Elektromanyetizmanın eşdeğişim formülasyonu

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çubuğuna taşı</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">gizle</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Giriş</div> </a> </li> <li id="toc-Eşdeğişimli_cisimler" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Eşdeğişimli_cisimler"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Eşdeğişimli cisimler</span> </div> </a> <button aria-controls="toc-Eşdeğişimli_cisimler-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>Eşdeğişimli cisimler alt bölümünü aç/kapa</span> </button> <ul id="toc-Eşdeğişimli_cisimler-sublist" class="vector-toc-list"> <li id="toc-Hazırlık_4-vektör" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hazırlık_4-vektör"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Hazırlık 4-vektör</span> </div> </a> <ul id="toc-Hazırlık_4-vektör-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elektromanyetik_tensör" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektromanyetik_tensör"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Elektromanyetik tensör</span> </div> </a> <ul id="toc-Elektromanyetik_tensör-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-dört_boyutlu_Akım_Vektörü" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#dört_boyutlu_Akım_Vektörü"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>dört boyutlu Akım Vektörü</span> </div> </a> <ul id="toc-dört_boyutlu_Akım_Vektörü-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-dört_boyutlu_Potansiyel" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#dört_boyutlu_Potansiyel"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>dört boyutlu Potansiyel</span> </div> </a> <ul id="toc-dört_boyutlu_Potansiyel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elektromanyetik_gerilim–enerji_tensöru" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektromanyetik_gerilim–enerji_tensöru"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Elektromanyetik gerilim–enerji tensöru</span> </div> </a> <ul id="toc-Elektromanyetik_gerilim–enerji_tensöru-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vakum_koşullarında_Maxwell_denklemleri" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Vakum_koşullarında_Maxwell_denklemleri"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Vakum koşullarında Maxwell denklemleri</span> </div> </a> <button aria-controls="toc-Vakum_koşullarında_Maxwell_denklemleri-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>Vakum koşullarında Maxwell denklemleri alt bölümünü aç/kapa</span> </button> <ul id="toc-Vakum_koşullarında_Maxwell_denklemleri-sublist" class="vector-toc-list"> <li id="toc-Lorenz_ölçüsünde_Maxwell_denklemleri" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lorenz_ölçüsünde_Maxwell_denklemleri"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Lorenz ölçüsünde Maxwell denklemleri</span> </div> </a> <ul id="toc-Lorenz_ölçüsünde_Maxwell_denklemleri-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Lorentz_kuvveti" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lorentz_kuvveti"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lorentz kuvveti</span> </div> </a> <button aria-controls="toc-Lorentz_kuvveti-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>Lorentz kuvveti alt bölümünü aç/kapa</span> </button> <ul id="toc-Lorentz_kuvveti-sublist" class="vector-toc-list"> <li id="toc-Yüklü_parçacık" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Yüklü_parçacık"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Yüklü parçacık</span> </div> </a> <ul id="toc-Yüklü_parçacık-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Yükün_devamlılığı" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Yükün_devamlılığı"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Yükün devamlılığı</span> </div> </a> <ul id="toc-Yükün_devamlılığı-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Korunum_yasaları" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Korunum_yasaları"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Korunum yasaları</span> </div> </a> <button aria-controls="toc-Korunum_yasaları-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>Korunum yasaları alt bölümünü aç/kapa</span> </button> <ul id="toc-Korunum_yasaları-sublist" class="vector-toc-list"> <li