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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 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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">Meissner effect</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 38 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-38" 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">38 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B8%D8%A7%D9%87%D8%B1%D8%A9_%D9%85%D8%A7%D9%8A%D8%B3%D9%86%D8%B1" title="ظاهرة مايسنر – Arabic" lang="ar" hreflang="ar" data-title="ظاهرة مايسنر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%9C%D0%B0%D0%B9%D1%81%D0%BD%D0%B5%D1%80" title="Ефект на Майснер – Bulgarian" lang="bg" hreflang="bg" data-title="Ефект на Майснер" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Meissner" title="Efecte Meissner – Catalan" lang="ca" hreflang="ca" data-title="Efecte Meissner" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Meissnereffekt" title="Meissnereffekt – Danish" lang="da" hreflang="da" data-title="Meissnereffekt" 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/Mei%C3%9Fner-Ochsenfeld-Effekt" title="Meißner-Ochsenfeld-Effekt – German" lang="de" hreflang="de" data-title="Meißner-Ochsenfeld-Effekt" 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/Meissneri_efekt" title="Meissneri efekt – Estonian" lang="et" hreflang="et" data-title="Meissneri efekt" 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%A6%CE%B1%CE%B9%CE%BD%CF%8C%CE%BC%CE%B5%CE%BD%CE%BF_%CE%9C%CE%AC%CE%B9%CF%83%CE%BD%CE%B5%CF%81" title="Φαινόμενο Μάισνερ – Greek" lang="el" hreflang="el" data-title="Φαινόμενο Μάισνερ" 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/Efecto_Meissner" title="Efecto Meissner – Spanish" lang="es" hreflang="es" data-title="Efecto Meissner" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%AB%D8%B1_%D9%85%D8%A7%DB%8C%D8%B3%D9%86%D8%B1" title="اثر مایسنر – Persian" lang="fa" hreflang="fa" data-title="اثر مایسنر" 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/Effet_Meissner" title="Effet Meissner – French" lang="fr" hreflang="fr" data-title="Effet Meissner" 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/Iarmhairt_Meissner" title="Iarmhairt Meissner – Irish" lang="ga" hreflang="ga" data-title="Iarmhairt Meissner" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%88%EC%9D%B4%EC%8A%A4%EB%84%88_%ED%9A%A8%EA%B3%BC" title="마이스너 효과 – Korean" lang="ko" hreflang="ko" data-title="마이스너 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%87%E0%A4%B8%E0%A4%A8%E0%A4%B0_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B5" title="माइसनर प्रभाव – Hindi" lang="hi" hreflang="hi" data-title="माइसनर प्रभाव" 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/Meissnerov_u%C4%8Dinak" title="Meissnerov učinak – Croatian" lang="hr" hreflang="hr" data-title="Meissnerov učinak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Meissner-Ochsenfeld" title="Effetto Meissner-Ochsenfeld – Italian" lang="it" hreflang="it" data-title="Effetto Meissner-Ochsenfeld" 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%90%D7%A4%D7%A7%D7%98_%D7%9E%D7%99%D7%99%D7%A1%D7%A0%D7%A8" title="אפקט מייסנר – Hebrew" lang="he" hreflang="he" data-title="אפקט מייסנר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%94%E1%83%98%E1%83%A1%E1%83%9C%E1%83%94%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%94%E1%83%A4%E1%83%94%E1%83%A5%E1%83%A2%E1%83%98" title="მეისნერის ეფექტი – Georgian" lang="ka" hreflang="ka" data-title="მეისნერის ეფექტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Meissner%E2%80%93Ochsenfeld-effektus" title="Meissner–Ochsenfeld-effektus – Hungarian" lang="hu" hreflang="hu" data-title="Meissner–Ochsenfeld-effektus" 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%D1%98%D1%81%D0%BD%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D1%82" title="Мајснеров ефект – Macedonian" lang="mk" hreflang="mk" data-title="Мајснеров ефект" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%B5%D0%B9%D1%81%D0%BD%D0%B5%D1%80%D0%B8%D0%B9%D0%BD_%D2%AF%D0%B9%D0%BB%D1%87%D0%BB%D1%8D%D0%BB" title="Мейснерийн үйлчлэл – Mongolian" lang="mn" hreflang="mn" data-title="Мейснерийн үйлчлэл" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Meissner-effect" title="Meissner-effect – Dutch" lang="nl" hreflang="nl" data-title="Meissner-effect" 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/%E3%83%9E%E3%82%A4%E3%82%B9%E3%83%8A%E3%83%BC%E5%8A%B9%E6%9E%9C" title="マイスナー効果 – Japanese" lang="ja" hreflang="ja" data-title="マイスナー効果" 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/Meissner-effekt" title="Meissner-effekt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Meissner-effekt" 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/Meissnereffekt" title="Meissnereffekt – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Meissnereffekt" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Efekt_Meissnera" title="Efekt Meissnera – Polish" lang="pl" hreflang="pl" data-title="Efekt Meissnera" 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/Efeito_Meissner" title="Efeito Meissner – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Meissner" 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/Efectul_Meissner" title="Efectul