1/2)=0}"></span>. The "<a href="/wiki/Singlet_state" title="Singlet state">singlet state</a>", i.e. the − sign, means: the spins are <i>antiparallel</i>, i.e. for the solid we have <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">antiferromagnetism</a>, and for two-atomic molecules one has <a href="/wiki/Diamagnetism" title="Diamagnetism">diamagnetism</a>. The tendency to form a (homoeopolar) chemical bond (this means: the formation of a <i>symmetric</i> molecular orbital, i.e. with the + sign) results through the Pauli principle automatically in an <i>antisymmetric</i> spin state (i.e. with the − sign). In contrast, the Coulomb repulsion of the electrons, i.e. the tendency that they try to avoid each other by this repulsion, would lead to an <i>antisymmetric</i> orbital function (i.e. with the − sign) of these two particles, and complementary to a <i>symmetric</i> spin function (i.e. with the + sign, one of the so-called "<a href="/wiki/Triplet_state" title="Triplet state">triplet functions</a>"). Thus, now the spins would be <i>parallel</i> (<a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetism</a> in a solid, <a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetism</a> in two-atomic gases). </p><p>The last-mentioned tendency dominates in the metals <a href="/wiki/Iron" title="Iron">iron</a>, <a href="/wiki/Cobalt" title="Cobalt">cobalt</a> and <a href="/wiki/Nickel" title="Nickel">nickel</a>, and in some rare earths, which are <i>ferromagnetic</i>. Most of the other metals, where the first-mentioned tendency dominates, are <i>nonmagnetic</i> (e.g. <a href="/wiki/Sodium" title="Sodium">sodium</a>, <a href="/wiki/Aluminium" title="Aluminium">aluminium</a>, and <a href="/wiki/Magnesium" title="Magnesium">magnesium</a>) or <i>antiferromagnetic</i> (e.g. <a href="/wiki/Manganese" title="Manganese">manganese</a>). Diatomic gases are also almost exclusively diamagnetic, and not paramagnetic. However, the oxygen molecule, because of the involvement of π-orbitals, is an exception important for the life-sciences. </p><p>The Heitler-London considerations can be generalized to the <a href="/wiki/Heisenberg_model_(classical)" class="mw-redirect" title="Heisenberg model (classical)">Heisenberg model</a> of magnetism (Heisenberg 1928). </p><p>The explanation of the phenomena is thus essentially based on all subtleties of quantum mechanics, whereas the electrodynamics covers mainly the phenomenology. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 15em;"> <ul><li><a href="/wiki/Coercivity" title="Coercivity">Coercivity</a></li> <li><a href="/wiki/Gravitomagnetism" class="mw-redirect" title="Gravitomagnetism">Gravitomagnetism</a></li> <li><a href="/wiki/Magnetic_hysteresis" title="Magnetic hysteresis">Magnetic hysteresis</a></li> <li><a href="/wiki/Magnetar" title="Magnetar">Magnetar</a></li> <li><a href="/wiki/Magnetic_bearing" title="Magnetic bearing">Magnetic bearing</a></li> <li><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></li> <li><a href="/wiki/Magnetic_cooling" class="mw-redirect" title="Magnetic cooling">Magnetic cooling</a></li> <li><a href="/wiki/Magnetic_field_viewing_film" title="Magnetic field viewing film">Magnetic field viewing film</a></li> <li><a href="/wiki/Magnetic_stirrer" title="Magnetic stirrer">Magnetic stirrer</a></li> <li><a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">Switched-mode power supply</a></li> <li><a href="/wiki/Magnetic_structure" title="Magnetic structure">Magnetic structure</a></li> <li><a href="/wiki/Micromagnetism" class="mw-redirect" title="Micromagnetism">Micromagnetism</a></li> <li><a href="/wiki/Neodymium_magnet" title="Neodymium magnet">Neodymium magnet</a></li> <li><a href="/wiki/Plastic_magnet" title="Plastic magnet">Plastic magnet</a></li> <li><a href="/wiki/Rare-earth_magnet" title="Rare-earth magnet">Rare-earth magnet</a></li> <li><a href="/wiki/Spin_wave" title="Spin wave">Spin wave</a></li> <li><a href="/wiki/Spontaneous_magnetization" title="Spontaneous magnetization">Spontaneous magnetization</a></li> <li><a href="/wiki/Vibrating-sample_magnetometer" title="Vibrating-sample magnetometer">Vibrating-sample magnetometer</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks in electromagnetism</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=26" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJiles,_David2015" class="citation book cs1">Jiles, David (2 September 2015). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/909323904"><i>Introduction to magnetism and magnetic materials</i></a> (Third ed.). Boca Raton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4822-3887-7" title="Special:BookSources/978-1-4822-3887-7"><bdi>978-1-4822-3887-7</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/909323904">909323904</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+magnetism+and+magnetic+materials&rft.place=Boca+Raton&rft.edition=Third&rft.date=2015-09-02&rft_id=info%3Aoclcnum%2F909323904&rft.isbn=978-1-4822-3887-7&rft.au=Jiles%2C+David&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F909323904&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuChengFarag1996" class="citation journal cs1">Du, Yaping; Cheng, T.C.; Farag, A.S. (August 1996). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/536075">"Principles of power-frequency magnetic field shielding with flat sheets in a source of long conductors"</a>. <i>IEEE Transactions on Electromagnetic Compatibility</i>. <b>38</b> (3): <span class="nowrap">450–</span>459. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F15.536075">10.1109/15.536075</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1558-187X">1558-187X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Electromagnetic+Compatibility&rft.atitle=Principles+of+power-frequency+magnetic+field+shielding+with+flat+sheets+in+a+source+of+long+conductors&rft.volume=38&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E450-%3C%2Fspan%3E459&rft.date=1996-08&rft_id=info%3Adoi%2F10.1109%2F15.536075&rft.issn=1558-187X&rft.aulast=Du&rft.aufirst=Yaping&rft.au=Cheng%2C+T.C.&rft.au=Farag%2C+A.S.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F536075&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-Tremolet-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tremolet_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDu_Trémolet_de_LacheisserieDamien_GignouxMichel_Schlenker2005" class="citation book cs1">Du Trémolet de Lacheisserie, Étienne; Damien Gignoux; Michel Schlenker (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MgCExarQD08C&pg=PA3"><i>Magnetism: Fundamentals</i></a>. Springer. pp. <span class="nowrap">3–</span>6. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-22967-6" title="Special:BookSources/978-0-387-22967-6"><bdi>978-0-387-22967-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Magnetism%3A+Fundamentals&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3-%3C%2Fspan%3E6&rft.pub=Springer&rft.date=2005&rft.isbn=978-0-387-22967-6&rft.aulast=Du+Tr%C3%A9molet+de+Lacheisserie&rft.aufirst=%C3%89tienne&rft.au=Damien+Gignoux&rft.au=Michel+Schlenker&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMgCExarQD08C%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_BkS2KW7u76MC"><i>Platonis Opera</i></a>, Meyer and Zeller, 1839, p. 989.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">The location of Magnesia is debated; it could be <a href="/wiki/Magnesia_(regional_unit)" title="Magnesia (regional unit)">the region in mainland Greece</a> or <a href="/wiki/Magnesia_ad_Sipylum" title="Magnesia ad Sipylum">Magnesia ad Sipylum</a>. See, for example, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.languagehat.com/archives/001914.php">"Magnet"</a>. <i>Language Hat blog</i>. 28 May 2005<span class="reference-accessdate">. Retrieved <span class="nowrap">22 March</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Language+Hat+blog&rft.atitle=Magnet&rft.date=2005-05-28&rft_id=http%3A%2F%2Fwww.languagehat.com%2Farchives%2F001914.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFowler1997" class="citation web cs1">Fowler, Michael (1997). <a rel="nofollow" class="external text" href="http://galileoandeinstein.physics.virginia.edu/more_stuff/E&M_Hist.html">"Historical Beginnings of Theories of Electricity and Magnetism"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-04-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Historical+Beginnings+of+Theories+of+Electricity+and+Magnetism&rft.date=1997&rft.aulast=Fowler&rft.aufirst=Michael&rft_id=http%3A%2F%2Fgalileoandeinstein.physics.virginia.edu%2Fmore_stuff%2FE%26M_Hist.