id="toc-Elektrik_yükü" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektrik_yükü"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Elektrik yükü</span> </div> </a> <ul id="toc-Elektrik_yükü-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-elektromanyetik_enerji–momentum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#elektromanyetik_enerji–momentum"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>elektromanyetik enerji–momentum</span> </div> </a> <ul id="toc-elektromanyetik_enerji–momentum-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Madde_içimdeki_eşdeğişimli_objeler" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Madde_içimdeki_eşdeğişimli_objeler"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Madde içimdeki eşdeğişimli objeler</span> </div> </a> <button aria-controls="toc-Madde_içimdeki_eşdeğişimli_objeler-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>Madde içimdeki eşdeğişimli objeler alt bölümünü aç/kapa</span> </button> <ul id="toc-Madde_içimdeki_eşdeğişimli_objeler-sublist" class="vector-toc-list"> <li id="toc-Serbest_ve_bağlı_dörtlü_akımları" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Serbest_ve_bağlı_dörtlü_akımları"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Serbest ve bağlı dörtlü akımları</span> </div> </a> <ul id="toc-Serbest_ve_bağlı_dörtlü_akımları-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Manyetizasyon-polarizasyon_tensörü" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Manyetizasyon-polarizasyon_tensörü"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Manyetizasyon-polarizasyon tensörü</span> </div> </a> <ul id="toc-Manyetizasyon-polarizasyon_tensörü-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elektriksel_yerdeğiştirme_tensörü" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektriksel_yerdeğiştirme_tensörü"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Elektriksel yerdeğiştirme tensörü</span> </div> </a> <ul id="toc-Elektriksel_yerdeğiştirme_tensörü-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Madde_içinde_Maxwell_denklemleri" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Madde_içinde_Maxwell_denklemleri"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Madde içinde Maxwell denklemleri</span> </div> </a> <button aria-controls="toc-Madde_içinde_Maxwell_denklemleri-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>Madde içinde Maxwell denklemleri alt bölümünü aç/kapa</span> </button> <ul id="toc-Madde_içinde_Maxwell_denklemleri-sublist" class="vector-toc-list"> <li id="toc-Geleneksel_Denklemler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geleneksel_Denklemler"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Geleneksel Denklemler</span> </div> </a> <ul id="toc-Geleneksel_Denklemler-sublist" class="vector-toc-list"> <li id="toc-Vakum" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Vakum"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1</span> <span>Vakum</span> </div> </a> <ul id="toc-Vakum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Madde" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Madde"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.2</span> <span>Madde</span> </div> </a> <ul id="toc-Madde-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Klasik_elektrodinamik_için_Lagrangian" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Klasik_elektrodinamik_için_Lagrangian"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Klasik elektrodinamik için Lagrangian</span> </div> </a> <button aria-controls="toc-Klasik_elektrodinamik_için_Lagrangian-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>Klasik elektrodinamik için Lagrangian alt bölümünü aç/kapa</span> </button> <ul id="toc-Klasik_elektrodinamik_için_Lagrangian-sublist" class="vector-toc-list"> <li id="toc-Vakum_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vakum_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Vakum</span> </div> </a> <ul id="toc-Vakum_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Madde_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Madde_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Madde</span> </div> </a> <ul id="toc-Madde_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Aynı_zamanda_bunlara_da_bakmanız_yararlı_olacaktır_(Kaynaklar_İngilizcedir)" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Aynı_zamanda_bunlara_da_bakmanız_yararlı_olacaktır_(Kaynaklar_İngilizcedir)"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Aynı