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<a class="vector-toc-link" href="#Théorie_semi-classique"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Théorie semi-classique</span> </div> </a> <ul id="toc-Théorie_semi-classique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gaz_d'électrons_libres" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gaz_d'électrons_libres"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Gaz d'électrons libres</span> </div> </a> <ul id="toc-Gaz_d'électrons_libres-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Supraconductivité" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Supraconductivité"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Supraconductivité</span> </div> </a> <ul id="toc-Supraconductivité-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notes et références</span> </div> </a> <ul id="toc-Notes_et_références-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Voir aussi</span> </div> </a> <button aria-controls="toc-Voir_aussi-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>Afficher / masquer la sous-section Voir aussi</span> </button> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liens_externes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liens_externes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Liens externes</span> </div> </a> <ul id="toc-Liens_externes-sublist" class="vector-toc-list"> </ul> </li> </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="Sommaire" 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="Basculer la table des matières" > <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">Basculer la table des matières</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">Diamagnétisme</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="Aller à un article dans une autre langue. Disponible en 54 langues." > <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-54" 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">54 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – afrikaans" lang="af" hreflang="af" data-title="Diamagnetisme" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%BA%D9%86%D8%A7%D8%B7%D9%8A%D8%B3%D9%8A%D8%A9_%D9%85%D8%B9%D8%A7%D9%83%D8%B3%D8%A9" title="مغناطيسية معاكسة – arabe" lang="ar" hreflang="ar" data-title="مغناطيسية معاكسة" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Diamaqnetizm" title="Diamaqnetizm – azerbaïdjanais" lang="az" hreflang="az" data-title="Diamaqnetizm" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D1%8A%D0%BC" title="Диамагнетизъм – bulgare" lang="bg" hreflang="bg" data-title="Диамагнетизъм" data-language-autonym="Български" data-language-local-name="bulgare" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A1%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%9A%E0%A7%8C%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%95_%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A5" title="ডায়াচৌম্বক পদার্থ – bengali" lang="bn" hreflang="bn" data-title="ডায়াচৌম্বক পদার্থ" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – catalan" lang="ca" hreflang="ca" data-title="Diamagnetisme" 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/Diamagnetismus" title="Diamagnetismus – tchèque" lang="cs" hreflang="cs" data-title="Diamagnetismus" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – danois" lang="da" hreflang="da" data-title="Diamagnetisme" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Diamagnetismus" title="Diamagnetismus – allemand" lang="de" hreflang="de" data-title="Diamagnetismus" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CE%BC%CE%B1%CE%B3%CE%BD%CE%B7%CF%84%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Διαμαγνητισμός – grec" lang="el" hreflang="el" data-title="Διαμαγνητισμός" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Diamagnetism" title="Diamagnetism – anglais" lang="en" hreflang="en" data-title="Diamagnetism" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Diamagnetismo" title="Diamagnetismo – espéranto" lang="eo" hreflang="eo" data-title="Diamagnetismo" data-language-autonym="Esperanto" data-language-local-name="espéranto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Diamagnetismo" title="Diamagnetismo – espagnol" lang="es" hreflang="es" data-title="Diamagnetismo" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Diamagnetism" title="Diamagnetism – estonien" lang="et" hreflang="et" data-title="Diamagnetism" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Diamagnetismo" title="Diamagnetismo – basque" lang="eu" hreflang="eu" data-title="Diamagnetismo" 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%AF%DB%8C%D8%A7%D9%85%D8%BA%D9%86%D8%A7%D8%B7%DB%8C%D8%B3" title="دیامغناطیس – persan" lang="fa" hreflang="fa" data-title="دیامغناطیس" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Diamagnetismi" title="Diamagnetismi – finnois" lang="fi" hreflang="fi" data-title="Diamagnetismi" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Diamaighn%C3%A9adas" title="Diamaighnéadas – irlandais" lang="ga" hreflang="ga" data-title="Diamaighnéadas" data-language-autonym="Gaeilge" data-language-local-name="irlandais" 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/Diamagnetismo" title="Diamagnetismo – galicien" lang="gl" hreflang="gl" data-title="Diamagnetismo" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%93%D7%99%D7%90%D7%9E%D7%92%D7%A0%D7%98%D7%99%D7%95%D7%AA" title="דיאמגנטיות – hébreu" lang="he" hreflang="he" data-title="דיאמגנטיות" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95%E0%A4%A4%E0%A5%8D%E0%A4%B5" title="प्रतिचुम्बकत्व – hindi" lang="hi" hreflang="hi" data-title="प्रतिचुम्बकत्व" 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/Dijamagnetizam" title="Dijamagnetizam – croate" lang="hr" hreflang="hr" data-title="Dijamagnetizam" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Diam%C3%A1gnesess%C3%A9g" title="Diamágnesesség – hongrois" lang="hu" hreflang="hu" data-title="Diamágnesesség" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%AB%D5%A1%D5%B4%D5%A1%D5%A3%D5%B6%D5%AB%D5%BD%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Դիամագնիսականություն – arménien" lang="hy" hreflang="hy" data-title="Դիամագնիսականություն" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – indonésien" lang="id" hreflang="id" data-title="Diamagnetisme" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Diamagnetismo" title="Diamagnetismo – italien" lang="it" hreflang="it" data-title="Diamagnetismo" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8F%8D%E7%A3%81%E6%80%A7" title="反磁性 – japonais" lang="ja" hreflang="ja" data-title="反磁性" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Диамагнетизм – kazakh" lang="kk" hreflang="kk" data-title="Диамагнетизм" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EC%9E%90%EC%84%B1" title="반자성 – coréen" lang="ko" hreflang="ko" data-title="반자성" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D0%B8%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Диамагнетизм – kirghize" lang="ky" hreflang="ky" data-title="Диамагнетизм" data-language-autonym="Кыргызча" data-language-local-name="kirghize" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Diamagnetismus" title="Diamagnetismus – latin" lang="la" hreflang="la" data-title="Diamagnetismus" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B4%A4" title="പ്രതികാന്തികത – malayalam" lang="ml" hreflang="ml" data-title="പ്രതികാന്തികത" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kediamagnetan" title="Kediamagnetan – malais" lang="ms" hreflang="ms" data-title="Kediamagnetan" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – néerlandais" lang="nl" hreflang="nl" data-title="Diamagnetisme" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Diamagnetisme" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Diamagnetisme" title="Diamagnetisme – norvégien bokmål" lang="nb" hreflang="nb" data-title="Diamagnetisme" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A1%E0%A8%BE%E0%A8%87%E0%A8%86%E0%A8%AE%E0%A9%88%E0%A8%97%E0%A8%A8%E0%A9%87%E0%A8%9F%E0%A8%BF%E0%A8%9C%E0%A8%BC%E0%A8%AE" title="ਡਾਇਆਮੈਗਨੇਟਿਜ਼ਮ – pendjabi" lang="pa" hreflang="pa" data-title="ਡਾਇਆਮੈਗਨੇਟਿਜ਼ਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pendjabi" 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/Diamagnetyzm" title="Diamagnetyzm – polonais" lang="pl" hreflang="pl" data-title="Diamagnetyzm" data-language-autonym="Polski" data-language-local-name="polonais" 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/Diamagnetismo" title="Diamagnetismo – portugais" lang="pt" hreflang="pt" data-title="Diamagnetismo" data-language-autonym="Português" data-language-local-name="portugais" 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/Diamagnetism" title="Diamagnetism – roumain" lang="ro" hreflang="ro" data-title="Diamagnetism" data-language-autonym="Română" data-language-local-name="roumain" 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%94%D0%B8%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Диамагнетизм – russe" lang="ru" hreflang="ru" data-title="Диамагнетизм" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Dijamagnetizam" title="Dijamagnetizam – serbo-croate" lang="sh" hreflang="sh" data-title="Dijamagnetizam" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Diamagnetism" title="Diamagnetism – Simple English" lang="en-simple" hreflang="en-simple" data-title="Diamagnetism" 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/Diamagnetizmus" title="Diamagnetizmus – slovaque" lang="sk" hreflang="sk" data-title="Diamagnetizmus" data-language-autonym="Slovenčina" data-language-local-name="slovaque" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Diamagnetizem" title="Diamagnetizem – slovène" lang="sl" hreflang="sl" data-title="Diamagnetizem" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Diamagnetizmi" title="Diamagnetizmi – albanais" lang="sq" hreflang="sq" data-title="Diamagnetizmi" data-language-autonym="Shqip" data-language-local-name="albanais" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B8%D1%98%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%B0%D0%BC" title="Дијамагнетизам – serbe" lang="sr" hreflang="sr" data-title="Дијамагнетизам" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Diamagnetism" title="Diamagnetism – suédois" lang="sv" hreflang="sv" data-title="Diamagnetism" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%94%E0%B8%AD%E0%B8%B0%E0%B9%81%E0%B8%A1%E0%B8%81%E0%B9%80%E0%B8%99%E0%B8%95%E0%B8%B4%E0%B8%81" title="ไดอะแมกเนติก – thaï" lang="th" hreflang="th" data-title="ไดอะแมกเนติก" data-language-autonym="ไทย" data-language-local-name="thaï" 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/Diyamanyetizma" title="Diyamanyetizma – turc" lang="tr" hreflang="tr" data-title="Diyamanyetizma" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D1%96%D0%B0%D0%BC%D0%B0%D0%B3%D0%BD%D0%B5%D1%82%D0%B8%D0%B7%D0%BC" title="Діамагнетизм – ukrainien" lang="uk" hreflang="uk" data-title="Діамагнетизм" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Diamagnetizm" title="Diamagnetizm – ouzbek" lang="uz" hreflang="uz" data-title="Diamagnetizm" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ouzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ngh%E1%BB%8Bch_t%E1%BB%AB" title="Nghịch từ – vietnamien" lang="vi" hreflang="vi" data-title="Nghịch từ" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8A%97%E7%A3%81%E6%80%A7" title="抗磁性 – 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class="noprint">Un article de Wikipédia, l'encyclopédie libre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fr" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Diamagnetic_graphite_levitation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Diamagnetic_graphite_levitation.jpg/220px-Diamagnetic_graphite_levitation.jpg" decoding="async" width="220" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Diamagnetic_graphite_levitation.jpg/330px-Diamagnetic_graphite_levitation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Diamagnetic_graphite_levitation.jpg/440px-Diamagnetic_graphite_levitation.jpg 2x" data-file-width="550" data-file-height="700" /></a><figcaption>Démonstration de la lévitation du <a href="/wiki/Carbone_pyrolytique" title="Carbone pyrolytique">carbone pyrolytique</a> au-dessus d'aimants permanents. Le carbone pyrolithique étant un matériau similaire au graphite, est donc un des matériaux possédant l'une des plus grandes susceptibilités diamagnétiques connues.