Meissner – Romanian" lang="ro" hreflang="ro" data-title="Efectul Meissner" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%9C%D0%B5%D0%B9%D1%81%D0%BD%D0%B5%D1%80%D0%B0" title="Эффект Мейснера – Russian" lang="ru" hreflang="ru" data-title="Эффект Мейснера" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Meissner_effect" title="Meissner effect – Simple English" lang="en-simple" hreflang="en-simple" data-title="Meissner effect" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%98%D1%81%D0%BD%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Мајснеров ефекат – Serbian" lang="sr" hreflang="sr" data-title="Мајснеров ефекат" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Meissnerin_ilmi%C3%B6" title="Meissnerin ilmiö – Finnish" lang="fi" hreflang="fi" data-title="Meissnerin ilmiö" 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/Meissnereffekten" title="Meissnereffekten – Swedish" lang="sv" hreflang="sv" data-title="Meissnereffekten" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%86%E0%AE%AF%E0%AF%8D%E0%AE%9A%E0%AE%A9%E0%AE%B0%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%B3%E0%AF%88%E0%AE%B5%E0%AF%81" title="மெய்சனர் விளைவு – Tamil" lang="ta" hreflang="ta" data-title="மெய்சனர் விளைவு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B2%E0%B8%81%E0%B8%8F%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%93%E0%B9%8C%E0%B9%84%E0%B8%A1%E0%B8%AA%E0%B9%80%E0%B8%99%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="ปรากฏการณ์ไมสเนอร์ – Thai" lang="th" hreflang="th" data-title="ปรากฏการณ์ไมสเนอร์" 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/Meissner_etkisi" title="Meissner etkisi – Turkish" lang="tr" hreflang="tr" data-title="Meissner etkisi" 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%95%D1%84%D0%B5%D0%BA%D1%82_%D0%9C%D0%B5%D0%B9%D1%81%D0%BD%D0%B5%D1%80%D0%B0" title="Ефект Мейснера – Ukrainian" lang="uk" hreflang="uk" data-title="Ефект Мейснера" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hi%E1%BB%87u_%E1%BB%A9ng_Meissner" title="Hiệu ứng Meissner – Vietnamese" lang="vi" hreflang="vi" data-title="Hiệu ứng Meissner" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%82%81%E6%96%AF%E7%B4%8D%E6%95%88%E6%87%89" title="邁斯納效應 – Chinese" lang="zh" hreflang="zh" data-title="邁斯納效應" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q220620#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Meissner_effect" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Meissner_effect" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input 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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> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Expulsion of a magnetic field from a superconductor</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:EfektMeisnera.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/EfektMeisnera.svg/220px-EfektMeisnera.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/EfektMeisnera.svg/330px-EfektMeisnera.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/EfektMeisnera.svg/440px-EfektMeisnera.svg.png 2x" data-file-width="525" data-file-height="525" /></a><figcaption>Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.</figcaption></figure> <p>In <a href="/wiki/Condensed-matter_physics" class="mw-redirect" title="Condensed-matter physics">condensed-matter physics</a>, the <b>Meissner effect</b> (or <b>Meißner–Ochsenfeld effect</b>) is the expulsion of a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> from a <a href="/wiki/Superconductor" class="mw-redirect" title="Superconductor">superconductor</a> during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby <a href="/wiki/Magnet" title="Magnet">magnet</a>. </p><p>The German physicists <a href="/wiki/Walther_Meissner" title="Walther Meissner">Walther Meißner</a> (anglicized <i>Meissner</i>) and <a href="/wiki/Robert_Ochsenfeld" title="Robert Ochsenfeld">Robert Ochsenfeld</a><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> discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples.<sup id="cite_ref-meissner1_2-0" class="reference"><a href="#cite_note-meissner1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The samples, in the presence of an applied magnetic field, were cooled below their <a href="/wiki/Superconductivity#Superconducting_phase_transition" title="Superconductivity">superconducting transition temperature</a>, whereupon the samples cancelled nearly all interior magnetic fields. They detected this effect only indirectly because the <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> is conserved by a superconductor: when the interior field decreases, the exterior field increases. The experiment demonstrated for the first time that superconductors were more than just perfect <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductors</a> and provided a uniquely defining property of the superconductor state. The ability for the expulsion effect is determined by the nature of equilibrium formed by the neutralization within the <a href="/wiki/Unit_cell" title="Unit cell">unit cell</a> of a superconductor. </p><p>A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too strong. Superconductors can be divided into two classes according to how this breakdown occurs. </p> <ul><li>In <a href="/wiki/Type-I_superconductor" title="Type-I superconductor">type-I superconductors</a>, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value <i>H<sub>c</sub></i>. Depending on the geometry of the sample, one may obtain an intermediate state<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> consisting of a <a href="https://en.wiktionary.org/wiki/baroque" class="extiw" title="wikt:baroque">baroque pattern</a><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> of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field.