zamanda bunlara da bakmanız yararlı olacaktır (Kaynaklar İngilizcedir)</span> </div> </a> <ul id="toc-Aynı_zamanda_bunlara_da_bakmanız_yararlı_olacaktır_(Kaynaklar_İngilizcedir)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kaynakça" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Kaynakça"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Kaynakça</span> </div> </a> <ul id="toc-Kaynakça-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konuyla_ilgili_yayınlar" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Konuyla_ilgili_yayınlar"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Konuyla ilgili yayınlar</span> </div> </a> <ul id="toc-Konuyla_ilgili_yayınlar-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="İçindekiler" 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="İçindekiler tablosunu değiştir" > <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">İçindekiler tablosunu değiştir</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">Elektromanyetizmanın eşdeğişim formülasyonu</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="Başka bir dildeki sayfaya gidin. 9 dilde mevcut" > <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-9" 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">9 dil</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%B5%D9%8A%D8%BA%D8%A9_%D9%85%D8%AA%D8%BA%D9%8A%D8%B1%D8%A9_%D9%84%D9%84%D9%83%D9%87%D8%B1%D9%88%D9%85%D8%BA%D9%86%D8%A7%D8%B7%D9%8A%D8%B3%D9%8A%D8%A9_%D8%A7%D9%84%D9%83%D9%84%D8%A7%D8%B3%D9%8A%D9%83%D9%8A%D8%A9" title="صيغة متغيرة للكهرومغناطيسية الكلاسيكية - Arapça" lang="ar" hreflang="ar" data-title="صيغة متغيرة للكهرومغناطيسية الكلاسيكية" data-language-autonym="العربية" data-language-local-name="Arapça" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A6%BF%E0%A6%B0%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A4_%E0%A6%A4%E0%A6%A1%E0%A6%BC%E0%A6%BF%E0%A7%8E%E0%A6%9A%E0%A7%81%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%95%E0%A6%A4%E0%A7%8D%E0%A6%AC%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A6%B9-%E0%A6%AD%E0%A7%87%E0%A6%A6%E0%A6%BE%E0%A6%82%E0%A6%95%E0%A6%AD%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A8" title="চিরায়ত তড়িৎচুম্বকত্বের সহ-ভেদাংকভিত্তিক সূত্রায়ন - Bengalce" lang="bn" hreflang="bn" data-title="চিরায়ত তড়িৎচুম্বকত্বের সহ-ভেদাংকভিত্তিক সূত্রায়ন" data-language-autonym="বাংলা" data-language-local-name="Bengalce" 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/Formulaci%C3%B3_covariant_de_l%27electrodin%C3%A0mica_cl%C3%A0ssica" title="Formulació covariant de l'electrodinàmica clàssica - Katalanca" lang="ca" hreflang="ca" data-title="Formulació covariant de l'electrodinàmica clàssica" data-language-autonym="Català" data-language-local-name="Katalanca" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism - İngilizce" lang="en" hreflang="en" data-title="Covariant formulation of classical electromagnetism" data-language-autonym="English" data-language-local-name="İngilizce" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Klassikalise_elektromagnetismi_kovariantne_formuleering" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="tr" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r33092931">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid #aaa;padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output 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.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:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar sidebar-collapse nomobile hlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Elektromanyetizma" title="Elektromanyetizma">Elektromanyetizma</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Dosya:VFPt_Solenoid_correct2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/220px-VFPt_Solenoid_correct2.svg.png" decoding="async" width="220" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/330px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/440px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Elektrik" title="Elektrik">Elektrik</a></li> <li><a href="/wiki/M%C4%B1knat%C4%B1sl%C4%B1k" title="Mıknatıslık">Manyetizma</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><a