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Frog_diamagnetic_levitation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/220px-Frog_diamagnetic_levitation.jpg" decoding="async" width="220" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/330px-Frog_diamagnetic_levitation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Frog_diamagnetic_levitation.jpg/440px-Frog_diamagnetic_levitation.jpg 2x" data-file-width="607" data-file-height="574" /></a><figcaption>Lévitation d'une grenouille vivante dans un champ magnétique de 16 <a href="/wiki/Tesla_(unit%C3%A9)" title="Tesla (unité)">teslas</a>.</figcaption></figure> <p>Le <b>diamagnétisme</b> est un comportement des matériaux qui les conduit, lorsqu'ils sont soumis à un <a href="/wiki/Champ_magn%C3%A9tique" title="Champ magnétique">champ magnétique</a>, à créer une très faible aimantation opposée au champ extérieur, et donc à engendrer un champ magnétique opposé au champ extérieur. Lorsque le champ n’est plus appliqué, l’aimantation disparaît. </p><p>Le diamagnétisme est un phénomène qui apparaît dans toute la <a href="/wiki/Mati%C3%A8re_baryonique" title="Matière baryonique">matière baryonique</a>, mais dans la plupart des cas, il est masqué par les effets du <a href="/wiki/Paramagn%C3%A9tisme" title="Paramagnétisme">paramagnétisme</a> ou du <a href="/wiki/Ferromagn%C3%A9tisme" title="Ferromagnétisme">ferromagnétisme</a> lorsque ceux-ci coexistent avec lui dans le matériau. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=1" title="Modifier la section : Description" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=1" title="Modifier le code source de la section : Description"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="float:right; clear:right; margin:20px" width="200px"> <caption>Susceptibilité <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }"></span> des matériaux diamagnétiques typiques (20 °C)<sup id="cite_ref-hyper_1-0" class="reference"><a href="#cite_note-hyper-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup> </caption> <tbody><tr> <th>Matériau</th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }"></span> </th></tr> <tr> <td><a href="/wiki/Bismuth" title="Bismuth">Bismuth</a> </td> <td>-16,6×10<sup>-5</sup> </td></tr> <tr> <td>Carbone (diamant) </td> <td>-2,1×10<sup>-5</sup> </td></tr> <tr> <td>Carbone (graphite) </td> <td>-1,6×10<sup>-5</sup> </td></tr> <tr> <td>Cuivre </td> <td>-1,0×10<sup>-5</sup> </td></tr> <tr> <td>Plomb </td> <td>-1,8×10<sup>-5</sup> </td></tr> <tr> <td>Mercure </td> <td>-2,9×10<sup>-5</sup> </td></tr> <tr> <td>Argent </td> <td>-2,6×10<sup>-5</sup> </td></tr> <tr> <td>Eau </td> <td>-0,91×10<sup>-5</sup> </td></tr></tbody></table> <p>Le diamagnétisme est une propriété générale de la <a href="/wiki/Mati%C3%A8re" title="Matière">matière</a> atomique (matière constituée d'atomes), qui provoque l'apparition d'un <a href="/wiki/Champ_magn%C3%A9tique" title="Champ magnétique">champ magnétique</a> faible dans le matériau, opposé à un champ magnétique appliqué. L'origine du diamagnétisme est un phénomène quantique (<a href="/wiki/Quantification_de_Landau" title="Quantification de Landau">quantification de Landau</a>), pouvant être expliqué par la modification du mouvement orbital des <a href="/wiki/%C3%89lectron" title="Électron">électrons</a> autour du <a href="/wiki/Noyau_atomique" title="Noyau atomique">noyau atomique</a>. </p><p>La <a href="/wiki/Susceptibilit%C3%A9_magn%C3%A9tique" title="Susceptibilité magnétique">susceptibilité magnétique</a> des matériaux diamagnétiques est très faible et négative, autour de -10<sup>-5</sup> ou -10<sup>-6</sup>. Le champ magnétique induit par ce phénomène est donc très faible. </p><p>L'eau est diamagnétique. La plupart des corps étant composés d'eau, comme les animaux, il est possible de faire léviter par exemple une souris, une grenouille, un humain dans un champ magnétique très fort. L'expérience a été faite avec une grenouille vivante (voir illustration ci-contre)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup>. Théoriquement un corps humain pourrait léviter de la même manière dans un champ magnétique très puissant, mais difficile à obtenir. Cependant cela n'a jamais été réalisé, d'autant que des conséquences dommageables sur l'organisme ne peuvent être exclues. </p><p>La susceptibilité d'un matériau diamagnétique reste constante quand la température varie. C'est une différence majeure avec les matériaux <a href="/wiki/Paramagn%C3%A9tisme" title="Paramagnétisme">paramagnétiques</a>, qui ont une susceptibilité positive plus importante et qui diminue lorsque la température augmente. </p> <div class="mw-heading mw-heading2"><h2 id="Théorie_semi-classique"><span id="Th.C3.A9orie_semi-classique"></span>Théorie semi-classique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=2" title="Modifier la section : Théorie semi-classique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=2" title="Modifier le code source de la section : Théorie semi-classique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On ne peut expliquer le diamagnétisme rigoureusement que par la théorie