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKumar_Goyal2017" class="citation book cs1">Kumar Goyal, Rajendra (2017). <i>Nanomaterials and Nanocomposites: Synthesis, Properties, Characterization Techniques, and Applications</i>. CRC Press. p. 171. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781498761673" title="Special:BookSources/9781498761673"><bdi>9781498761673</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nanomaterials+and+Nanocomposites%3A+Synthesis%2C+Properties%2C+Characterization+Techniques%2C+and+Applications&rft.pages=171&rft.pub=CRC+Press&rft.date=2017&rft.isbn=9781498761673&rft.aulast=Kumar+Goyal&rft.aufirst=Rajendra&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">The section "Fanying 2" (<a href="https://en.wikisource.org/wiki/%E9%AC%BC%E8%B0%B7%E5%AD%90" class="extiw" title="s:鬼谷子">反應第二</a>) of <i>The <a href="/wiki/Guiguzi" title="Guiguzi">Guiguzi</a></i>: "<span title="Chinese-language text"><span lang="zh">其察言也，不失若磁石之取鍼，舌之取燔骨</span></span>".</span> </li> <li id="cite_note-Li54-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Li54_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLi1954" class="citation journal cs1 cs1-prop-foreign-lang-source">Li, Shu-hua (1954). "Origine de la Boussole II. Aimant et Boussole". <i>Isis</i> (in French). <b>45</b> (2): <span class="nowrap">175–</span>196. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F348315">10.1086/348315</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/227361">227361</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:143585290">143585290</a>. <q>un passage dans le <i><a href="/wiki/L%C3%BCshi_Chunqiu" title="Lüshi Chunqiu">Liu-che-tch'ouen-ts'ieou</a></i> [...]: "La pierre d'aimant fait venir le fer ou elle l'attire."<span class="cs1-kern-right"></span></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Origine+de+la+Boussole+II.+Aimant+et+Boussole&rft.volume=45&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E175-%3C%2Fspan%3E196&rft.date=1954&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A143585290%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F227361%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F348315&rft.aulast=Li&rft.aufirst=Shu-hua&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span><br /> From the section "<i>Jingtong</i>" (<span title="Chinese-language text"><span lang="zh">精通</span></span>) of the "Almanac of the Last Autumn Month" (<span title="Chinese-language text"><span lang="zh">季秋紀</span></span>): "<span title="Chinese-language text"><span lang="zh">慈石召鐵，或引之也</span></span>]"</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">In the section "<a rel="nofollow" class="external text" href="https://archive.org/stream/lunheng02wang#page/350/mode/1up">A Last Word on Dragons</a>" (<span title="Chinese-language text"><span lang="zh">亂龍篇</span></span> <i>Luanlong</i>) of the <i><a href="/wiki/Lunheng" title="Lunheng">Lunheng</a></i>: "<a href="/wiki/Amber" title="Amber">Amber</a> takes up straws, and a load-stone attracts needles" (<span title="Chinese-language text"><span lang="zh">頓牟掇芥，磁石引針</span></span>).</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmidl1996–1997" class="citation journal cs1">Schmidl, Petra G. (1996–1997). "Two Early Arabic Sources On The Magnetic Compass". <i>Journal of Arabic and Islamic Studies</i>. <b>1</b>: <span class="nowrap">81–</span>132.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Arabic+and+Islamic+Studies&rft.atitle=Two+Early+Arabic+Sources+On+The+Magnetic+Compass&rft.volume=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E81-%3C%2Fspan%3E132&rft.date=1996%2F1997&rft.aulast=Schmidl&rft.aufirst=Petra+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-Gauss1835-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gauss1835_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gauss1835_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGauss1867" class="citation book cs1">Gauss, Carl Friedrich (1867). <i>Carl Friedrich Gauss Werke. Fünfter Band</i>. Königliche Gesellschaft der Wissenschaften zu Göttingen. p. 617.