</li> <li>In <a href="/wiki/Type-II_superconductor" title="Type-II superconductor">type-II superconductors</a>, raising the applied field past a critical value <i>H</i><sub><i>c</i>1</sub> leads to a mixed state (also known as the vortex state) in which an increasing amount of <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> penetrates the material, but there remains no resistance to the <a href="/wiki/Electric_current" title="Electric current">electric current</a> as long as the current is not too large. Some type-II superconductors exhibit a small but finite resistance in the mixed state due to motion of the flux vortices induced by the Lorentz forces from the current. As the cores of the vortices are normal electrons, their motion will have dissipation. At a second critical field strength <i>H</i><sub><i>c</i>2</sub>, superconductivity is destroyed. The mixed state is caused by vortices in the electronic superfluid, sometimes called <a href="/wiki/Fluxon" title="Fluxon">fluxons</a> because the flux carried by these vortices is <a href="/wiki/Quantum" title="Quantum">quantized</a>.</li></ul> <p>Most pure <a href="/wiki/Chemical_element" title="Chemical element">elemental</a> superconductors, except <a href="/wiki/Niobium" title="Niobium">niobium</a> and <a href="/wiki/Carbon_nanotube" title="Carbon nanotube">carbon nanotubes</a>, are type I, while almost all impure and compound superconductors are type II. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanation">Explanation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=1" title="Edit section: Explanation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Meissner effect was given a phenomenological explanation by the brothers <a href="/wiki/Fritz_London" title="Fritz London">Fritz</a> and <a href="/wiki/Heinz_London" title="Heinz London">Heinz London</a>, who showed that the electromagnetic <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a> in a superconductor is minimized provided </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 \nabla ^{2}\mathbf {H} =\lambda ^{-2}\mathbf {H} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>=</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla ^{2}\mathbf {H} =\lambda ^{-2}\mathbf {H} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57d717daee621d38ce18f56caf7ddb65f191e567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.347ex; height:2.676ex;" alt="{\displaystyle \nabla ^{2}\mathbf {H} =\lambda ^{-2}\mathbf {H} \,}"></span></dd></dl> <p>where <b>H</b> is the magnetic field and λ is the <a href="/wiki/London_penetration_depth" title="London penetration depth">London penetration depth</a>. </p><p>This equation, known as the <a href="/wiki/London_equation" class="mw-redirect" title="London equation">London equation</a>, predicts that the magnetic field in a superconductor <a href="/wiki/Exponential_decay" title="Exponential decay">decays exponentially</a> from whatever value it possesses at the surface. This exclusion of magnetic field is a manifestation of the <a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">superdiamagnetism</a> emerged during the phase transition from conductor to superconductor, for example by reducing the temperature below critical temperature. </p><p>In a weak applied field (less than the critical field that breaks down the superconducting phase), a superconductor expels nearly all <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> by setting up electric currents near its surface, as the magnetic field <b>H</b> induces <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> <b>M</b> within the London penetration depth from the surface. These surface currents <a href="/wiki/Electromagnetic_shielding#Magnetic_shielding" title="Electromagnetic shielding">shield</a> the internal bulk of the superconductor from the external applied field. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called <a href="/wiki/Persistent_current" title="Persistent current">persistent currents</a> or screening currents) do not decay with time. </p><p>Near the surface, within the <a href="/wiki/London_penetration_depth" title="London penetration depth">London penetration depth</a>, the magnetic field is not completely canceled. Each superconducting material has its own characteristic penetration depth. </p><p>Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary <a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">electromagnetic induction</a> at zero resistance. However, the Meissner effect is distinct from this: when an ordinary conductor is cooled so that it makes the transition to a superconducting state in the presence of a constant