quantique. Cependant, on peut utiliser une approche semi-classique, qui permet de comprendre le phénomène sans pour autant aller jusqu’à étudier la théorie quantique. </p><p>On considère un électron se déplaçant sur une orbite circulaire de rayon <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>, avec une vitesse <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 v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>. </p><p>On applique un champ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span> sur le système. D’après la <a href="/wiki/Loi_de_Lenz" class="mw-redirect" title="Loi de Lenz">loi de Lenz</a>, si on considère le cercle comme une spire de courant, un flux magnétique <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 \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> est créé, traversant le circuit, et induisant une force électromotrice <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 \varepsilon =-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon =-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28b0b302fe6b4e650b1b90630da587fea542cb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.797ex; height:5.509ex;" alt="{\displaystyle \varepsilon =-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"></span> dans le circuit. Cette <a href="/wiki/Force_%C3%A9lectromotrice" title="Force électromotrice">force électromotrice</a> équivaut à un <a href="/wiki/Champ_%C3%A9lectrique" title="Champ électrique">champ électrique</a> qui freine l’électron. </p><p>La diminution de la vitesse de l’électron entraîne une diminution du moment magnétique <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 {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24e08685bde682d6b67c3a22b026d16dbbf8dfcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:2.343ex;" alt="{\displaystyle {\vec {m}}}"></span>, d’amplitude </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}r^{2}}{4m_{e}}}\mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}r^{2}}{4m_{e}}}\mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a984ea37e5ec6077dc3a28d9e0fd93ae4f07e4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.046ex; height:6.009ex;" alt="{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}r^{2}}{4m_{e}}}\mathbf {B} }"></span>.</dd></dl> <p>Dans le cas d’un atome, on a Z électrons gravitant sur des orbites sphériques autour du noyau. </p><p>On a donc </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}Z\langle r^{2}\rangle }{6m_{e}}}\mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>Z</mi> <mo fence="false" stretchy="false">⟨</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow> <mn>6</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}Z\langle r^{2}\rangle }{6m_{e}}}\mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3392e422936746f38d6f4262c2f688ac76f82d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.536ex; height:6.176ex;" alt="{\displaystyle \Delta \mathbf {m} =-{\frac {e^{2}Z\langle r^{2}\rangle }{6m_{e}}}\mathbf {B} }"></span>,</dd></dl> <p>avec <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 \langle r^{2}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle r^{2}\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/089684b1048796cfa989cc0ac044571b77d3017a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.912ex; height:3.176ex;" alt="{\displaystyle \langle r^{2}\rangle }"></span> la valeur moyenne du carré du rayon des différentes orbites. </p><p>Enfin, on peut calculer la <a href="/wiki/Susceptibilit%C3%A9_magn%C3%A9tique" title="Susceptibilité magnétique">susceptibilité magnétique</a>. Avec <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/V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N/V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eaa155f67e3e587c18df95a5afefbeb5201bd715" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.013ex; height:2.843ex;" alt="{\displaystyle N/V}"></span> atomes par unité de volume, on a : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi =-{\frac {\mu _{0}e^{2}}{6m_{e}}}\left(Z{\frac {N}{V}}\right)\langle r^{2}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>6</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <mi>V</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo fence="false" stretchy="false">⟨</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi =-{\frac {\mu _{0}e^{2}}{6m_{e}}}\left(Z{\frac {N}{V}}\right)\langle r^{2}\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/438f1f72c23b7f7375e94dff726f6b2e2bb276f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.479ex; height:6.343ex;" alt="{\displaystyle \chi =-{\frac {\mu _{0}e^{2}}{6m_{e}}}\left(Z{\frac {N}{V}}\right)\langle r^{2}\rangle }"></span>.</dd></dl> <p>Cette contribution est découverte par <a href="/wiki/Paul_Langevin" title="Paul Langevin">Paul Langevin</a> en 1905<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Gaz_d'électrons_libres"><span id="Gaz_d.27.C3.A9lectrons_libres"></span>Gaz d'électrons libres</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=3" title="Modifier la section : Gaz d'électrons libres" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=3" title="Modifier le code source de la section : Gaz d'électrons libres"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-modere"><div class="bandeau-cell bandeau-icone"><span class="mw-valign-text-top noviewer" typeof="mw:File"><a href="/wiki/Fichier:Emojione_267B.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Emojione_267B.svg/17px-Emojione_267B.svg.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Emojione_267B.svg/26px-Emojione_267B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Emojione_267B.svg/34px-Emojione_267B.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div><div class="bandeau-cell">Cette section a besoin d'être <b><a href="/wiki/Aide:Recyclage" title="Aide:Recyclage">recyclée</a></b><small> (5 juillet 2018)</small>.