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Carl+Friedrich+Gauss+Werke.+F%C3%BCnfter+Band&rft.pages=617&rft.pub=K%C3%B6nigliche+Gesellschaft+der+Wissenschaften+zu+G%C3%B6ttingen&rft.date=1867&rft.aulast=Gauss&rft.aufirst=Carl+Friedrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-Moving-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Moving_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Moving_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.fourmilab.ch/etexts/einstein/specrel/www/">A. Einstein: "On the Electrodynamics of Moving Bodies"</a>, June 30, 1905.</span> </li> <li id="cite_note-Meyers1-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Meyers1_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHP_Meyers1997" class="citation book cs1">HP Meyers (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Uc1pCo5TrYUC&pg=PA322"><i>Introductory solid state physics</i></a> (2 ed.). CRC Press. p. 362; Figure 11.1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781420075021" title="Special:BookSources/9781420075021"><bdi>9781420075021</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+solid+state+physics&rft.pages=362%3B+Figure+11.1&rft.edition=2&rft.pub=CRC+Press&rft.date=1997&rft.isbn=9781420075021&rft.au=HP+Meyers&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUc1pCo5TrYUC%26pg%3DPA322&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-Westbrook-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Westbrook_15-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCatherine_WestbrookCarolyn_KautCarolyn_Kaut-Roth1998" class="citation book cs1">Catherine Westbrook; Carolyn Kaut; Carolyn Kaut-Roth (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Qq1SHDtS2G8C&pg=PA217"><i>MRI (Magnetic Resonance Imaging) in practice</i></a> (2 ed.). Wiley-Blackwell. p. 217. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-632-04205-0" title="Special:BookSources/978-0-632-04205-0"><bdi>978-0-632-04205-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=MRI+%28Magnetic+Resonance+Imaging%29+in+practice&rft.pages=217&rft.edition=2&rft.pub=Wiley-Blackwell&rft.date=1998&rft.isbn=978-0-632-04205-0&rft.au=Catherine+Westbrook&rft.au=Carolyn+Kaut&rft.au=Carolyn+Kaut-Roth&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQq1SHDtS2G8C%26pg%3DPA217&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreshko2024" class="citation magazine cs1">Greshko, Michael (January 20, 2024). <a rel="nofollow" class="external text" href="https://www.wired.com/story/scientists-discovered-new-type-magnetism-physics-electrons/">"Scientists Just Discovered a New Type of Magnetism"</a>. <i>Wired</i>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1059-1028">1059-1028</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-02-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wired&rft.atitle=Scientists+Just+Discovered+a+New+Type+of+Magnetism&rft.date=2024-01-20&rft.issn=1059-1028&rft.aulast=Greshko&rft.aufirst=Michael&rft_id=https%3A%2F%2Fwww.wired.com%2Fstory%2Fscientists-discovered-new-type-magnetism-physics-electrons%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><a href="#CITEREFPurcell2012">Purcell 2012</a>, p. 320,584</span> </li> <li id="cite_note-Merzouki-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Merzouki_18-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMerzoukiSamantarayPathak2012" class="citation book cs1">Merzouki, Rochdi; Samantaray, Arun Kumar; Pathak, Pushparaj Mani (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=k81ECeMxyk8C&q=ferromagnetic+electromagnet&pg=PA404"><i>Intelligent Mechatronic Systems: Modeling, Control and Diagnosis</i></a>. Springer Science & Business Media. pp. <span class="nowrap">403–</span>405. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1447146285" title="Special:BookSources/978-1447146285"><bdi>978-1447146285</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intelligent+Mechatronic+Systems%3A+Modeling%2C+Control+and+Diagnosis&rft.pages=%3Cspan+class%3D%22nowrap%22%3E403-%3C%2Fspan%3E405&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=978-1447146285&rft.aulast=Merzouki&rft.aufirst=Rochdi&rft.au=Samantaray%2C+Arun+Kumar&rft.au=Pathak%2C+Pushparaj+Mani&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dk81ECeMxyk8C%26q%3Dferromagnetic%2Belectromagnet%26pg%3DPA404&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSturgeon1825" class="citation journal cs1">Sturgeon, W. (1825). "Improved Electro Magnetic Apparatus". <i>Trans. Royal Society of Arts, Manufactures, & Commerce</i>. <b>43</b>: <span class="nowrap">37–</span>52.