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class="vector-toc-numb">2</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Theory</span> </div> </a> <ul id="toc-Theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Properties</span> </div> </a> <button aria-controls="toc-Properties-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 Properties subsection</span> </button> <ul id="toc-Properties-sublist" class="vector-toc-list"> <li id="toc-Power_dissipation_of_eddy_currents" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Power_dissipation_of_eddy_currents"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Power dissipation of eddy currents</span> </div> </a> <ul id="toc-Power_dissipation_of_eddy_currents-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Skin_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Skin_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Skin effect</span> </div> </a> <ul id="toc-Skin_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diffusion_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diffusion_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Diffusion equation</span> </div> </a> <ul id="toc-Diffusion_equation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-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 Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Electromagnetic_braking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetic_braking"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Electromagnetic braking</span> </div> </a> <ul id="toc-Electromagnetic_braking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Repulsive_effects_and_levitation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Repulsive_effects_and_levitation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Repulsive effects and levitation</span> </div> </a> <ul id="toc-Repulsive_effects_and_levitation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Identification_of_metals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identification_of_metals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Identification of metals</span> </div> </a> <ul id="toc-Identification_of_metals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vibration_and_position_sensing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vibration_and_position_sensing"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Vibration and position sensing</span> </div> </a> <ul id="toc-Vibration_and_position_sensing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structural_testing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Structural_testing"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Structural testing</span> </div> </a> <ul id="toc-Structural_testing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Skin_effects" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Skin_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Skin effects</span> </div> </a> <ul id="toc-Skin_effects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_applications" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7</span> <span>Other applications</span> </div> </a> <ul id="toc-Other_applications-sublist" class="vector-toc-list"> </ul> </li> </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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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" > <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">Eddy current</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 50 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-50" 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">50 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%AA%D9%8A%D8%A7%D8%B1_%D8%AF%D9%88%D8%A7%D9%85%D9%8A_(%D9%83%D9%87%D8%B1%D8%B7%D9%8A%D8%B3%D9%8A%D8%A9)" title="تيار دوامي (كهرطيسية) – Arabic" lang="ar" hreflang="ar" data-title="تيار دوامي (كهرطيسية)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Corriente_de_Foucault" title="Corriente de Foucault – Asturian" lang="ast" hreflang="ast" data-title="Corriente de Foucault" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%98%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3%E0%A6%BF_%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A7%8E%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AC%E0%A6%BE%E0%A6%B9" title="ঘূর্ণি বিদ্যুৎপ্রবাহ – Bangla" lang="bn" hreflang="bn" data-title="ঘূর্ণি বিদ্যুৎপ্রবাহ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BA%D0%BE%D0%B2%D0%B5_%D0%BD%D0%B0_%D0%A4%D1%83%D0%BA%D0%BE" title="Токове на Фуко – Bulgarian" lang="bg" hreflang="bg" data-title="Токове на Фуко" 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/Corrent_de_Foucault" title="Corrent de Foucault – Catalan" lang="ca" hreflang="ca" data-title="Corrent de Foucault" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/V%C3%AD%C5%99iv%C3%BD_proud" title="Vířivý proud – Czech" lang="cs" hreflang="cs" data-title="Vířivý proud" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wirbelstrom" title="Wirbelstrom – German" lang="de" hreflang="de" data-title="Wirbelstrom" 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/P%C3%B6%C3%B6risvool" title="Pöörisvool – Estonian" lang="et" hreflang="et" data-title="Pöörisvool" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Corriente_de_Foucault" title="Corriente de Foucault – Spanish" lang="es" hreflang="es" data-title="Corriente de Foucault" 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/Kirlokurento" title="Kirlokurento – Esperanto" lang="eo" hreflang="eo" data-title="Kirlokurento" 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/Foucaulten_korronte" title="Foucaulten korronte – Basque" lang="eu" hreflang="eu" data-title="Foucaulten korronte" 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/%D8%AC%D8%B1%DB%8C%D8%A7%D9%86_%DA%AF%D8%B1%D8%AF%D8%A7%D8%A8%DB%8C" title="جریان گردابی – Persian" lang="fa" hreflang="fa" data-title="جریان گردابی" 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/Courants_de_Foucault" title="Courants de Foucault – French" lang="fr" hreflang="fr" data-title="Courants de Foucault" 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/Sruthanna_guairne%C3%A1in" title="Sruthanna guairneáin – Irish" lang="ga" hreflang="ga" data-title="Sruthanna guairneáin" 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/Corrente_de_Foucault" title="Corrente de Foucault – Galician" lang="gl" hreflang="gl" data-title="Corrente de Foucault" 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%99%80%EC%A0%84%EB%A5%98" title="와전류 – Korean" lang="ko" hreflang="ko" data-title="와전류" 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%D6%80%D6%80%D5%AF%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B0%D5%B8%D5%BD%D5%A1%D5%B6%D6%84%D5%B6%D5%A5%D6%80" title="Մրրկային հոսանքներ – Armenian" lang="hy" hreflang="hy" data-title="Մրրկային հոսանքներ" 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%AD%E0%A4%81%E0%A4%B5%E0%A4%B0_%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A4%BE" title="भँवर धारा – Hindi" lang="hi" hreflang="hi" data-title="भँवर धारा" 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/Foucaultove_struje" title="Foucaultove struje – Croatian" lang="hr" hreflang="hr" data-title="Foucaultove struje" 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/Vortica_flui" title="Vortica flui – Ido" lang="io" hreflang="io" data-title="Vortica flui" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Corrente_parassita" title="Corrente parassita – Italian" lang="it" hreflang="it" data-title="Corrente parassita" 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%96%D7%A8%D7%9E%D7%99_%D7%A4%D7%95%D7%A7%D7%95" title="זרמי פוקו – Hebrew" lang="he" hreflang="he" data-title="זרמי פוקו" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kouran-toubiyon" title="Kouran-toubiyon – Haitian Creole" lang="ht" hreflang="ht" data-title="Kouran-toubiyon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Virpu%C4%BCstr%C4%81va" title="Virpuļstrāva – Latvian" lang="lv" hreflang="lv" data-title="Virpuļstrāva" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%96rv%C3%A9ny%C3%A1ram" title="Örvényáram – Hungarian" lang="hu" hreflang="hu" data-title="Örvényáram" 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%92%D0%B8%D1%82%D0%B5%D0%BB%D0%BD%D0%B8_%D1%81%D1%82%D1%80%D1%83%D0%B8" title="Вителни струи – Macedonian" lang="mk" hreflang="mk" data-title="Вителни струи" 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%A5%D1%83%D0%B9%D0%BB%D0%B0%D1%80%D1%81%D0%B0%D0%BD_%D0%B3%D2%AF%D0%B9%D0%B4%D1%8D%D0%BB" title="Хуйларсан гүйдэл – Mongolian" lang="mn" hreflang="mn" data-title="Хуйларсан