<br /> Une réorganisation et une clarification du contenu sont nécessaires. <span class="navigation-only"><span class="noprint plainlinks"><a href="/wiki/Sp%C3%A9cial:EditPage/Diamagn%C3%A9tisme" title="Spécial:EditPage/Diamagnétisme">Améliorez-la</a></span> ou <a href="/wiki/Discussion:Diamagn%C3%A9tisme" title="Discussion:Diamagnétisme">discutez des points à améliorer</a>.</span></div></div> <p>Un gaz d'électrons libres dilué comme dans le cas d'un gaz d'électrons conducteur dans un métal présente une susceptibilité négative différente du diamagnétisme atomique présenté ci-dessus<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>. Les deux contributions sont présentes dans un métal. </p><p>Ce phénomène était prédit par <a href="/wiki/Lev_Landau" title="Lev Landau">Lev Landau</a>, on parle donc de <b>diamagnétisme de Landau</b>. Sous l'effet d'un champ magnétique, l'énergie des électrons est perturbée. </p><p>Pour étudier ce phénomène, il faut incorporer dans l'hamiltonien du système le champ magnétique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span> défini tel que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/436aaad562d4e3626ff807cadb0185658e4e6c51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.795ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }"></span>, avec <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0795cc96c75d81520a120482662b90f024c9a1a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {A} }"></span> le <a href="/wiki/Potentiel_vecteur_du_champ_magn%C3%A9tique" title="Potentiel vecteur du champ magnétique">potentiel vecteur du champ magnétique</a>. On supposera dans la suite que le champ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span> est parallèle à l'axe <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 z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span>. </p><p>L'<a href="/wiki/%C3%89quation_de_Schr%C3%B6dinger" title="Équation de Schrödinger">équation de Schrödinger</a> indépendante du temps pour un électron de <a href="/wiki/Masse_effective" title="Masse effective">masse effective</a> <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 m^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f2650f1055b63acf24bf275e50b4f59c3e53685" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.095ex; height:2.343ex;" alt="{\displaystyle m^{*}}"></span> soumis à un champ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span> constant s'écrit donc : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2m^{*}}}\left({\frac {\hbar }{i}}\nabla +e\mathbf {A} (\mathbf {r} )\right)^{2}\psi (\mathbf {r} )=E\psi (\mathbf {r} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mi>i</mi> </mfrac> </mrow> <mi mathvariant="normal">∇</mi> <mo>+</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2m^{*}}}\left({\frac {\hbar }{i}}\nabla +e\mathbf {A} (\mathbf {r} )\right)^{2}\psi (\mathbf {r} )=E\psi (\mathbf {r} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f4c858d97fbd40e88f864da172b6e9d251c89d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.225ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{2m^{*}}}\left({\frac {\hbar }{i}}\nabla +e\mathbf {A} (\mathbf {r} )\right)^{2}\psi (\mathbf {r} )=E\psi (\mathbf {r} )}"></span>.</dd></dl> <p>Si nous choisissons la jauge de Landau : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {A} =(0,x|\mathbf {B} |,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {A} =(0,x|\mathbf {B} |,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56b8c37771ff2430e720ebf34cc6d98eddf65c1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.844ex; height:2.843ex;" alt="{\displaystyle \mathbf {A} =(0,x|\mathbf {B} |,0)}"></span>, nous obtenons alors que la solution de l'équation de Schrödinger aura une forme <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (\mathbf {r} )=u(x)\exp[i(k_{y}y+k_{z}z)]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">[</mo> <mi>i</mi> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>y</mi> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (\mathbf {r} )=u(x)\exp[i(k_{y}y+k_{z}z)]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6258defafb4f2e70b699558507941f9a0c111af2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.394ex; height:3.009ex;" alt="{\displaystyle \psi (\mathbf {r} )=u(x)\exp[i(k_{y}y+k_{z}z)]}"></span>. </p><p>L'énergie de l'électron sera donc de la forme : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\left(n+{\frac {1}{2}}\right)\hbar \omega _{\rm {c}}+{\frac {\hbar ^{2}k_{z}^{2}}{2m^{*}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>2</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\left(n+{\frac {1}{2}}\right)\hbar \omega _{\rm {c}}+{\frac {\hbar ^{2}k_{z}^{2}}{2m^{*}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b6b4c76bd51c221c8c2902cbedaa2f475cebff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.949ex; height:6.343ex;" alt="{\displaystyle E=\left(n+{\frac {1}{2}}\right)\hbar \omega _{\rm {c}}+{\frac {\hbar ^{2}k_{z}^{2}}{2m^{*}}}}"></span> avec <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 \omega _{\rm {c}}={\frac {e|\mathbf {B} |}{m^{*}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{\rm {c}}={\frac {e|\mathbf {B} |}{m^{*}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fd8b53e34ea678464e28a4aecb03b411d55934c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.621ex; height:5.676ex;" alt="{\displaystyle \omega _{\rm {c}}={\frac {e|\mathbf {B} |}{m^{*}}}}"></span> la <a href="/wiki/Fr%C3%A9quence_cyclotron" title="Fréquence cyclotron">fréquence cyclotron</a>.