applied magnetic field, the magnetic flux is expelled during the transition. This effect cannot be explained by infinite conductivity, but only by the London equation. The placement and subsequent levitation of a magnet above an already superconducting material does not demonstrate the Meissner effect, while an initially stationary magnet later being repelled by a superconductor as it is cooled below its critical <a href="/wiki/Temperature" title="Temperature">temperature</a> does. </p><p>The persisting currents that exist in the superconductor to expel the magnetic field is commonly misconceived as a result of <a href="/wiki/Lenz%27s_Law" class="mw-redirect" title="Lenz's Law">Lenz's Law</a> or <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's Law</a>. A reason this is not the case is that no change in flux was made to induce the current. Another explanation is that since the superconductor experiences zero resistance, there cannot be an induced emf in the superconductor. The persisting current therefore is not a result of Faraday's Law. </p> <div class="mw-heading mw-heading2"><h2 id="Perfect_diamagnetism">Perfect diamagnetism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=2" title="Edit section: Perfect diamagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Superconductors in the Meissner state exhibit perfect diamagnetism, or <a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">superdiamagnetism</a>, meaning that the total magnetic field is very close to zero deep inside them (many penetration depths from the surface). This means that their volume <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a> is <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 _{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi _{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b32faa75b318d420fcea4f44307a1a25b3ebd628" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.485ex; height:2.009ex;" alt="{\displaystyle \chi _{v}}"></span> = −1. <a href="/wiki/Diamagnetics" class="mw-redirect" title="Diamagnetics">Diamagnetics</a> are defined by the generation of a spontaneous magnetization of a material which directly opposes the direction of an applied field. However, the fundamental origins of diamagnetism in superconductors and normal materials are very different. In normal materials diamagnetism arises as a direct result of the orbital spin of electrons about the nuclei of an atom induced electromagnetically by the application of an applied field. In superconductors the illusion of perfect diamagnetism arises from persistent screening currents which flow to oppose the applied field (the Meissner effect); not solely the orbital spin. </p> <div class="mw-heading mw-heading2"><h2 id="Consequences">Consequences</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=3" title="Edit section: Consequences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The discovery of the Meissner effect led to the <a href="/wiki/Phenomenology_(particle_physics)" class="mw-redirect" title="Phenomenology (particle physics)">phenomenological</a> theory of superconductivity by <a href="/wiki/Fritz_London" title="Fritz London">Fritz</a> and <a href="/wiki/Heinz_London" title="Heinz London">Heinz London</a> in 1935. This theory explained resistanceless transport and the Meissner effect, and allowed the first theoretical predictions for superconductivity to be made. However, this theory only explained experimental observations—it did not allow the microscopic origins of the superconducting properties to be identified. This was done successfully by the <a href="/wiki/BCS_theory" title="BCS theory">BCS theory</a> in 1957, from which the penetration depth and the Meissner effect result.<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> However, some physicists argue that BCS theory does not explain the Meissner effect.<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> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Tin_4.2K_Electromagnet.jpg" class="mw-file-description" title="A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 millitesla (80 G)."><img alt="A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 millitesla (80 G)." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Tin_4.2K_Electromagnet.jpg/167px-Tin_4.2K_Electromagnet.jpg" decoding="async" width="167" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Tin_4.2K_Electromagnet.jpg/250px-Tin_4.2K_Electromagnet.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/Tin_4.2K_Electromagnet.jpg/333px-Tin_4.2K_Electromagnet.jpg 2x" data-file-width="1874" data-file-height="1350" /></a></span></div> <div class="gallerytext">A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 <a href="/wiki/Millitesla" class="mw-redirect" title="Millitesla">millitesla</a> (80 <a href="/wiki/Gauss_(unit)" title="Gauss (unit)">G</a>).</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Tin_80gauss_4.2K.jpg" class="mw-file-description" title="T = 4.2 K, B = 8 mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder."><img alt="T = 4.2 K, B = 8 mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder." src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Tin_80gauss_4.2K.jpg/161px-Tin_80gauss_4.2K.jpg" decoding="async" width="161" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Tin_80gauss_4.2K.jpg/241px-Tin_80gauss_4.2K.