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Royal+Society+of+Arts%2C+Manufactures%2C+%26+Commerce&rft.atitle=Improved+Electro+Magnetic+Apparatus&rft.volume=43&rft.pages=%3Cspan+class%3D%22nowrap%22%3E37-%3C%2Fspan%3E52&rft.date=1825&rft.aulast=Sturgeon&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span> cited in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiller2001" class="citation book cs1">Miller, T.J.E (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E8VroIWyjB8C&pg=PA7"><i>Electronic Control of Switched Reluctance Machines</i></a>. Newnes. p. 7. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-5073-1" title="Special:BookSources/978-0-7506-5073-1"><bdi>978-0-7506-5073-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electronic+Control+of+Switched+Reluctance+Machines&rft.pages=7&rft.pub=Newnes&rft.date=2001&rft.isbn=978-0-7506-5073-1&rft.aulast=Miller&rft.aufirst=T.J.E&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE8VroIWyjB8C%26pg%3DPA7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><a href="#CITEREFGriffiths1998">Griffiths 1998</a>, chapter 12</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoozer2006" class="citation journal cs1">Boozer, Allen H. (2006-04-01). <a rel="nofollow" class="external text" href="https://aip.scitation.org/doi/10.1063/1.2192511">"Perturbation to the magnetic field strength"</a>. <i>Physics of Plasmas</i>. <b>13</b> (4): 044501. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006PhPl...13d4501B">2006PhPl...13d4501B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.2192511">10.1063/1.2192511</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1070-664X">1070-664X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+of+Plasmas&rft.atitle=Perturbation+to+the+magnetic+field+strength&rft.volume=13&rft.issue=4&rft.pages=044501&rft.date=2006-04-01&rft.issn=1070-664X&rft_id=info%3Adoi%2F10.1063%2F1.2192511&rft_id=info%3Abibcode%2F2006PhPl...13d4501B&rft.aulast=Boozer&rft.aufirst=Allen+H.&rft_id=https%3A%2F%2Faip.scitation.org%2Fdoi%2F10.1063%2F1.2192511&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJackson1999" class="citation book cs1"><a href="/wiki/John_David_Jackson_(physicist)" title="John David Jackson (physicist)">Jackson, John David</a> (1999). <i>Classical electrodynamics</i> (3rd ed.). New York: <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">Wiley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-30932-1" title="Special:BookSources/978-0-471-30932-1"><bdi>978-0-471-30932-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+electrodynamics&rft.place=New+York&rft.edition=3rd&rft.pub=Wiley&rft.date=1999&rft.isbn=978-0-471-30932-1&rft.aulast=Jackson&rft.aufirst=John+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Milton mentions some inconclusive events (p. 60) and still concludes that "no evidence at all of magnetic monopoles has survived" (p.3). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMilton2006" class="citation journal cs1">Milton, Kimball A. (June 2006). "Theoretical and experimental status of magnetic monopoles". <i>Reports on Progress in Physics</i>. <b>69</b> (6): <span class="nowrap">1637–</span>1711. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ex/0602040">hep-ex/0602040</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006RPPh...69.1637M">2006RPPh...69.1637M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F69%2F6%2FR02">10.1088/0034-4885/69/6/R02</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119061150">119061150</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reports+on+Progress+in+Physics&rft.atitle=Theoretical+and+experimental+status+of+magnetic+monopoles&rft.volume=69&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1637-%3C%2Fspan%3E1711&rft.date=2006-06&rft_id=info%3Aarxiv%2Fhep-ex%2F0602040&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119061150%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F69%2F6%2FR02&rft_id=info%3Abibcode%2F2006RPPh...69.1637M&rft.aulast=Milton&rft.aufirst=Kimball+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span>.