</dd></dl> <p>On reconnaît dans le premier terme l'expression de l'énergie d'un <a href="/wiki/Oscillateur_harmonique" title="Oscillateur harmonique">oscillateur harmonique</a>. L’énergie est quantifiée sur le nombre quantique <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/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> à <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 k_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{z}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff8fad407df5995ada49dea20bffa5c66d8ba7e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.213ex; height:2.509ex;" alt="{\displaystyle k_{z}}"></span> fixe. La susceptibilité de Landau peut être retrouvée grâce à la <a href="/wiki/Physique_statistique" title="Physique statistique">physique statistique</a>. </p><p>Effectivement, grâce à la <a href="/wiki/Fonction_de_partition" title="Fonction de partition">fonction de partition</a> pour un électron <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 {\mathcal {Z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {Z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9be1e2c3c82e7b8055fe26eb4cf2caac6f8ec73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle {\mathcal {Z}}}"></span>, et sachant que l’aimantation est : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=-Nk_{\rm {B}}T{\frac {\partial {\mathcal {Z}}}{\partial B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mo>−</mo> <mi>N</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">Z</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>B</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=-Nk_{\rm {B}}T{\frac {\partial {\mathcal {Z}}}{\partial B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/193185b35fc9240a30ebbb4ae98c0847d4a83577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.593ex; height:5.509ex;" alt="{\displaystyle M=-Nk_{\rm {B}}T{\frac {\partial {\mathcal {Z}}}{\partial B}}}"></span>,</dd></dl> <p>on trouve que la susceptibilité de Landau vaut : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi _{\rm {Landau}}=-{\frac {1}{3}}\chi _{\rm {Pauli}}=-\mu _{0}{\frac {\mu _{\rm {B}}^{2}}{2E_{\rm {F}}}}{\frac {N}{V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>2</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <mi>V</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi _{\rm {Landau}}=-{\frac {1}{3}}\chi _{\rm {Pauli}}=-\mu _{0}{\frac {\mu _{\rm {B}}^{2}}{2E_{\rm {F}}}}{\frac {N}{V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4d44a5248c2814c7521a9817d38a37584534d91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:34.745ex; height:6.343ex;" alt="{\displaystyle \chi _{\rm {Landau}}=-{\frac {1}{3}}\chi _{\rm {Pauli}}=-\mu _{0}{\frac {\mu _{\rm {B}}^{2}}{2E_{\rm {F}}}}{\frac {N}{V}}}"></span>,</dd></dl> <p>avec <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 E_{\rm {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\rm {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d3ad20412ac49158727f3369a6d2b2498e29f49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.021ex; height:2.509ex;" alt="{\displaystyle E_{\rm {F}}}"></span> l'<a href="/wiki/%C3%89nergie_de_Fermi" title="Énergie de Fermi">énergie de Fermi</a> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi _{\rm {Pauli}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi _{\rm {Pauli}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82019e1179bdc5cd85315e60eba22f2b65f94f81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.457ex; height:2.009ex;" alt="{\displaystyle \chi _{\rm {Pauli}}}"></span> la <a href="/wiki/Paramagn%C3%A9tisme#Paramagnétisme_de_Pauli" title="Paramagnétisme">susceptibilité paramagnétique de Pauli</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Supraconductivité"><span id="Supraconductivit.C3.A9"></span>Supraconductivité</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=4" title="Modifier la section : Supraconductivité" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=4" title="Modifier le code source de la section : Supraconductivité"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les <a href="/wiki/Supraconductivit%C3%A9" title="Supraconductivité">supraconducteurs</a> peuvent être considérés comme des matériaux diamagnétiques parfaits de susceptibilité magnétique -1. Tout champ magnétique entraîne en son sein des super-courants sans apport d'énergie du fait de l'absence de résistance électrique. Ces super-courants créent un champ magnétique qui compense exactement le champ magnétique extérieur à l'intérieur du supraconducteur. Cette propriété est utilisée pour réaliser la <a href="/wiki/L%C3%A9vitation_magn%C3%A9tique" class="mw-redirect" title="Lévitation magnétique">lévitation magnétique</a> des supraconducteurs. </p> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=5" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=5" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-hyper-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-hyper_1-0">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Nave"><span class="ouvrage" id="Carl_L._Nave"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Carl L. <span class="nom_auteur">Nave</span>, « <a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html"><cite style="font-style:normal;" lang="en">Magnetic Properties of Solids</cite></a> », <span class="italique">HyperPhysics</span> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2008-11-09" data-sort-value="2008-11-09">9 novembre 2008</time>)</small></span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text"><span class="ouvrage" id="1997"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="http://www.ru.nl/hfml/research/levitation/diamagnetic/"><cite style="font-style:normal;" lang="en">Diamagnetic Levitation</cite></a> », sur <span class="italique"><a href="/wiki/Universit%C3%A9_Radboud_de_Nim%C3%A8gue" title="Université Radboud de Nimègue">Université Radboud de Nimègue</a> aux Pays-Bas</span>, <time class="nowrap" datetime="1997-04" data-sort-value="1997-04">avril 1997</time> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2019-04-06" data-sort-value="2019-04-06">6 avril 2019</time>)</small></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-3">↑</a> </span><span class="reference-text"><a href="/wiki/Andre_Geim" title="Andre Geim">Andre Geim</a> recevra le <a href="/wiki/Prix_Ig-Nobel" title="Prix Ig-Nobel">prix Ignobel</a> 2000, pour avoir réalisé l'expérience de la lévitation de la grenouille</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-4">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Langevin1905"><span class="ouvrage" id="Paul_Langevin1905"><a href="/wiki/Paul_Langevin" title="Paul Langevin">Paul Langevin</a>, « <cite style="font-style:normal">Sur la théorie du magnétisme</cite> », <i>Journal of Theoretical and Applied Physics</i>, <abbr class="abbr" title="volume">vol.