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Tin_80gauss_4.2K.jpg/322px-Tin_80gauss_4.2K.jpg 2x" data-file-width="2994" data-file-height="2234" /></a></span></div> <div class="gallerytext"><i>T</i> = 4.2 K, <b>B</b> = 8 mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Tin_80gauss_1.6K.jpg" class="mw-file-description" title="The cylinder has been cooled from 4.2 K to 1.6 K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3 K. Magnetic flux has been expelled from the cylinder (the Meissner effect)."><img alt="The cylinder has been cooled from 4.2 K to 1.6 K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3 K. Magnetic flux has been expelled from the cylinder (the Meissner effect)." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Tin_80gauss_1.6K.jpg/81px-Tin_80gauss_1.6K.jpg" decoding="async" width="81" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Tin_80gauss_1.6K.jpg/122px-Tin_80gauss_1.6K.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Tin_80gauss_1.6K.jpg/163px-Tin_80gauss_1.6K.jpg 2x" data-file-width="1344" data-file-height="1982" /></a></span></div> <div class="gallerytext">The cylinder has been cooled from 4.2 K to 1.6 K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3 K. Magnetic flux has been expelled from the cylinder (the Meissner effect).</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Paradigm_for_the_Higgs_mechanism">Paradigm for the Higgs mechanism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=4" title="Edit section: Paradigm for the Higgs mechanism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Meissner superconductivity effect serves as an important paradigm for the generation mechanism of a mass <i>M</i> (i.e., a reciprocal <i>range</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 \lambda _{M}:=h/(Mc)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>:=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{M}:=h/(Mc)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7826080e7c60d96af51355e3e26b168f63f69be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.819ex; height:2.843ex;" alt="{\displaystyle \lambda _{M}:=h/(Mc)}"></span> where <i>h</i> is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> and <i>c</i> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>) for a <a href="/wiki/Gauge_field" class="mw-redirect" title="Gauge field">gauge field</a>. In fact, this analogy is an <a href="/wiki/Abelian_(disambiguation)#In_physics" class="mw-redirect mw-disambig" title="Abelian (disambiguation)">abelian</a> example for the <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a>,<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> which generates the masses of the <a href="/wiki/Electroweak" class="mw-redirect" title="Electroweak">electroweak</a> <a href="/wiki/W_and_Z_bosons" title="W and Z bosons"><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">±</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> and <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Z<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span></a> gauge particles in <a href="/wiki/High-energy_physics" class="mw-redirect" title="High-energy physics">high-energy physics</a>. The length <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 \lambda _{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56716be6b9b0a56a945c8e19dca2ba3eab33a2da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.314ex; height:2.509ex;" alt="{\displaystyle \lambda _{M}}"></span> is identical with the <a href="/wiki/London_penetration_depth" title="London penetration depth">London penetration depth</a> in the theory of <a href="/wiki/Superconductivity" title="Superconductivity">superconductivity</a>.<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><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </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=Meissner_effect&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid 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class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=6" 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"><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 class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/Meissner-effect">"Meissner effect | physics"</a>. <i>Encyclopedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Encyclopedia+Britannica&rft.atitle=Meissner+effect+%7C+physics&rft_id=https%3A%2F%2Fwww.britannica.com%2Fscience%2FMeissner-effect&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span></span> </li> <li id="cite_note-meissner1-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-meissner1_2-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeissnerOchsenfeld1933" class="citation journal cs1">Meissner, W.; Ochsenfeld, R. (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". <i><a href="/wiki/Naturwissenschaften" class="mw-redirect" title="Naturwissenschaften">Naturwissenschaften</a></i>. <b>21</b> (44): 787–788. <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/1933NW.....21..787M">1933NW.....21..787M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01504252">10.1007/BF01504252</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:37842752">37842752</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Naturwissenschaften&rft.atitle=Ein+neuer+Effekt+bei+Eintritt+der+Supraleitf%C3%A4higkeit&rft.volume=21&rft.issue=44&rft.pages=787-788&rft.date=1933&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37842752%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01504252&rft_id=info%3Abibcode%2F1933NW.....21..787M&rft.aulast=Meissner&rft.aufirst=W.