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuth1997" class="citation book cs1"><a href="/wiki/Alan_Guth" title="Alan Guth">Guth, Alan</a> (1997). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/inflationaryuniv0000guth"><i>The Inflationary Universe: The Quest for a New Theory of Cosmic Origins</i></a></span>. Perseus. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-32840-0" title="Special:BookSources/978-0-201-32840-0"><bdi>978-0-201-32840-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/38941224">38941224</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Inflationary+Universe%3A+The+Quest+for+a+New+Theory+of+Cosmic+Origins&rft.pub=Perseus&rft.date=1997&rft_id=info%3Aoclcnum%2F38941224&rft.isbn=978-0-201-32840-0&rft.aulast=Guth&rft.aufirst=Alan&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finflationaryuniv0000guth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span>.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">International Union of Pure and Applied Chemistry</a> (1993). <i><a href="/wiki/Quantities,_Units_and_Symbols_in_Physical_Chemistry" title="Quantities, Units and Symbols in Physical Chemistry">Quantities, Units and Symbols in Physical Chemistry</a></i>, 2nd edition, Oxford: Blackwell Science. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-632-03583-8" title="Special:BookSources/0-632-03583-8">0-632-03583-8</a>. pp. 14–15. <a rel="nofollow" class="external text" href="https://old.iupac.org/publications/books/gbook/green_book_2ed.pdf">Electronic version.</a></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKirschvinkKobayashi-KirshvinkDiaz-RicciKirschvink1992" class="citation journal cs1">Kirschvink, Joseph L.; Kobayashi-Kirshvink, Atsuko; Diaz-Ricci, Juan C.; Kirschvink, Steven J. (1992). <a rel="nofollow" class="external text" href="http://web.gps.caltech.edu/~jkirschvink/pdfs/KirschvinkBEMS92.pdf">"Magnetite in Human Tissues: A Mechanism for the Biological Effects of Weak ELF Magnetic Fields"</a> <span class="cs1-format">(PDF)</span>. <i>Bioelectromagnetics Supplement</i>. <b>1</b>: <span class="nowrap">101–</span>113. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fbem.2250130710">10.1002/bem.2250130710</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/1285705">1285705</a><span class="reference-accessdate">. Retrieved <span class="nowrap">29 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bioelectromagnetics+Supplement&rft.atitle=Magnetite+in+Human+Tissues%3A+A+Mechanism+for+the+Biological+Effects+of+Weak+ELF+Magnetic+Fields&rft.volume=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E101-%3C%2Fspan%3E113&rft.date=1992&rft_id=info%3Adoi%2F10.1002%2Fbem.2250130710&rft_id=info%3Apmid%2F1285705&rft.aulast=Kirschvink&rft.aufirst=Joseph+L.&rft.au=Kobayashi-Kirshvink%2C+Atsuko&rft.au=Diaz-Ricci%2C+Juan+C.&rft.au=Kirschvink%2C+Steven+J.&rft_id=http%3A%2F%2Fweb.gps.caltech.edu%2F~jkirschvink%2Fpdfs%2FKirschvinkBEMS92.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAssisJ._P._M._C._Chaib2015" class="citation book cs1">Assis, A. K. T.; J. P. M. C. Chaib (2015). <i>Ampère's electrodynamics: Analysis of the meaning and evolution of Ampère's force between current elements, together with a complete translation of his masterpiece: Theory of electrodynamic phenomena, uniquely deduced from experience</i>. C. Roy Keys Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-987980-03-5" title="Special:BookSources/978-1-987980-03-5"><bdi>978-1-987980-03-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Amp%C3%A8re%27s+electrodynamics%3A+Analysis+of+the+meaning+and+evolution+of+Amp%C3%A8re%27s+force+between+current+elements%2C+together+with+a+complete+translation+of+his+masterpiece%3A+Theory+of+electrodynamic+phenomena%2C+uniquely+deduced+from+experience&rft.pub=C.+Roy+Keys+Inc.&rft.date=2015&rft.isbn=978-1-987980-03-5&rft.aulast=Assis&rft.aufirst=A.+K.+T.&rft.au=J.+P.+M.+C.