</abbr> 4, <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 1,‎ <time>1905</time>, <abbr class="abbr" title="page(s)">p.</abbr> 678--693 <small style="line-height:1em;">(<a rel="nofollow" class="external text" href="https://hal.archives-ouvertes.fr/jpa-00241050/document">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sur+la+th%C3%A9orie+du+magn%C3%A9tisme&rft.jtitle=Journal+of+Theoretical+and+Applied+Physics&rft.issue=1&rft.aulast=Langevin&rft.aufirst=Paul&rft.date=1905&rft.volume=4&rft.pages=678--693&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADiamagn%C3%A9tisme"></span></span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-5">↑</a> </span><span class="reference-text"><span class="ouvrage" id="M.2013"><span class="ouvrage" id="Héritier,_M.2013">Héritier, <span class="nom_auteur">M.</span>, <cite class="italique">Physique de la matière condensée : Des atomes froids aux supraconducteurs à haute température critique</cite>, <time>2013</time>, 640 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-7598-1097-0" title="Spécial:Ouvrages de référence/978-2-7598-1097-0"><span class="nowrap">978-2-7598-1097-0</span></a>, <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2759810976" title="Spécial:Ouvrages de référence/2759810976"><span class="nowrap">2759810976</span></a> et <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/1306073367" title="Spécial:Ouvrages de référence/1306073367"><span class="nowrap">1306073367</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/861536206">861536206</a></span>, <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/861536206">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physique+de+la+mati%C3%A8re+condens%C3%A9e&rft.stitle=Des+atomes+froids+aux+supraconducteurs+%C3%A0+haute+temp%C3%A9rature+critique&rft.aulast=M.&rft.aufirst=H%C3%A9ritier%2C&rft.date=2013&rft.tpages=640&rft.isbn=978-2-7598-1097-0&rft_id=info%3Aoclcnum%2F861536206&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADiamagn%C3%A9tisme"></span></span></span></span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=6" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=6" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r194021218">.mw-parser-output .autres-projets>.titre{text-align:center;margin:0.2em 0}.mw-parser-output .autres-projets>ul{margin:0;padding:0}.mw-parser-output .autres-projets>ul>li{list-style:none;margin:0.2em 0;text-indent:0;padding-left:24px;min-height:20px;text-align:left;display:block}.mw-parser-output .autres-projets>ul>li>a{font-style:italic}@media(max-width:720px){.mw-parser-output .autres-projets{float:none}}</style><div class="autres-projets boite-grise boite-a-droite noprint js-interprojets"> <p class="titre">Sur les autres projets Wikimedia :</p> <ul class="noarchive plainlinks"> <li class="commons"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Diamagnetism?uselang=fr">Diamagnétisme</a>, sur <span class="project">Wikimedia Commons</span></li> </ul> </div> <div class="mw-heading mw-heading3"><h3 id="Articles_connexes">Articles connexes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=7" title="Modifier la section : Articles connexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=7" title="Modifier le code source de la section : Articles connexes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="column-width:30em;column-count:2;column-gap:1em;" class="colonnes"> <ul><li><a href="/wiki/Magn%C3%A9tisme" title="Magnétisme">Magnétisme</a></li> <li><a href="/wiki/Paramagn%C3%A9tisme" title="Paramagnétisme">Paramagnétisme</a></li> <li><a href="/wiki/Ferromagn%C3%A9tisme" title="Ferromagnétisme">Ferromagnétisme</a></li> <li><a href="/wiki/Effet_Meissner" title="Effet Meissner">Effet Meissner</a></li> <li><a href="/wiki/Effet_de_Haas-Van_Alphen" title="Effet de Haas-Van Alphen">Effet de Haas-Van Alphen</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Liens_externes">Liens externes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Diamagn%C3%A9tisme&veaction=edit&section=8" title="Modifier la section : Liens externes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Diamagn%C3%A9tisme&action=edit&section=8" title="Modifier le code source de la section : Liens externes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><div class="liste-horizontale"><span class="wd_identifiers"><a href="/wiki/Autorit%C3%A9_(sciences_de_l%27information)" title="Autorité (sciences de l'information)">Notices d'autorité</a><span class="noprint wikidata-linkback skin-invert"><span class="mw-valign-baseline noviewer" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q201048?uselang=fr#identifiers" title="Voir et modifier les données sur Wikidata"><img alt="Voir et modifier les données sur Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></span> : <ul><li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/sh85037541">LCCN</a></span></li> <li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4149487-8">GND</a></span></li> <li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00562969">Japon</a></span></li> <li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007553037205171">Israël</a></span></li> </ul></div></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_%C3%89lectromagn%C3%A9tisme" title="Modèle:Palette