&rft.au=Ochsenfeld%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauLifschitz1984" class="citation book cs1">Landau, L. D.; Lifschitz, E. M. (1984). <i>Electrodynamics of Continuous Media</i>. <a href="/wiki/Course_of_Theoretical_Physics" title="Course of Theoretical Physics">Course of Theoretical Physics</a>. Vol. 8 (2nd ed.). <a href="/wiki/Butterworth-Heinemann" title="Butterworth-Heinemann">Butterworth-Heinemann</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7506-2634-8" title="Special:BookSources/0-7506-2634-8"><bdi>0-7506-2634-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics+of+Continuous+Media&rft.series=Course+of+Theoretical+Physics&rft.edition=2nd&rft.pub=Butterworth-Heinemann&rft.date=1984&rft.isbn=0-7506-2634-8&rft.aulast=Landau&rft.aufirst=L.+D.&rft.au=Lifschitz%2C+E.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" 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"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCallaway1990" class="citation journal cs1">Callaway, D. J. E. (1990). 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N.; Schrieffer, J. R. 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E. (2012). 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W. (1966). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.145.1156">"Spontaneous symmetry breakdown without massless bosons"</a>. <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>145</b> (4): 1156–1163. <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/1966PhRv..145.1156H">1966PhRv..145.1156H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.145.1156">10.1103/PhysRev.145.1156</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Spontaneous+symmetry+breakdown+without+massless+bosons&rft.volume=145&rft.issue=4&rft.pages=1156-1163&rft.date=1966&rft_id=info%3Adoi%2F10.1103%2FPhysRev.145.1156&rft_id=info%3Abibcode%2F1966PhRv..145.1156H&rft.aulast=Higgs&rft.aufirst=P.+W.&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.145.1156&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" 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"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilczek2000" class="citation journal cs1">Wilczek, F. (2000). "The recent excitement in high-density QCD". <i><a href="/wiki/Nuclear_Physics_A" class="mw-redirect" title="Nuclear Physics A">Nuclear Physics A</a></i>. <b>663</b>: 257–271. <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-ph/9908480">hep-ph/9908480</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/2000NuPhA.663..257W">2000NuPhA.663..257W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0375-9474%2899%2900601-6">10.1016/S0375-9474(99)00601-6</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:119354272">119354272</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nuclear+Physics+A&rft.atitle=The+recent+excitement+in+high-density+QCD&rft.volume=663&rft.pages=257-271&rft.date=2000&rft_id=info%3Aarxiv%2Fhep-ph%2F9908480&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119354272%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2FS0375-9474%2899%2900601-6&rft_id=info%3Abibcode%2F2000NuPhA.663..257W&rft.aulast=Wilczek&rft.aufirst=F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeinberg1986" class="citation journal cs1">Weinberg, S. (1986). <a rel="nofollow" class="external text" href="https://doi.org/10.1143%2FPTPS.86.43">"Superconductivity for particular theorists"</a>. <i><a href="/wiki/Progress_of_Theoretical_Physics_Supplement" class="mw-redirect" title="Progress of Theoretical Physics Supplement">Progress of Theoretical Physics Supplement</a></i>. <b>86</b>: 43–53. <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/1986PThPS..86...43W">1986PThPS..86...43W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1143%2FPTPS.86.43">10.1143/PTPS.86.43</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Progress+of+Theoretical+Physics+Supplement&rft.atitle=Superconductivity+for+particular+theorists&rft.volume=86&rft.pages=43-53&rft.date=1986&rft_id=info%3Adoi%2F10.1143%2FPTPS.86.43&rft_id=info%3Abibcode%2F1986PThPS..86...43W&rft.aulast=Weinberg&rft.aufirst=S.&rft_id=https%3A%2F%2Fdoi.org%2F10.1143%252FPTPS.86.43&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" 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=Meissner_effect&action=edit&section=7" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1922" class="citation arxiv cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, A.</a> (1922). "Theoretical remark on the superconductivity of metals". <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/physics/0510251">physics/0510251</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Theoretical+remark+on+the+superconductivity+of+metals&rft.date=1922&rft_id=info%3Aarxiv%2Fphysics%2F0510251&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLondon1960" class="citation book cs1"><a href="/wiki/Fritz_Wolfgang_London" class="mw-redirect" title="Fritz Wolfgang London">London, F. W.