+Chaib&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilhelm_Weber2021" class="citation book cs1">Wilhelm Weber (2021). Andre Koch Torres Assis (ed.). <i>Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume I: Gauss und Weber's Absolute System of Units</i>. Apeiron Montreal.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wilhelm+Weber%27s+Main+Works+in+Electrodynamics+Translated+into+English.+Volume+I%3A+Gauss+und+Weber%27s+Absolute+System+of+Units&rft.pub=Apeiron+Montreal&rft.date=2021&rft.au=Wilhelm+Weber&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilhelm_Weber2021" class="citation book cs1">Wilhelm Weber (2021). Andre Koch Torres Assis (ed.). <i>Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume II: Weber's Fundamental Force and the Unification of the Laws of Coulomb, Ampere and Faraday</i>. Apeiron Montreal.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wilhelm+Weber%27s+Main+Works+in+Electrodynamics+Translated+into+English.+Volume+II%3A+Weber%27s+Fundamental+Force+and+the+Unification+of+the+Laws+of+Coulomb%2C+Ampere+and+Faraday&rft.pub=Apeiron+Montreal&rft.date=2021&rft.au=Wilhelm+Weber&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilhelm_Weber2021" class="citation book cs1">Wilhelm Weber (2021). Andre Koch Torres Assis (ed.). <i>Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume III: Measurement of Weber's Constant c, Diamagnetism, the Telegraph Equation and the Propagation of Electric Waves at Light Velocity</i>. Apeiron Montreal.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wilhelm+Weber%27s+Main+Works+in+Electrodynamics+Translated+into+English.+Volume+III%3A+Measurement+of+Weber%27s+Constant+c%2C+Diamagnetism%2C+the+Telegraph+Equation+and+the+Propagation+of+Electric+Waves+at+Light+Velocity&rft.pub=Apeiron+Montreal&rft.date=2021&rft.au=Wilhelm+Weber&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaxwell1881" class="citation book cs1">Maxwell, James Clerk (1881). <i>Treatise on Electricity and Magnetism. Volume 2</i>. Vol. 2 (2 ed.). The Clarendon Press, Oxdord. p. 162.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Treatise+on+Electricity+and+Magnetism.+Volume+2&rft.pages=162&rft.edition=2&rft.pub=The+Clarendon+Press%2C+Oxdord&rft.date=1881&rft.aulast=Maxwell&rft.aufirst=James+Clerk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/II_34.html">"The Feynman Lectures on Physics Vol. II Ch. 34: The Magnetism of Matter"</a>. <i>www.feynmanlectures.caltech.edu</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.feynmanlectures.caltech.edu&rft.atitle=The+Feynman+Lectures+on+Physics+Vol.+II+Ch.+34%3A+The+Magnetism+of+Matter&rft_id=https%3A%2F%2Fwww.feynmanlectures.caltech.edu%2FII_34.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/II_36.html">"The Feynman Lectures on Physics Vol. II Ch. 36: Ferromagnetism"</a>. <i>www.feynmanlectures.caltech.edu</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.feynmanlectures.caltech.edu&rft.atitle=The+Feynman+Lectures+on+Physics+Vol.+II+Ch.+36%3A+Ferromagnetism&rft_id=https%3A%2F%2Fwww.feynmanlectures.caltech.edu%2FII_36.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=27" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_K._Cheng1992" class="citation book cs1">David K. Cheng (1992). <i>Field and Wave Electromagnetics</i>. Addison-Wesley Publishing Company, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-12819-2" title="Special:BookSources/978-0-201-12819-2"><bdi>978-0-201-12819-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Field+and+Wave+Electromagnetics&rft.pub=Addison-Wesley+Publishing+Company%2C+Inc.&rft.date=1992&rft.isbn=978-0-201-12819-2&rft.au=David+K.+Cheng&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFurlani,_Edward_P.2001" class="citation book cs1">Furlani, Edward P. (2001). <i>Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications</i>. <a href="/wiki/Academic_Press" title="Academic Press">Academic Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-269951-1" title="Special:BookSources/978-0-12-269951-1"><bdi>978-0-12-269951-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/162129430">162129430</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Permanent+Magnet+and+Electromechanical+Devices%3A+Materials%2C+Analysis+and+Applications&rft.pub=Academic+Press&rft.date=2001&rft_id=info%3Aoclcnum%2F162129430&rft.isbn=978-0-12-269951-1&rft.au=Furlani%2C+Edward+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriffiths1998" class="citation book cs1">Griffiths, David J. (1998). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoel00grif_0"><i>Introduction to Electrodynamics (3rd ed.)</i></a></span>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-805326-0" title="Special:BookSources/978-0-13-805326-0"><bdi>978-0-13-805326-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/40251748">40251748</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Electrodynamics+%283rd+ed.%29&rft.pub=Prentice+Hall&rft.date=1998&rft_id=info%3Aoclcnum%2F40251748&rft.isbn=978-0-13-805326-0&rft.aulast=Griffiths&rft.aufirst=David+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoel00grif_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKronmüller,_Helmut.2007" class="citation book cs1">Kronmüller, Helmut. (2007). <i>Handbook of Magnetism and Advanced Magnetic Materials, 5 Volume Set</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-02217-7" title="Special:BookSources/978-0-470-02217-7"><bdi>978-0-470-02217-7</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/124165851">124165851</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Magnetism+and+Advanced+Magnetic+Materials%2C+5+Volume+Set&rft.pub=John+Wiley+%26+Sons&rft.date=2007&rft_id=info%3Aoclcnum%2F124165851&rft.isbn=978-0-470-02217-7&rft.au=Kronm%C3%BCller%2C+Helmut.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPurcell2012" class="citation book cs1">Purcell, Edward M. (2012). <i>Electricity and magnetism</i> (3rd ed.). Cambridge: Cambridge Univ. Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781-10701-4022" title="Special:BookSources/9781-10701-4022"><bdi>9781-10701-4022</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity+and+magnetism&rft.place=Cambridge&rft.edition=3rd&rft.pub=Cambridge+Univ.+Press&rft.date=2012&rft.isbn=9781-10701-4022&rft.aulast=Purcell&rft.aufirst=Edward+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTipler,_Paul2004" class="citation book cs1">Tipler, Paul (2004). <i>Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.)</i>. W.H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0810-0" title="Special:BookSources/978-0-7167-0810-0"><bdi>978-0-7167-0810-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/51095685">51095685</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers%3A+Electricity%2C+Magnetism%2C+Light%2C+and+Elementary+Modern+Physics+%285th+ed.%29&rft.pub=W.H.+Freeman&rft.date=2004&rft_id=info%3Aoclcnum%2F51095685&rft.isbn=978-0-7167-0810-0&rft.au=Tipler%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCoey2019" class="citation book cs1">Coey, J. M. D. (2019). <i>Magnetism and Magnetic Materials</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1108717519" title="Special:BookSources/978-1108717519"><bdi>978-1108717519</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Magnetism+and+Magnetic+Materials&rft.pub=Cambridge+University+Press&rft.date=2019&rft.isbn=978-1108717519&rft.aulast=Coey&rft.aufirst=J.+M.+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMagnetism" class="Z3988"></span></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnetism&action=edit&section=28" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output 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title="Superparamagnetism">superparamagnetism</a></li> <li><a href="/wiki/Van_Vleck_paramagnetism" title="Van Vleck paramagnetism">Van Vleck paramagnetism</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Magnetic states</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Altermagnetism" title="Altermagnetism">altermagnetism</a></li> <li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">antiferromagnetism</a></li> <li><a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">ferrimagnetism</a></li> <li><a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetism</a> <ul><li><a href="/wiki/Superferromagnetism" title="Superferromagnetism">superferromagnetism</a></li> <li><a href="/wiki/Ferromagnetic_superconductor" title="Ferromagnetic superconductor">ferromagnetic superconductor</a></li></ul></li> <li><a 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