Électromagnétisme"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_%C3%89lectromagn%C3%A9tisme&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/%C3%89lectromagn%C3%A9tisme" title="Électromagnétisme">Électromagnétisme</a></div></th> </tr> <tr> <th class="navbox-group" style="width:100px"><a href="/wiki/%C3%89lectrostatique" title="Électrostatique">Électrostatique</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Champ_%C3%A9lectrique" title="Champ électrique">Champ électrique</a></li> <li><a href="/wiki/Charge_%C3%A9lectrique" title="Charge électrique">Charge électrique</a></li> <li><a href="/wiki/Loi_de_Coulomb_(%C3%A9lectrostatique)" title="Loi de Coulomb (électrostatique)">Loi de Coulomb</a></li> <li><a href="/wiki/Potentiel_%C3%A9lectrique" title="Potentiel électrique">Potentiel électrique</a></li> <li><a href="/wiki/Pression_%C3%A9lectrostatique" title="Pression électrostatique">Pression électrostatique</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:100px"><a href="/wiki/Magn%C3%A9tostatique" title="Magnétostatique">Magnétostatique</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Champ_magn%C3%A9tique" title="Champ magnétique">Champ magnétique</a></li> <li><a href="/wiki/Moment_magn%C3%A9tique" title="Moment magnétique">Moment magnétique</a></li> <li><a href="/wiki/Aimantation" title="Aimantation">Aimantation</a></li> <li><a href="/wiki/Loi_de_Biot_et_Savart" title="Loi de Biot et Savart">Loi de Biot et Savart</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:100px"><a href="/wiki/%C3%89lectrocin%C3%A9tique" title="Électrocinétique">Électrocinétique</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Amp%C3%A8re" title="Ampère">Ampère</a></li> <li><a href="/wiki/Champ_%C3%A9lectromagn%C3%A9tique" title="Champ électromagnétique">Champ électromagnétique</a></li> <li><a href="/wiki/Courant_de_d%C3%A9placement" title="Courant de déplacement">Courant de déplacement</a></li> <li><a href="/wiki/Courant_%C3%A9lectrique" title="Courant électrique">Courant électrique</a></li> <li><a href="/wiki/Courants_de_Foucault" title="Courants de Foucault">Courants de Foucault</a></li> <li><a href="/wiki/%C3%89quations_de_Jefimenko" title="Équations de Jefimenko">Équations de Jefimenko</a></li> <li><a href="/wiki/%C3%89quations_de_Maxwell" title="Équations de Maxwell">Équations de Maxwell</a></li> <li><a href="/wiki/Force_%C3%A9lectromotrice" title="Force électromotrice">Force électromotrice</a></li> <li><a href="/wiki/Force_%C3%A9lectromagn%C3%A9tique" title="Force électromagnétique">Force de Lorentz</a></li> <li><a href="/wiki/Induction_%C3%A9lectromagn%C3%A9tique" title="Induction électromagnétique">Induction électromagnétique</a></li> <li><a href="/wiki/Loi_de_Lenz-Faraday" title="Loi de Lenz-Faraday">Loi de Lenz-Faraday</a></li> <li><a href="/wiki/Potentiels_de_Li%C3%A9nard-Wiechert" title="Potentiels de Liénard-Wiechert">Potentiels de Liénard-Wiechert</a></li> <li><a href="/wiki/Rayonnement_%C3%A9lectromagn%C3%A9tique" title="Rayonnement électromagnétique">Rayonnement électromagnétique</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:100px"><a href="/wiki/Magn%C3%A9tisme" title="Magnétisme">Magnétisme</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Bobine_(%C3%A9lectricit%C3%A9)" title="Bobine (électricité)">Bobine</a></li> <li><a href="/wiki/Circuit_magn%C3%A9tique" title="Circuit magnétique">Circuit magnétique</a></li> <li><a href="/wiki/Domaine_de_Weiss" title="Domaine de Weiss">Domaine de Weiss</a></li> <li><a href="/wiki/Inversion_du_champ_magn%C3%A9tique_terrestre" title="Inversion du champ magnétique terrestre">Inversion du champ magnétique terrestre</a></li> <li><a href="/wiki/Loi_de_Curie" title="Loi de Curie">Loi de Curie</a></li> <li><a href="/wiki/Loi_de_Curie-Weiss" title="Loi de Curie-Weiss">Loi de Curie-Weiss</a></li> <li><a href="/wiki/Perm%C3%A9abilit%C3%A9_magn%C3%A9tique" title="Perméabilité magnétique">Perméabilité magnétique</a></li> <li><a href="/wiki/Susceptibilit%C3%A9_magn%C3%A9tique" title="Susceptibilité magnétique">Susceptibilité magnétique</a></li> <li>Comportements magnétiques <ul><li><a href="/wiki/Altermagn%C3%A9tisme" title="Altermagnétisme">Altermagnétisme</a></li> <li><a href="/wiki/Antiferromagn%C3%A9tisme" title="Antiferromagnétisme">Antiferromagnétisme</a></li> <li><a class="mw-selflink selflink">Diamagnétisme</a></li> <li><a href="/wiki/Ferrimagn%C3%A9tisme" title="Ferrimagnétisme">Ferrimagnétisme</a></li> <li><a href="/wiki/Ferromagn%C3%A9tisme" title="Ferromagnétisme">Ferromagnétisme</a></li> <li><a href="/wiki/H%C3%A9limagn%C3%A9tisme" title="Hélimagnétisme">Hélimagnétisme</a></li> <li><a href="/wiki/Paramagn%C3%A9tisme" title="Paramagnétisme">Paramagnétisme</a></li> <li><a href="/wiki/Superparamagn%C3%A9tisme" title="Superparamagnétisme">Superparamagnétisme</a></li> <li><a href="/wiki/Verre_de_spin" title="Verre de spin">Verre de spin</a></li></ul></li></ul> </div></td> </tr> <tr> <td class="navbox-banner" style="" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Automatique" title="Automatique">Automatique</a></li> <li><a href="/wiki/%C3%89lectricit%C3%A9" title="Électricité">Électricité</a></li> <li><a href="/wiki/%C3%89lectrochimie" title="Électrochimie">Électrochimie</a></li> <li><a href="/wiki/%C3%89lectronique_(technique)" title="Électronique (technique)">Électronique</a></li> <li><a href="/wiki/%C3%89lectrotechnique" title="Électrotechnique">Électrotechnique</a></li> <li><a href="/wiki/Robotique" title="Robotique">Robotique</a></li> <li><a href="/wiki/Traitement_du_signal" title="Traitement du signal">Traitement du signal</a></li></ul> </div></td></tr></tbody></table> </div> 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