гүйдэл" 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/Wervelstroom" title="Wervelstroom – Dutch" lang="nl" hreflang="nl" data-title="Wervelstroom" 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/%E6%B8%A6%E9%9B%BB%E6%B5%81" title="渦電流 – Japanese" lang="ja" hreflang="ja" data-title="渦電流" 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/Virvelstr%C3%B8m" title="Virvelstrøm – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Virvelstrøm" 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/Virvelstraum" title="Virvelstraum – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Virvelstraum" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%90%E0%A8%A1%E0%A9%80_%E0%A8%95%E0%A8%B0%E0%A9%B0%E0%A8%9F" title="ਐਡੀ ਕਰੰਟ – Punjabi" lang="pa" hreflang="pa" data-title="ਐਡੀ ਕਰੰਟ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pr%C4%85d_wirowy" title="Prąd wirowy – Polish" lang="pl" hreflang="pl" data-title="Prąd wirowy" 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/Corrente_de_Foucault" title="Corrente de Foucault – Portuguese" lang="pt" hreflang="pt" data-title="Corrente de Foucault" 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/Curen%C8%9Bi_Foucault" title="Curenți Foucault – Romanian" lang="ro" hreflang="ro" data-title="Curenți Foucault" 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%92%D0%B8%D1%85%D1%80%D0%B5%D0%B2%D1%8B%D0%B5_%D1%82%D0%BE%D0%BA%D0%B8" title="Вихревые токи – Russian" lang="ru" hreflang="ru" data-title="Вихревые токи" 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/Eddy_current" title="Eddy current – Simple English" lang="en-simple" hreflang="en-simple" data-title="Eddy current" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/V%C3%ADriv%C3%BD_pr%C3%BAd" title="Vírivý prúd – Slovak" lang="sk" hreflang="sk" data-title="Vírivý prúd" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D1%80%D1%82%D0%BB%D0%BE%D0%B6%D0%BD%D0%B5_%D1%81%D1%82%D1%80%D1%83%D1%98%D0%B5" title="Вртложне струје – Serbian" lang="sr" hreflang="sr" data-title="Вртложне струје" 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/Vrtlo%C5%BEne_struje" title="Vrtložne 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href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B4%E0%AE%B2%E0%AF%8D_%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%A9%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="சுழல் மின்னோட்டம் – Tamil" lang="ta" hreflang="ta" data-title="சுழல் மின்னோட்டம்" 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%81%E0%B8%A3%E0%B8%B0%E0%B9%81%E0%B8%AA%E0%B8%9F%E0%B8%B9%E0%B9%82%E0%B8%81" title="กระแสฟูโก – Thai" lang="th" hreflang="th" data-title="กระแสฟูโก" 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/Eddy_ak%C4%B1m%C4%B1" title="Eddy akımı – Turkish" lang="tr" hreflang="tr" data-title="Eddy akımı" data-language-autonym="Türkçe" 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searchaux" style="display:none">Loops of electric current induced within conductors by a changing magnetic field</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">For the comic-book series, see <a href="/wiki/Eddy_Current_(comics)" title="Eddy Current (comics)">Eddy Current (comics)</a>. For the Australian rock band, see <a href="/wiki/Eddy_Current_Suppression_Ring" title="Eddy Current Suppression Ring">Eddy Current Suppression Ring</a>.</div> <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 ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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.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 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 href="/wiki/Magnetism" title="Magnetism">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"><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 class="mw-selflink selflink">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>In <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>, an <b>eddy current</b> (also called <b>Foucault's current</b>) is a loop of <a href="/wiki/Electric_current" title="Electric current">electric current</a> induced within <a href="/wiki/Conductor_(material)" class="mw-redirect" title="Conductor (material)">conductors</a> by a changing <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> in the conductor according to <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a> or by the relative motion of a conductor in a magnetic field. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be <a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">induced</a> within nearby stationary conductors by a time-varying magnetic field created by an AC <a href="/wiki/Electromagnet" title="Electromagnet">electromagnet</a> or <a href="/wiki/Transformer" title="Transformer">transformer</a>, for example, or by relative motion between a <a href="/wiki/Magnet" title="Magnet">magnet</a> and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of <a href="/wiki/Flux" title="Flux">flux</a>, and inversely proportional to the <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a> of the material. When graphed, these circular currents within a piece of metal look vaguely like <a href="/wiki/Eddy_(fluid_dynamics)" title="Eddy (fluid dynamics)">eddies</a> or whirlpools in a liquid. </p><p>By <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, an eddy current creates a magnetic field that opposes the change in the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field. For example, a nearby conductive surface will exert a drag force on a moving magnet that opposes its motion, due to eddy currents induced in the surface by the moving magnetic field. This effect is employed in <a href="/wiki/Eddy_current_brake" title="Eddy current brake">eddy current brakes</a> which are used to stop rotating power tools quickly when they are turned off. The current flowing through the resistance of the conductor also dissipates energy as <a href="/wiki/Heat" title="Heat">heat</a> in the material. Thus eddy currents are a cause of energy loss in alternating current (AC) <a href="/wiki/Inductor" title="Inductor">inductors</a>, <a href="/wiki/Transformer" title="Transformer">transformers</a>, <a href="/wiki/Electric_motor" title="Electric motor">electric motors</a> and <a href="/wiki/Electric_generator" title="Electric generator">generators</a>, and other AC machinery, requiring special construction such as <a href="/wiki/Laminated_core" class="mw-redirect" title="Laminated core">laminated magnetic cores</a> or <a href="/wiki/Ferrite_core" title="Ferrite core">ferrite cores</a> to minimize them. Eddy currents are also used to heat objects in <a href="/wiki/Induction_heating" title="Induction heating">induction heating</a> furnaces and equipment, and to detect cracks and flaws in metal parts using <a href="/wiki/Eddy-current_testing" title="Eddy-current testing">eddy-current testing</a> instruments. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origin_of_term">Origin of term</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=1" title="Edit section: Origin of term"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <i>eddy current</i> comes from analogous currents seen in <a href="/wiki/Water" title="Water">water</a> in <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, causing localised areas of turbulence known as <i><a href="/wiki/Eddy_(fluid_dynamics)" title="Eddy (fluid dynamics)">eddies</a></i> giving rise to persistent vortices. Somewhat analogously, eddy currents can take time to build up and can persist for very long times in conductors due to their inductance. </p> <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=Eddy_current&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first person to observe eddy currents was <a href="/wiki/Fran%C3%A7ois_Arago" title="François Arago">François Arago</a> (1786–1853), the President of the Council of Ministers of the 2nd French Republic during the brief period 10th May to June 24, 1848 (equivalent to the current position of the French Prime Minister), who was also a mathematician, physicist and astronomer. In 1824 he observed what has been called rotatory magnetism, and that most conductive bodies could be magnetized; these discoveries were completed and explained by <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> (1791–1867). </p><p>In 1834, <a href="/wiki/Emil_Lenz" title="Emil Lenz">Emil Lenz</a> stated <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the change of magnetic flux that caused the current flow. Eddy currents produce a secondary field that cancels a part of the external field and causes some of the external flux to avoid the conductor. </p><p>French physicist <a href="/wiki/L%C3%A9on_Foucault" title="Léon Foucault">Léon Foucault</a> (1819–1868) is credited with having discovered eddy currents. In September 1855, he discovered that the force required for the rotation of a copper disc becomes greater when it is made to rotate with its rim between the poles of a magnet, the disc at the same time becoming heated by the eddy current induced in the metal. The first use of eddy current for non-destructive testing occurred in 1879 when <a href="/wiki/David_E._Hughes" class="mw-redirect" title="David E. Hughes">David E. Hughes</a> used the principles to conduct metallurgical sorting tests. </p> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=3" title="Edit section: Theory"><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:Eddy_currents_due_to_magnet.