</a> (1960). "Macroscopic Theory of Superconductivity". <i>Superfluids</i>. Structure of matter series. Vol. 1 (Revised 2nd ed.). <a href="/wiki/Dover" title="Dover">Dover</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60044-4" title="Special:BookSources/978-0-486-60044-4"><bdi>978-0-486-60044-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Macroscopic+Theory+of+Superconductivity&rft.btitle=Superfluids&rft.series=Structure+of+matter+series&rft.edition=Revised+2nd&rft.pub=Dover&rft.date=1960&rft.isbn=978-0-486-60044-4&rft.aulast=London&rft.aufirst=F.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span> By the man who explained the Meissner effect. pp. 34–37 gives a technical discussion of the Meissner effect for a superconducting sphere.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSaslow2002" class="citation book cs1">Saslow, W. M. (2002). <i>Electricity, Magnetism, and Light</i>. Academic. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-619455-5" title="Special:BookSources/978-0-12-619455-5"><bdi>978-0-12-619455-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity%2C+Magnetism%2C+and+Light&rft.pub=Academic&rft.date=2002&rft.isbn=978-0-12-619455-5&rft.aulast=Saslow&rft.aufirst=W.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span> pp. 486–489 gives a simple mathematical discussion of the surface currents responsible for the Meissner effect, in the case of a long magnet levitated above a superconducting plane.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTinkham2004" class="citation book cs1">Tinkham, M. (2004). <i>Introduction to Superconductivity</i>. Dover Books on Physics (2nd ed.). Dover. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-43503-9" title="Special:BookSources/978-0-486-43503-9"><bdi>978-0-486-43503-9</bdi></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+Superconductivity&rft.series=Dover+Books+on+Physics&rft.edition=2nd&rft.pub=Dover&rft.date=2004&rft.isbn=978-0-486-43503-9&rft.aulast=Tinkham&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMeissner+effect" class="Z3988"></span> A good technical reference.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meissner_effect&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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class="external text" href="https://web.archive.org/web/20160125175255/http://alfredleitner.com/superconductors.html">Introduction to superconductivity</a> Video about Type 1 Superconductors: <i>R</i> = 0/Transition temperatures/<b>B</b> is a state variable/Meissner effect/Energy gap (Giaever)/BCS model.</li> <li><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/solids/meis.html">Meissner Effect (Hyperphysics)</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140828152921/http://web.ornl.gov/info/reports/m/ornlm3063r1/pt2.html">Historical Background of the Meissner Effect</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 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aria-labelledby="Superconductivity" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><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:Superconductivity" title="Template:Superconductivity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Superconductivity" title="Template talk:Superconductivity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Superconductivity" title="Special:EditPage/Template:Superconductivity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Superconductivity" style="font-size:114%;margin:0 4em"><a href="/wiki/Superconductivity" title="Superconductivity">Superconductivity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BCS_theory" title="BCS theory">BCS</a></li> <li><a href="/wiki/Bean%27s_critical_state_model" title="Bean's critical state model">Bean's critical state</a></li> <li><a href="/wiki/Ginzburg%E2%80%93Landau_theory" title="Ginzburg–Landau theory">Ginzburg–Landau</a></li> <li><a href="/wiki/Kohn%E2%80%93Luttinger_superconductivity" title="Kohn–Luttinger superconductivity">Kohn–Luttinger</a></li> <li><a href="/wiki/London_equations" title="London equations">London</a></li> <li><a href="/wiki/Matthias_rules" title="Matthias rules">Matthias</a></li> <li><a href="/wiki/Mattis%E2%80%93Bardeen_theory" title="Mattis–Bardeen theory">Mattis–Bardeen</a></li> <li><a href="/wiki/Resonating_valence_bond_theory" title="Resonating valence bond theory">RVB</a></li> <li><a href="/wiki/Werthamer%E2%80%93Helfand%E2%80%93Hohenberg_theory" title="Werthamer–Helfand–Hohenberg theory">WHH</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Characteristic parameters</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Superconducting_coherence_length" title="Superconducting coherence length">coherence length</a></li> <li><a href="/wiki/Critical_field" title="Critical field">critical field</a></li> <li><a href="/wiki/London_penetration_depth" title="London penetration depth">London penetration depth</a></li> <li><a href="/wiki/Silsbee_effect" title="Silsbee effect">Silsbee current</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abrikosov_vortex" title="Abrikosov