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Eddy_currents_due_to_magnet.svg/330px-Eddy_currents_due_to_magnet.svg.png" decoding="async" width="330" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Eddy_currents_due_to_magnet.svg/495px-Eddy_currents_due_to_magnet.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Eddy_currents_due_to_magnet.svg/660px-Eddy_currents_due_to_magnet.svg.png 2x" data-file-width="1742" data-file-height="973" /></a><figcaption>Eddy currents <i>(<span style="color:red;"><span class="texhtml mvar" style="font-style:italic;">I</span>, red</span>)</i> induced in a conductive metal plate <i>(C)</i> as it moves to the right under a magnet <i>(N)</i>. The magnetic field <i>(<span style="color:green;"><span class="texhtml"><b>B</b></span>, green</span>)</i> is directed down through the plate. The Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag force on the sheet. The <span style="color:blue;">blue arrows</span> are counter magnetic fields generated by the circular motion of the charges.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Eddy_currents_-_explanation_of_drag_force.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Eddy_currents_-_explanation_of_drag_force.svg/330px-Eddy_currents_-_explanation_of_drag_force.svg.png" decoding="async" width="330" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Eddy_currents_-_explanation_of_drag_force.svg/495px-Eddy_currents_-_explanation_of_drag_force.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Eddy_currents_-_explanation_of_drag_force.svg/660px-Eddy_currents_-_explanation_of_drag_force.svg.png 2x" data-file-width="1752" data-file-height="967" /></a><figcaption>Forces on an electron in the metal sheet under the magnet, explaining where the drag force on the sheet comes from. The red dot <span class="texhtml"><b>e</b><sub>1</sub></span> shows a conduction electron in the sheet right after it has undergone a collision with an atom, and <span class="texhtml"><b>e</b><sub>2</sub></span> shows the same electron after it has been accelerated by the magnetic field. On average at <span class="texhtml"><b>e</b><sub>1</sub></span> the electron has the same velocity as the sheet (<span class="texhtml"><b>v</b></span>, <i>black arrow</i>) in the <span class="texhtml">+<b>x</b></span> direction. The magnetic field (<span class="texhtml"><b>B</b></span>, <i>green arrow</i>) of the magnet's North pole N is directed down in the <span class="texhtml">−<b>y</b></span> direction. The magnetic field exerts a <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> on the electron <i>(pink arrow)</i> of <span class="texhtml"><b>F</b><sub>1</sub> = −<i>e</i>(<b>v</b> × <b>B</b>)</span>, where <span class="texhtml"><i>e</i></span> is the <a href="/wiki/Elementary_charge" title="Elementary charge">electron's charge</a>. Since the electron has a negative charge, from the <a href="/wiki/Right_hand_rule" class="mw-redirect" title="Right hand rule">right hand rule</a> this is directed in the <span class="texhtml">+<b>z</b></span> direction. At <span class="texhtml"><b>e</b><sub>2</sub></span> this force gives the electron a component of velocity in the sideways direction (<span class="texhtml"><b>v</b><sub>2</sub></span>, <i>black arrow</i>) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of <span class="texhtml"><b>F</b><sub>2</sub> = −<i>e</i>(<b>v</b><sub>2</sub> × <b>B</b>)</span>. From the right hand rule, this is directed in the <span class="texhtml">−<b>x</b></span> direction, opposite to the velocity <span class="texhtml"><b>v</b></span> of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet. </figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Eddy_current_brake_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Eddy_current_brake_diagram.svg/330px-Eddy_current_brake_diagram.svg.png" decoding="async" width="330" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Eddy_current_brake_diagram.svg/495px-Eddy_current_brake_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Eddy_current_brake_diagram.svg/660px-Eddy_current_brake_diagram.svg.png 2x" data-file-width="1691" data-file-height="1140" /></a><figcaption>Eddy current brake. The North magnetic pole piece <i>(top)</i> in this drawing is shown further away from the disk than the South; this is just to leave room to show the currents. In an actual eddy current brake the pole pieces are positioned as close to the disk as possible.</figcaption></figure> <p>A magnet induces circular <a href="/wiki/Electric_current" title="Electric current">electric currents</a> in a metal sheet moving through its magnetic field. The diagram alongside shows a metal sheet <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 C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> moving to the right with velocity <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 {\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span> under a stationary magnet. The magnetic field <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 {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83ae7d80cab55b606de217162280b2279142bbb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}}"></span> (in green arrows) from the magnet's north pole <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> passes down through the metal sheet. </p><p>Since the metal is moving, the <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> through a given area of the sheet is changing. In particular, the part of the sheet moving into place under the edge of the magnet (here, the left side) experiences an increase in magnetic flux density <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 {\frac {dB}{dt}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>B</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dB}{dt}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d04a8f8ee0448160ae2cd2d5884ca7eaf1b429e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.077ex; height:5.509ex;" alt="{\displaystyle {\frac {dB}{dt}}>0}"></span>. This change in magnetic flux, in turn, induces an emf in the sheet, in accordance with Faraday's law of induction. The potential difference between regions on the sheet closer to and further away from the magnet induces an anti-clockwise flow of electric current <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> in the sheet. This is an eddy current. Similarly, the part of the sheet moving away from the edge of the magnet (here, the right side) experiences a decrease in magnetic flux density <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 {\frac {dB}{dt}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>B</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dB}{dt}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a0b51b0067bcf6977ccf215799159dd02f0dbe6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.077ex; height:5.509ex;" alt="{\displaystyle {\frac {dB}{dt}}<0}"></span>, inducing a second eddy current, this time in a clockwise direction. </p><p>An equivalent way to understand the origin of eddy currents is to see that the free <a href="/wiki/Charge_carrier" title="Charge carrier">charge carriers</a> (<a href="/wiki/Electron" title="Electron">electrons</a>) in the metal sheet are moving with the sheet to the right, so the magnetic field <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 {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83ae7d80cab55b606de217162280b2279142bbb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}}"></span> exerts a sideways <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> on them given by <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 {\vec {F}}=q{\vec {v}}\times {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=q{\vec {v}}\times {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb2105b357c6cb3a7960308901ac9b2cb0e3958b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.719ex; height:3.176ex;" alt="{\displaystyle {\vec {F}}=q{\vec {v}}\times {\vec {B}}}"></span>. Since the charge here is negative, the force acts outwards with respect to the plane of the diagram. The resulting flow of electrons causes a current <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> to flow in the opposite direction. This is an eddy current. </p><p>The electrons collide with the metal lattice atoms, exerting a drag force on the sheet proportional to its velocity. The <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> used to overcome this drag is dissipated as heat by the currents flowing through the metal, so the metal gets warm under the magnet. As described by <a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère's circuital law</a>, each of the circular currents in the sheet induces its own magnetic field (marked in blue arrows in the diagram). </p><p>Another way to understand the drag is to observe that in accordance with <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, the induced emf must oppose the change in magnetic flux through the sheet. At the leading edge of the magnet (left side), the anti-clockwise current creates a magnetic field pointing up (as can be shown using the right hand rule), opposing the magnet's field. This causes a repulsive force to develop between the sheet and the leading edge of the magnet. In contrast, at the trailing edge (right side), the clockwise current causes a magnetic field pointed down, in the same direction as the magnet's field, resulting in an attractive force between the sheet and the trailing edge of the magnet. In both cases, the resulting force is not in the direction of motion of the sheet. </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=4" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eddy currents in conductors of non-zero <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a> generate heat as well as electromagnetic forces. The heat can be used for <a href="/wiki/Induction_heating" title="Induction heating">induction heating</a>. The electromagnetic forces can be used for levitation, creating movement, or to give a strong <a href="/wiki/Eddy_current_brake" title="Eddy current brake">braking</a> effect. Eddy currents can also have undesirable effects, for instance power loss in <a href="/wiki/Transformer" title="Transformer">transformers</a>. In this application, they are minimized with thin plates, by <a href="/wiki/Electrical_steel#Lamination_coatings" title="Electrical steel">lamination</a> of conductors or other details of conductor shape. </p><p>Self-induced eddy currents are responsible for the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> in conductors.<sup id="cite_ref-VagnerLembrikov2003_1-0" class="reference"><a href="#cite_note-VagnerLembrikov2003-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks.<sup id="cite_ref-Boyes2009_2-0" class="reference"><a href="#cite_note-Boyes2009-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A similar effect is the <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>, which is caused by externally induced eddy currents.<sup id="cite_ref-JohnsonJohnson2003_3-0" class="reference"><a href="#cite_note-JohnsonJohnson2003-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where the currents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within the object and these charges then produce static electric potentials that oppose any further current. Currents may be initially associated with the creation of static potentials, but these may be transitory and small. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Laminated_core_eddy_currents_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Laminated_core_eddy_currents_2.svg/310px-Laminated_core_eddy_currents_2.svg.png" decoding="async" width="310" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Laminated_core_eddy_currents_2.svg/465px-Laminated_core_eddy_currents_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Laminated_core_eddy_currents_2.svg/620px-Laminated_core_eddy_currents_2.svg.png 2x" data-file-width="1132" data-file-height="539" /></a><figcaption><i>(left)</i> Eddy currents <i>(<span style="color:red;"><span class="texhtml mvar" style="font-style:italic;">I</span>, red</span>)</i> within a solid iron transformer core. <i>(right)</i> Making the core out of thin <a href="/wiki/Laminations" class="mw-redirect" title="Laminations">laminations</a> parallel to the field <i>(<span style="color:green;"><span class="texhtml"><b>B</b></span>, green</span>)</i> with insulation <i>(C)</i> between them reduces the eddy currents. Although the field and currents are shown in one direction, they actually reverse direction with the alternating current in the transformer winding.</figcaption></figure> <p>Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This <a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a> reduces efficiency of iron-core <a href="/wiki/Transformer" title="Transformer">transformers</a> and <a href="/wiki/Electric_motors" class="mw-redirect" title="Electric motors">electric motors</a> and other devices that use changing magnetic fields. Eddy currents are minimized in these devices by selecting <a href="/wiki/Magnetic_core" title="Magnetic core">magnetic core</a> materials that have low electrical conductivity (e.g., <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrites</a> or iron powder mixed with <a href="/wiki/Resin" title="Resin">resin</a>) or by using thin sheets of magnetic material, known as <a href="/wiki/Laminations" class="mw-redirect" title="Laminations">laminations</a>. Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs. Charges gather at the lamination boundaries, in a process analogous to the <a href="/wiki/Hall_effect" title="Hall effect">Hall effect</a>, producing electric fields that oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents. </p><p>The conversion of input energy to heat is not always undesirable, however, as there are some practical applications. One is in the brakes of some trains known as <a href="/wiki/Eddy_current_brake" title="Eddy current brake">eddy current brakes</a>. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. This eddy current is formed by the movement of the wheels. So, by <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, the magnetic field formed by the eddy current will oppose its cause. Thus the wheel will face a force opposing the initial movement of the wheel. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion. </p><p><a href="/wiki/Induction_heating" title="Induction heating">Induction heating</a> makes use of eddy currents to provide heating of metal objects. </p> <div class="mw-heading mw-heading3"><h3 id="Power_dissipation_of_eddy_currents">Power dissipation of eddy currents</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=5" title="Edit section: Power dissipation of eddy currents"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Under certain assumptions (uniform material, uniform magnetic field, no <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a>, etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:<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> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {\pi ^{2}{B_{\text{p}}}^{2}d^{2}f^{2}}{6k\rho D}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>6</mn> <mi>k</mi> <mi>ρ</mi> <mi>D</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {\pi ^{2}{B_{\text{p}}}^{2}d^{2}f^{2}}{6k\rho D}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efad2f3eb005476a79c682c6988e6c98499fc749" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.327ex; height:6.509ex;" alt="{\displaystyle P={\frac {\pi ^{2}{B_{\text{p}}}^{2}d^{2}f^{2}}{6k\rho D}},}"></span> where </p> <ul><li><span class="texhtml"><i>P</i></span> is the power lost per unit mass (W/kg),</li> <li><span class="texhtml"><i>B</i><sub>p</sub></span> is the peak magnetic field (T),</li> <li><span class="texhtml"><i>d</i></span> is the thickness of the sheet or diameter of the wire (m),</li> <li><span class="texhtml"><i>f</i></span> is the frequency (Hz),</li> <li><span class="texhtml"><i>k</i></span> is a constant equal to 1 for a thin sheet and 2 for a thin wire,</li> <li><span class="texhtml"><i>ρ</i></span> is the <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a> of the material (Ω m), and</li> <li><span class="texhtml"><i>D</i></span> is the <a href="/wiki/Density" title="Density">density</a> of the material (kg/m<sup>3</sup>).</li></ul> <p>This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a>; that is, the electromagnetic wave fully penetrates the material. </p> <div class="mw-heading mw-heading3"><h3 id="Skin_effect">Skin effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=6" title="Edit section: Skin effect"><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/Skin_effect" title="Skin effect">Skin effect</a></div> <p>In very fast-changing fields, the magnetic field does not penetrate completely into the interior of the material. This <i>skin effect</i> renders the above equation invalid. However, in any case increased frequency of the same value of field will always increase eddy currents, even with non-uniform field penetration.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2012)">citation needed</span></a></i>]</sup> </p><p>The penetration depth for a good conductor can be calculated from the following equation:<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> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta ={\frac {1}{\sqrt {\pi f\mu \sigma }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mi>π</mi> <mi>f</mi> <mi>μ</mi> <mi>σ</mi> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta ={\frac {1}{\sqrt {\pi f\mu \sigma }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8eebaf7a24a322efcfc2428a4dbc01b35d61434c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.296ex; height:6.509ex;" alt="{\displaystyle \delta ={\frac {1}{\sqrt {\pi f\mu \sigma }}},}"></span> where <span class="texhtml"><i>δ</i></span> is the penetration depth (m), <span class="texhtml"><i>f</i></span> is the frequency (Hz), <span class="texhtml"><i>μ</i></span> is the <a href="/wiki/Magnetic_permeability" class="mw-redirect" title="Magnetic permeability">magnetic permeability</a> of the material (H/m), and <span class="texhtml"><i>σ</i></span> is the <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a> of the material (S/m). </p> <div class="mw-heading mw-heading3"><h3 id="Diffusion_equation">Diffusion equation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=7" title="Edit section: Diffusion equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of <a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère's Law</a>,<sup id="cite_ref-bertotti_6-0" class="reference"><a href="#cite_note-bertotti-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> providing an expression for the <a href="/wiki/Magnetizing_field" class="mw-redirect" title="Magnetizing field">magnetizing field</a> <span class="texhtml"><b>H</b></span> surrounding a current density <span class="texhtml"><b>J</b></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dd89f6c064b8f0673c15f0ae913d8da228351b6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.994ex; height:2.176ex;" alt="{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} .}"></span> </p><p>Taking the <a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">curl</a> on both sides of this equation and then using a common vector calculus identity for the <a href="/wiki/Vector_calculus_identities#Curl_of_the_curl" title="Vector calculus identities">curl of the curl</a> results in <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \left(\nabla \cdot \mathbf {H} \right)-\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <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> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \left(\nabla \cdot \mathbf {H} \right)-\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5767ed602e0c364d850f499ba5f7a807ded7e18a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.663ex; height:3.176ex;" alt="{\displaystyle \nabla \left(\nabla \cdot \mathbf {H} \right)-\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}"></span> </p><p>From <a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss's law for magnetism</a>, <span class="texhtml">∇ ⋅ <b>H</b> = 0</span>, so <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <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> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34e688dcf9c6903cbb5169025a562de017061dda" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.792ex; height:2.843ex;" alt="{\displaystyle -\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}"></span> </p><p>Using <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>, <span class="texhtml"><b>J</b> = <i>σ</i><b>E</b></span>, which relates current density <span class="texhtml"><b>J</b></span> to electric field <span class="texhtml"><b>E</b></span> in terms of a material's conductivity <span class="texhtml"><i>σ</i></span>, and assuming isotropic homogeneous conductivity, the equation can be written as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\nabla ^{2}\mathbf {H} =\sigma \nabla \times \mathbf {E} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <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> <mi>σ</mi> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\nabla ^{2}\mathbf {H} =\sigma \nabla \times \mathbf {E} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22b66b7c05ef37aa1231133004094da271eb3637" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.498ex; height:2.843ex;" alt="{\displaystyle -\nabla ^{2}\mathbf {H} =\sigma \nabla \times \mathbf {E} .}"></span> </p><p>Using the differential form of <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law</a>, <span class="texhtml">∇ × <b>E</b> = −<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.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="sfrac">⁠<span class="tion"><span class="num">∂<b>B</b></span><span class="sr-only">/</span><span class="den">∂<i>t</i></span></span>⁠</span></span>, this gives <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla ^{2}\mathbf {H} =\sigma {\frac {\partial \mathbf {B} }{\partial t}}.}"> <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> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla ^{2}\mathbf {H} =\sigma {\frac {\partial \mathbf {B} }{\partial t}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d284c9793ed69cbd6f4ac65328f6083b157d37d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.212ex; height:5.509ex;" alt="{\displaystyle \nabla ^{2}\mathbf {H} =\sigma {\frac {\partial \mathbf {B} }{\partial t}}.}"></span> </p><p>By definition, <span class="texhtml"><b>B</b> = <i>μ</i><sub>0</sub>(<b>H</b> + <b>M</b>)</span>, where <span class="texhtml"><b>M</b></span> is the <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> of the material and <span class="texhtml"><i>μ</i><sub>0</sub></span> is the <a href="/wiki/Vacuum_permeability" title="Vacuum permeability">vacuum permeability</a>. The diffusion equation therefore is <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla ^{2}\mathbf {H} =\mu _{0}\sigma \left({\frac {\partial \mathbf {M} }{\partial t}}+{\frac {\partial \mathbf {H} }{\partial t}}\right).}"> <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> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>σ</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla ^{2}\mathbf {H} =\mu _{0}\sigma \left({\frac {\partial \mathbf {M} }{\partial t}}+{\frac {\partial \mathbf {H} }{\partial t}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bda399c6aa3530c519411deedf84badd0a031d3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.586ex; height:6.176ex;" alt="{\displaystyle \nabla ^{2}\mathbf {H} =\mu _{0}\sigma \left({\frac {\partial \mathbf {M} }{\partial t}}+{\frac {\partial \mathbf {H} }{\partial t}}\right).}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=8" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Electromagnetic_braking">Electromagnetic braking</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=9" title="Edit section: Electromagnetic braking"><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/Eddy_current_brake" title="Eddy current brake">Eddy current brake</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/280px--20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="280" height="158" data-durationhint="51" data-mwtitle="20._Валтенхофеново_правило.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.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/5/5f/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv/20._%D0%92%D0%B0%D0%BB%D1%82%D0%B5%D0%BD%D1%85%D0%BE%D1%84%D0%B5%D0%BD%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Demonstration of Waltenhofen's pendulum, precursor of eddy current brakes. The formation and suppression of eddy currents is here demonstrated by means of this pendulum, a metal plate oscillating between the pole pieces of a strong electromagnet. As soon as a sufficiently strong magnetic field has been switched on, the pendulum is stopped on entering the field.