vortex">Abrikosov vortices</a></li> <li><a href="/wiki/Andreev_reflection" title="Andreev reflection">Andreev reflection</a></li> <li><a href="/wiki/Cooper_pair" title="Cooper pair">Cooper pairs</a></li> <li><a href="/wiki/Flux_pinning" title="Flux pinning">flux pinning</a></li> <li><a href="/wiki/Flux_pumping" title="Flux pumping">flux pumping</a></li> <li><a href="/wiki/Josephson_effect" title="Josephson effect">Josephson effect</a></li> <li><a href="/wiki/Little%E2%80%93Parks_effect" title="Little–Parks effect">Little–Parks effect</a></li> <li><a class="mw-selflink selflink">Meissner effect</a></li> <li><a href="/wiki/Homes%27s_law" title="Homes's law">Homes's law</a></li> <li><a href="/wiki/Persistent_current" title="Persistent current">persistent currents</a></li> <li><a href="/wiki/Proximity_effect_(superconductivity)" title="Proximity effect (superconductivity)">proximity effect</a></li> <li><a href="/wiki/Reentrant_superconductivity" title="Reentrant superconductivity">reentrance</a></li> <li><a href="/wiki/SU(2)_color_superconductivity" title="SU(2) color superconductivity">SU(2) color</a></li> <li><a href="/wiki/Supercurrent" title="Supercurrent">supercurrents</a></li> <li><a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">superdiamagnetism</a></li> <li><a href="/wiki/Superstripes" title="Superstripes">superstripes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Superconductor_classification" title="Superconductor classification">Classification</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">By magnetic response</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Types <ul><li><a href="/wiki/Type-I_superconductor" title="Type-I superconductor">I</a></li> <li><a href="/wiki/Type-II_superconductor" title="Type-II superconductor">II</a></li> <li><a href="/wiki/Type-1.5_superconductor" title="Type-1.5 superconductor">1.5</a></li></ul></li> <li><a href="/wiki/Ferromagnetic_superconductor" title="Ferromagnetic superconductor">ferromagnetic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By explanation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Conventional_superconductor" title="Conventional superconductor">conventional</a></li> <li><a href="/wiki/Unconventional_superconductor" title="Unconventional superconductor">unconventional</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By critical temperature</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>low temperature</li> <li><a href="/wiki/High-temperature_superconductivity" title="High-temperature superconductivity">high temperature</a></li> <li><a href="/wiki/Room-temperature_superconductor" title="Room-temperature superconductor">room temperature</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By composition</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Covalent_superconductor" title="Covalent superconductor">covalent</a></li> <li><a href="/wiki/Cuprate_superconductor" title="Cuprate superconductor">cuprates</a></li> <li><a href="/wiki/Heavy_fermion_superconductor" title="Heavy fermion superconductor">heavy fermion</a></li> <li><a href="/wiki/Iron-based_superconductor" title="Iron-based superconductor">iron-based</a></li> <li><a href="/wiki/Oxypnictide" title="Oxypnictide">oxypnictides</a></li> <li><a href="/wiki/Organic_superconductor" title="Organic superconductor">organic</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Technological_applications_of_superconductivity" title="Technological applications of superconductivity">Technological applications</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cryotron" title="Cryotron">cryotron</a></li> <li><a href="/wiki/Superconducting_magnet" title="Superconducting magnet">electromagnets</a></li> <li><a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">MRI</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">NMR</a></li> <li><a href="/wiki/Superconducting_quantum_computing" title="Superconducting quantum computing">quantum computing</a></li> <li><a href="/wiki/Rutherford_cable" title="Rutherford cable">Rutherford cable</a></li> <li><a href="/wiki/SQUID" title="SQUID">SQUID</a></li> <li><a href="/wiki/Superconducting_wire" title="Superconducting wire">wires</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">List of superconductors</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bilayer_graphene" title="Bilayer graphene">bilayer graphene</a></li> <li><a href="/wiki/BSCCO" class="mw-redirect" title="BSCCO">BSCCO</a></li> <li><a href="/wiki/Lanthanum_barium_copper_oxide" title="Lanthanum barium copper oxide">LBCO</a></li> <li><a href="/wiki/Magnesium_diboride" title="Magnesium diboride">MgB<sub>2</sub></a></li> <li><a href="/wiki/Niobium%E2%80%93tin" title="Niobium–tin">NbSn</a></li> <li><a href="/wiki/Niobium%E2%80%93titanium" title="Niobium–titanium">NbTi</a></li> <li><a href="/wiki/Thallium_barium_calcium_copper_oxide" title="Thallium barium calcium copper oxide">TBCCO</a></li> <li><a href="/wiki/YBCO" class="mw-redirect" title="YBCO">YBCO</a></li> <li><a href="/wiki/List_of_superconductors" title="List of superconductors">more...</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control 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