</figcaption></figure> <p><a href="/wiki/Eddy_current_brake" title="Eddy current brake">Eddy current brakes</a> use the drag force created by eddy currents as a <a href="/wiki/Brake_(technology)" class="mw-redirect" title="Brake (technology)">brake</a> to slow or stop moving objects. Since there is no contact with a brake shoe or drum, there is no mechanical wear. However, an eddy current brake cannot provide a "holding" torque and so may be used in combination with mechanical brakes, for example, on overhead cranes. Another application is on some roller coasters, where heavy <a href="/wiki/Copper" title="Copper">copper</a> plates extending from the car are moved between pairs of very strong permanent magnets. <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">Electrical resistance</a> within the plates causes a dragging effect analogous to friction, which dissipates the kinetic energy of the car. The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws. Using electromagnets, as opposed to permanent magnets, the strength of the magnetic field can be adjusted and so the magnitude of braking effect changed. </p> <div class="mw-heading mw-heading3"><h3 id="Repulsive_effects_and_levitation">Repulsive effects and levitation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=10" title="Edit section: Repulsive effects and levitation"><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/Electrodynamic_suspension" title="Electrodynamic suspension">electrodynamic suspension</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Linear_motor_field.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Linear_motor_field.gif/220px-Linear_motor_field.gif" decoding="async" width="220" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Linear_motor_field.gif/330px-Linear_motor_field.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Linear_motor_field.gif/440px-Linear_motor_field.gif 2x" data-file-width="914" data-file-height="643" /></a><figcaption>A cross section through a linear motor placed above a thick aluminium slab. As the <a href="/wiki/Linear_induction_motor" title="Linear induction motor">linear induction motor</a>'s field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.</figcaption></figure> <p>In a varying magnetic field, the induced currents exhibit diamagnetic-like repulsion effects. A conductive object will experience a repulsion force. This can lift objects against gravity, though with continual power input to replace the energy dissipated by the eddy currents. An example application is separation of <a href="/wiki/Aluminum_can" title="Aluminum can">aluminum cans</a> from other metals in an <a href="/wiki/Eddy_current_separator" title="Eddy current separator">eddy current separator</a>. Ferrous metals cling to the magnet, and aluminum (and other non-ferrous conductors) are forced away from the magnet; this can separate a waste stream into ferrous and non-ferrous scrap metal. </p><p>With a very strong handheld magnet, such as those made from <a href="/wiki/Neodymium" title="Neodymium">neodymium</a>, one can easily observe a very similar effect by rapidly sweeping the magnet over a coin with only a small separation. Depending on the strength of the magnet, identity of the coin, and separation between the magnet and coin, one may induce the coin to be pushed slightly ahead of the magnet – even if the coin contains no magnetic elements, such as the US <a href="/wiki/Penny_(United_States_coin)" title="Penny (United States coin)">penny</a>. Another example involves dropping a strong magnet down a tube of copper<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> – the magnet falls at a dramatically slow pace. </p><p>In a perfect conductor with no <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>, surface eddy currents exactly cancel the field inside the conductor, so no magnetic field penetrates the conductor. Since no energy is lost in resistance, eddy currents created when a magnet is brought near the conductor persist even after the magnet is stationary, and can exactly balance the force of gravity, allowing <a href="/wiki/Magnetic_levitation" title="Magnetic levitation">magnetic levitation</a>. Superconductors also exhibit a separate inherently <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> phenomenon called the <a href="/wiki/Meissner_effect" title="Meissner effect">Meissner effect</a> in which any magnetic field lines present in the material when it becomes superconducting are expelled, thus the magnetic field in a superconductor is always zero. </p><p>Using <a href="/wiki/Electromagnet" title="Electromagnet">electromagnets</a> with electronic switching comparable to <a href="/wiki/Electronic_speed_control" title="Electronic speed control">electronic speed control</a> it is possible to generate electromagnetic fields moving in an arbitrary direction. As described in the section above about eddy current brakes, a non-ferromagnetic conductor surface tends to rest within this moving field. When however this field is moving, a vehicle can be levitated and propelled. This is comparable to a <a href="/wiki/Maglev" title="Maglev">maglev</a> but is not bound to a rail.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Identification_of_metals">Identification of metals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=11" title="Edit section: Identification of metals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In some coin-operated <a href="/wiki/Vending_machine" title="Vending machine">vending machines</a>, eddy currents are used to detect counterfeit coins, or <a href="/wiki/Slug_(coin)" title="Slug (coin)">slugs</a>. The coin rolls past a stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the retardation, depends on the conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and this is used to send them into the rejection slot. </p> <div class="mw-heading mw-heading3"><h3 id="Vibration_and_position_sensing">Vibration and position sensing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=12" title="Edit section: Vibration and position sensing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eddy currents are used in certain types of <a href="/wiki/Proximity_sensors" class="mw-redirect" title="Proximity sensors">proximity sensors</a> to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at <a href="/wiki/General_Electric" title="General Electric">General Electric</a> using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by <a href="/wiki/Donald_E._Bently" title="Donald E. Bently">Donald E. Bently</a> at <a href="/wiki/Bently_Nevada" title="Bently Nevada">Bently Nevada</a> Corporation. These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern <a href="/wiki/Turbomachinery" title="Turbomachinery">turbomachinery</a>. A typical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="millimeter or milli-inch? (June 2022)">clarification needed</span></a></i>]</sup> Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application. Examples of such standards are <a href="/wiki/American_Petroleum_Institute" title="American Petroleum Institute">American Petroleum Institute</a> (API) Standard 670 and <a href="/wiki/International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a> 7919. </p><p>A Ferraris acceleration sensor, also called a <a href="/w/index.php?title=Ferraris_sensor&action=edit&redlink=1" class="new" title="Ferraris sensor (page does not exist)">Ferraris sensor</a>, is a contactless sensor that uses eddy currents to measure relative acceleration.<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><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><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> <div class="mw-heading mw-heading3"><h3 id="Structural_testing">Structural testing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=13" title="Edit section: Structural testing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eddy current techniques are commonly used for the <a href="/wiki/Nondestructive_testing" title="Nondestructive testing">nondestructive examination</a> (NDE) and condition monitoring of a large variety of metallic structures, including <a href="/wiki/Heat_exchanger" title="Heat exchanger">heat exchanger</a> tubes, aircraft fuselage, and aircraft structural components. </p> <div class="mw-heading mw-heading3"><h3 id="Skin_effects">Skin effects</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=14" title="Edit section: Skin effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eddy currents are the root cause of the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> in conductors carrying <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a>. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:EI-transformer_core_interleaved.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/EI-transformer_core_interleaved.svg/220px-EI-transformer_core_interleaved.svg.png" decoding="async" width="220" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/EI-transformer_core_interleaved.svg/330px-EI-transformer_core_interleaved.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/EI-transformer_core_interleaved.svg/440px-EI-transformer_core_interleaved.svg.png 2x" data-file-width="500" data-file-height="563" /></a><figcaption>Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents</figcaption></figure> <p>Similarly, in magnetic materials of finite conductivity, eddy currents cause the confinement of the majority of the magnetic fields to only a couple <a href="/wiki/Skin_depth" class="mw-redirect" title="Skin depth">skin depths</a> of the surface of the material. This effect limits the <a href="/wiki/Flux_linkage" title="Flux linkage">flux linkage</a> in <a href="/wiki/Inductor" title="Inductor">inductors</a> and <a href="/wiki/Transformer" title="Transformer">transformers</a> having <a href="/wiki/Magnetic_core" title="Magnetic core">magnetic cores</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:EI-transformer_core_interleaved_with_flux_paths.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/220px-EI-transformer_core_interleaved_with_flux_paths.png" decoding="async" width="220" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/330px-EI-transformer_core_interleaved_with_flux_paths.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/440px-EI-transformer_core_interleaved_with_flux_paths.png 2x" data-file-width="8656" data-file-height="3200" /></a><figcaption>E-I transformer laminations showing flux paths. The effect of the gap where the laminations are butted together can be mitigated by alternating pairs of E laminations with pairs of I laminations, providing a path for the magnetic flux around the gap.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Other_applications">Other applications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Eddy_current&action=edit&section=15" title="Edit section: Other applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Rock climbing auto belays<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>Zip line brakes<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li> <li>Free fall devices<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Metal_detector" title="Metal detector">Metal detectors</a></li> <li>Conductivity meters for non-magnetic metals<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><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></li> <li><a href="/wiki/Adjustable-speed_drive#Eddy_current_drives" class="mw-redirect" title="Adjustable-speed drive">Eddy current adjustable-speed drives</a></li> <li><a href="/wiki/Eddy-current_testing" title="Eddy-current testing">Eddy-current testing</a></li> <li><a href="/wiki/Eddy_current_brake" title="Eddy current brake">Eddy current brake</a></li> <li><a href="/wiki/Electricity_meter" title="Electricity meter">Electricity meters</a> (electromechanical induction meters)</li> <li><a href="/wiki/Induction_heating" title="Induction heating">Induction heating</a></li> <li>Cooking (<a href="/wiki/Induction_cooking" title="Induction cooking">induction cooking</a>)</li> <li><a href="/wiki/Proximity_sensor" title="Proximity sensor">Proximity sensor</a> (displacement sensors)</li> <li><a href="/wiki/Vending_machine" title="Vending machine">Vending machines</a> (detection of coins)</li> <li>Coating thickness measurements<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></li> <li>Sheet resistance measurement<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Eddy_current_separator" title="Eddy current separator">Eddy current separator</a> for metal separation<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></li> <li>Mechanical <a href="/wiki/Speedometer" title="Speedometer">speedometers</a></li> <li>Safety hazard and defect detection applications</li> <li><a href="/wiki/Magnetic_damping" title="Magnetic damping">Magnetic damping</a></li></ul> <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=Eddy_current&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Online citations</dt></dl> <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-VagnerLembrikov2003-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-VagnerLembrikov2003_1-0">^</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="CITEREFIsrael_D._VagnerB.I._LembrikovPeter_Rudolf_Wyder2003" class="citation book cs1">Israel D. Vagner; B.I. Lembrikov; Peter Rudolf Wyder (17 November 2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E8caSplsF28C&pg=PA73"><i>Electrodynamics of Magnetoactive Media</i></a>. Springer Science & Business Media. pp. 73–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-43694-2" title="Special:BookSources/978-3-540-43694-2"><bdi>978-3-540-43694-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics+of+Magnetoactive+Media&rft.pages=73-&rft.pub=Springer+Science+%26+Business+Media&rft.date=2003-11-17&rft.isbn=978-3-540-43694-2&rft.au=Israel+D.+Vagner&rft.au=B.I.+Lembrikov&rft.au=Peter+Rudolf+Wyder&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE8caSplsF28C%26pg%3DPA73&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-Boyes2009-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Boyes2009_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalt_Boyes2009" class="citation book cs1">Walt Boyes (25 November 2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZvscLzOlkNgC&pg=PA570"><i>Instrumentation Reference Book</i></a>. Butterworth-Heinemann. pp. 570–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-094188-2" title="Special:BookSources/978-0-08-094188-2"><bdi>978-0-08-094188-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Instrumentation+Reference+Book&rft.pages=570-&rft.pub=Butterworth-Heinemann&rft.date=2009-11-25&rft.isbn=978-0-08-094188-2&rft.au=Walt+Boyes&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZvscLzOlkNgC%26pg%3DPA570&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-JohnsonJohnson2003-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-JohnsonJohnson2003_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoward_JohnsonHoward_W._JohnsonMartin_Graham2003" class="citation book cs1">Howard Johnson; Howard W. Johnson; Martin Graham (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mMJxcWqm_1oC&pg=PA80"><i>High-speed Signal Propagation: Advanced Black Magic</i></a>. Prentice Hall Professional. pp. 80–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-084408-8" title="Special:BookSources/978-0-13-084408-8"><bdi>978-0-13-084408-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=High-speed+Signal+Propagation%3A+Advanced+Black+Magic&rft.pages=80-&rft.pub=Prentice+Hall+Professional&rft.date=2003&rft.isbn=978-0-13-084408-8&rft.au=Howard+Johnson&rft.au=Howard+W.+Johnson&rft.au=Martin+Graham&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DmMJxcWqm_1oC%26pg%3DPA80&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" 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">F. Fiorillo, Measurement and Characterization of Magnetic Materials, Elsevier Academic Press, 2004, <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/0-12-257251-3" title="Special:BookSources/0-12-257251-3">0-12-257251-3</a>, page. 31</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangsness" class="citation book cs1">Wangsness, Roald. <i>Electromagnetic Fields</i> (2nd ed.). pp. 387–8.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Fields&rft.pages=387-8&rft.edition=2nd&rft.aulast=Wangsness&rft.aufirst=Roald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-bertotti-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-bertotti_6-0">^</a></b></span> <span class="reference-text">G. <i>Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers</i>, San Diego: Academic Press, 1998.</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">Archived at <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211205/nrw-i5Ku0mI">Ghostarchive</a> and the <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110329200359/http://www.youtube.com/watch?v=nrw-i5Ku0mI&feature=related">Wayback Machine</a>: <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.youtube.com/watch?v=nrw-i5Ku0mI">"Eddy Current Tubes"</a>. <i><a href="/wiki/YouTube" title="YouTube">YouTube</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=Eddy+Current+Tubes&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dnrw-i5Ku0mI&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" 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"><a rel="nofollow" class="external text" href="https://www.kickstarter.com/projects/142464853/hendo-hoverboards-worlds-first-real-hoverboard">Hendo Hoverboards - World's first REAL hoverboard</a></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">Bernhard Hiller. <a rel="nofollow" class="external text" href="http://www.baumerhuebner.com/pdf/ferraris_acceleration_sensor.pdf">"Ferraris Acceleration Sensor - Principle and Field of Application in Servo Drives"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140727103811/http://www.baumerhuebner.com/pdf/ferraris_acceleration_sensor.pdf">Archived</a> 27 July 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</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"> Jian Wang, Paul Vanherck, Jan Swevers, Hendrik Van Brussel. <a rel="nofollow" class="external text" href="http://people.mech.kuleuven.be/~jwang/paper/ferraris_speed.pdf">"Speed Observer Based on Sensor Fusion Combining Ferraris Sensor and Linear Position Encoder Signals"</a>.</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"> J. Fassnacht and P. Mutschler. <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=955949">"Benefits and limits of using an acceleration sensor in actively damping high frequent mechanical oscillations"</a>. 2001. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><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%2FIAS.2001.955949">10.1109/IAS.2001.955949</a>.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</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="http://headrushtech.com/trublue-auto-belay/">"TRUBLUE Auto Belay"</a>. <i>Head Rush Technologies</i><span class="reference-accessdate">. Retrieved <span class="nowrap">8 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Head+Rush+Technologies&rft.atitle=TRUBLUE+Auto+Belay&rft_id=http%3A%2F%2Fheadrushtech.com%2Ftrublue-auto-belay%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</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://web.archive.org/web/20170606182712/http://headrushtech.com/zipstop-zip-line-brake/">"zipSTOP Zip Line Brake System"</a>. <i>Head Rush Technologies</i>. Archived from <a rel="nofollow" class="external text" href="http://headrushtech.com/zipstop-zip-line-brake">the original</a> on 6 June 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">8 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Head+Rush+Technologies&rft.atitle=zipSTOP+Zip+Line+Brake+System&rft_id=http%3A%2F%2Fheadrushtech.com%2Fzipstop-zip-line-brake&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</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://web.archive.org/web/20160308233228/http://headrushtech.com/about/technology.html">"Our Patented Technology"</a>. <i>Head Rush Technologies</i>. Archived from <a rel="nofollow" class="external text" href="http://headrushtech.com/about/technology.html">the original</a> on 8 March 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">8 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Head+Rush+Technologies&rft.atitle=Our+Patented+Technology&rft_id=http%3A%2F%2Fheadrushtech.com%2Fabout%2Ftechnology.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</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="http://zappitec.com/en/products.php">"Zappi - Eddy Current Conductivity Meter - Products"</a>. <i>zappitec.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">8 May</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=zappitec.com&rft.atitle=Zappi+-+Eddy+Current+Conductivity+Meter+-+Products&rft_id=http%3A%2F%2Fzappitec.com%2Fen%2Fproducts.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.foerstergroup.de/en/deu/products/sigmatest-2069/">"Institut Dr. Foerster: SIGMATEST"</a>. <i>www.foerstergroup.de</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.foerstergroup.de&rft.atitle=Institut+Dr.+Foerster%3A+SIGMATEST&rft_id=https%3A%2F%2Fwww.foerstergroup.de%2Fen%2Fdeu%2Fproducts%2Fsigmatest-2069%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" 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 rel="nofollow" class="external text" href="http://www.fischer-technology.com/en/us/coating-thickness/electromagnetic-methods">Coating Thickness Measurement with Electromagnetic Methods </a></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</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://web.archive.org/web/20160304065805/http://www.nagy-instruments.de/ohm_sq___od1.html">"Ohm/sq & OD"</a>. <i>www.nagy-instruments.de</i>. Archived from <a rel="nofollow" class="external text" href="http://www.nagy-instruments.de/ohm_sq___od1.html">the original</a> on 4 March 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">8 May</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.nagy-instruments.de&rft.atitle=Ohm%2Fsq+%26+OD&rft_id=http%3A%2F%2Fwww.nagy-instruments.de%2Fohm_sq___od1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cogelme.com/eng/e-eddy-current-metal-separator.htm">"Eddy Current Separator for metal separation"</a>. <i>www.cogelme.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">8 May</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.cogelme.com&rft.atitle=Eddy+Current+Separator+for+metal+separation&rft_id=http%3A%2F%2Fwww.cogelme.com%2Feng%2Fe-eddy-current-metal-separator.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></span> </li> </ol></div></div> <dl><dt>General references</dt></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFitzgeraldKingsley,_Charles_Jr.Umans,_Stephen_D.1983" class="citation book cs1">Fitzgerald, A. E.; Kingsley, Charles Jr.; Umans, Stephen D. (1983). <a rel="nofollow" class="external text" href="https://archive.org/details/electricmachifitz00fitz/page/20"><i>Electric Machinery</i></a> (4th ed.). Mc-Graw-Hill, Inc. p. <a rel="nofollow" class="external text" href="https://archive.org/details/electricmachifitz00fitz/page/20">20</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-021145-2" title="Special:BookSources/978-0-07-021145-2"><bdi>978-0-07-021145-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+Machinery&rft.pages=20&rft.edition=4th&rft.pub=Mc-Graw-Hill%2C+Inc.&rft.date=1983&rft.isbn=978-0-07-021145-2&rft.aulast=Fitzgerald&rft.aufirst=A.+E.&rft.au=Kingsley%2C+Charles+Jr.&rft.au=Umans%2C+Stephen+D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectricmachifitz00fitz%2Fpage%2F20&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSearsZemansky,_Mark_W.1955" class="citation book cs1">Sears, Francis Weston; Zemansky, Mark W. (1955). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/universityphysic00searrich"><i>University Physics</i></a></span> (2nd ed.). Addison-Wesley. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/universityphysic00searrich/page/616">616</a>–618.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=University+Physics&rft.pages=616-618&rft.edition=2nd&rft.pub=Addison-Wesley&rft.date=1955&rft.aulast=Sears&rft.aufirst=Francis+Weston&rft.au=Zemansky%2C+Mark+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Funiversityphysic00searrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></li></ul> <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=Eddy_current&action=edit&section=17" 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="CITEREFStoll1974" class="citation book cs1">Stoll, R. L. (1974). <i>The Analysis of Eddy Currents</i>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Analysis+of+Eddy+Currents&rft.pub=Oxford+University+Press&rft.date=1974&rft.aulast=Stoll&rft.aufirst=R.+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></li> <li>Reitz, J. R. (1970). Forces on Moving Magnets due to Eddy Currents. Journal of Applied Physics 41, 2067-2071. <a rel="nofollow" class="external free" href="https://doi.org/10.1063/1.1659166">https://doi.org/10.1063/1.1659166</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrawczykJ._A._Tegopoulos" class="citation book cs1">Krawczyk, Andrzej; J. A. Tegopoulos. <i>Numerical Modelling of Eddy Currents</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+Modelling+of+Eddy+Currents&rft.aulast=Krawczyk&rft.aufirst=Andrzej&rft.au=J.+A.+Tegopoulos&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEddy+current" class="Z3988"></span></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=Eddy_current&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output 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