href="/wiki/Elektrostatik" title="Elektrostatik">Elektrostatik</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Elektriksel_y%C3%BCk" class="mw-redirect" title="Elektriksel yük">Elektriksel yük</a></li> <li><a href="/wiki/Statik_elektrik" title="Statik elektrik">Statik elektrik</a></li> <li><a href="/wiki/Coulomb_yasas%C4%B1" class="mw-redirect" title="Coulomb yasası">Coulomb yasası</a></li> <li><a href="/wiki/Elektriksel_alan" class="mw-redirect" title="Elektriksel alan">Elektriksel alan</a></li> <li><a href="/wiki/Elektrik_ak%C4%B1s%C4%B1" title="Elektrik akısı">Elektrik akısı</a></li> <li><a href="/wiki/Gauss_yasas%C4%B1" title="Gauss yasası">Gauss yasası</a></li> <li><a href="/wiki/Elektriksel_potansiyel_enerji" title="Elektriksel potansiyel enerji">Elektriksel potansiyel enerji</a></li> <li><a href="/wiki/Elektrik_potansiyeli" title="Elektrik potansiyeli">Elektrik potansiyeli</a></li> <li><a href="/w/index.php?title=Elektrostatik_ind%C3%BCksiyon&action=edit&redlink=1" class="new" title="Elektrostatik indüksiyon (sayfa mevcut değil)">Elektrostatik indüksiyon</a></li> <li><a href="/w/index.php?title=Elektrik_%C3%A7ift_kutup_momenti&action=edit&redlink=1" class="new" title="Elektrik çift kutup momenti (sayfa mevcut değil)">Elektrik çift kutup momenti</a></li> <li><a href="/w/index.php?title=Kutuplanma_yo%C4%9Funlu%C4%9Fu&action=edit&redlink=1" class="new" title="Kutuplanma yoğunluğu (sayfa mevcut değil)">Kutuplanma yoğunluğu</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><a href="/wiki/Magnetostatik" title="Magnetostatik">Magnetostatik</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Amp%C3%A8re_yasas%C4%B1" class="mw-redirect" title="Ampère yasası">Ampère yasası</a></li> <li><a href="/wiki/Elektrik_ak%C4%B1m%C4%B1" title="Elektrik akımı">Elektrik akımı</a></li> <li><a href="/wiki/Manyetik_alan" title="Manyetik alan">Manyetik alan</a></li> <li><a href="/wiki/M%C4%B1knat%C4%B1slanma" title="Mıknatıslanma">Mıknatıslanma</a></li> <li><a href="/wiki/Manyetik_ak%C4%B1" title="Manyetik akı">Manyetik akı</a></li> <li><a href="/wiki/Biot-savart_yasas%C4%B1" title="Biot-savart yasası">Biot-savart yasası</a></li> <li><a href="/wiki/Manyetik_moment" title="Manyetik moment">Manyetik moment</a></li> <li><a href="/wiki/Manyetizma_i%C3%A7in_Gauss_yasas%C4%B1" title="Manyetizma için Gauss yasası">Manyetizma için Gauss yasası</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title">Elektrodinamik</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Lorentz_kuvveti" title="Lorentz kuvveti">Lorentz kuvveti</a></li> <li><a href="/wiki/Elektromotor_kuvvet" title="Elektromotor kuvvet">Elektromotor kuvvet</a></li> <li><a href="/wiki/Elektromanyetik_ind%C3%BCksiyon" title="Elektromanyetik indüksiyon">Elektromanyetik indüksiyon</a></li> <li><a href="/wiki/Faraday%27in_ind%C3%BCksiyon_kanunu" title="Faraday'in indüksiyon kanunu">Faraday yasası</a></li> <li><a href="/wiki/Lenz_yasas%C4%B1" title="Lenz yasası">Lenz yasası</a></li> <li><a href="/wiki/Yer_de%C4%9Fi%C5%9Ftirme_ak%C4%B1m%C4%B1" title="Yer değiştirme akımı">Yer değiştirme akımı</a></li> <li><a href="/wiki/Maxwell_denklemleri" title="Maxwell denklemleri">Maxwell denklemleri</a></li> <li><a href="/wiki/Elektromanyetik_alan" title="Elektromanyetik alan">EM alan</a></li> <li><a href="/wiki/Elektromanyetik_radyasyon" title="Elektromanyetik radyasyon">Elektromanyetik radyasyon</a></li> <li><a href="/w/index.php?title=Maxwell_stres_tens%C3%B6r%C3%BC&action=edit&redlink=1" class="new" title="Maxwell stres tensörü (sayfa mevcut değil)">Maxwell tensörü</a></li> <li><a href="/wiki/Poynting_vekt%C3%B6r%C3%BC" title="Poynting vektörü">Poynting vektörü</a></li> <li><a href="/wiki/Li%C3%A9nard-Wiechert_potansiyelleri" title="Liénard-Wiechert potansiyelleri">Liénard-Wiechert potansiyelleri</a></li> <li><a href="/w/index.php?title=Jefimenko_denklemleri&action=edit&redlink=1" class="new" title="Jefimenko denklemleri (sayfa mevcut değil)">Jefimenko denklemleri</a></li> <li><a href="/wiki/Eddy_ak%C4%B1m%C4%B1" title="Eddy akımı">Eddy akımı</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><a href="/wiki/Elektrik_devresi" title="Elektrik devresi">Elektrik devresi</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Elektriksel_%C3%B6zdiren%C3%A7_ve_iletkenlik" title="Elektriksel özdirenç ve iletkenlik">Direnç</a></li> <li><a href="/wiki/Kapasite_(elektrik)" title="Kapasite (elektrik)">Kapasite</a></li> <li><a href="/wiki/%C4%B0nd%C3%BCktans" title="İndüktans">İndüktans</a></li> <li><a href="/wiki/Empedans" class="mw-redirect" title="Empedans">Empedans</a></li> <li><a href="/wiki/Dalga_rehberi" title="Dalga rehberi">Dalga rehberi</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title">Bilim adamları</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Andre_Marie_Ampere" title="Andre Marie Ampere">Ampère</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</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/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Rudolf_Hertz" class="mw-redirect" title="Heinrich Rudolf Hertz">Hertz</a></li> <li><a href="/wiki/Hendrik_A._Lorentz" class="mw-redirect" title="Hendrik A. Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" class="mw-redirect" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r25548259">.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-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}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="plainlinks hlist navbar navbar-mini"><ul><li class="nv-view"><a href="/wiki/%C5%9Eablon:Elektromanyetizma" title="Şablon:Elektromanyetizma"><abbr title="Bu şablonu görüntüle">g</abbr></a></li><li class="nv-talk"><a href="/wiki/%C5%9Eablon_tart%C4%B1%C5%9Fma:Elektromanyetizma" title="Şablon tartışma:Elektromanyetizma"><abbr title="Bu şablonu tartış">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://tr.wikipedia.org/w/index.php?title=%C5%9Eablon:Elektromanyetizma&action=edit"><abbr title="Bu şablonu değiştir">d</abbr></a></li></ul></div></td></tr></tbody></table> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Elektromanyetik_alan%C4%B1n_matematiksel_g%C3%B6sterimleri&action=edit&redlink=1" class="new" title="Elektromanyetik alanın matematiksel gösterimleri (sayfa mevcut değil)">Elektromanyetik alanın matematiksel gösterimleri</a></div> <p>Klasik manyetizmanın eşdeğişimli formülasyonu klasik elektromanyetizma kanunlarının(özellikle de, Maxwell denklemlerini ve Lorentz kuvvetinin) Lorentz dönüşümlerine göre açıkça varyanslarının olmadığı, rektilineer eylemsiz koordinat sistemleri kullanılarak özel görelilik disiplini çerçevesinde yazılma sekillerini ima eder. Bu ifadeler hem klasik elektromanyetizma kanunlarının herhangi bir eylemsiz koordinat sisteminde aynı formu aldıklarını kanıtlamakta kolaylık sağlar hem de alanların ve kuvvetlerin bir referans sisteminden başka bir referans sistemine uyarlanması için bir yol sağlar. Bununla birlikte, bu Maxwell denklemlerinin uzay ve zamanda bükülmesi ya da rektilineer olmayan koordinat sistemleri kadar genel değildir. </p><p>Bu makalede tensörlerin uzaysal birleşenleri için (vektörler de dahil) SI birimleri kullanılmıştır, tensörlerin klasik kullanımı ve geleneksel Einstein toplamı ve Minkowski metriği (+1, −1, −1, −1) şeklindedir. Denklemlerin vakum koşullarına göre özelleştirildiği yerde, onlara Maxwell denklemlerinin toplam yük ve akım cinsinden formülasyonu olarak bakılabilir. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Eşdeğişimli_cisimler"><span id="E.C5.9Fde.C4.9Fi.C5.9Fimli_cisimler"></span>Eşdeğişimli cisimler</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=1" title="Değiştirilen bölüm: Eşdeğişimli cisimler" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=1" title="Bölümün kaynak kodunu değiştir: Eşdeğişimli cisimler"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hazırlık_4-vektör"><span id="Haz.C4.B1rl.C4.B1k_4-vekt.C3.B6r"></span>Hazırlık 4-vektör</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=2" title="Değiştirilen bölüm: Hazırlık 4-vektör" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=2" title="Bölümün kaynak kodunu değiştir: Hazırlık 4-vektör"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Lorentz_kovaryans%C4%B1&action=edit&redlink=1" class="new" title="Lorentz kovaryansı (sayfa mevcut değil)">Lorentz kovaryansı</a></div> <p>Arka plan bilgi maksadıyla, elektromanyetizmaya direkt olarak bağlı olmayan, fakat bu makalenin anlaşılması için yararlı olacak dört boyutlu vektörden üçünü sunuyoruz: </p> <ul><li>Metre cinsinden, "pozisyon" yahut "koordinat" dört boyutlu vektörü</li></ul> <dl><dd><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 x^{\alpha }=(ct,x,y,z)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>c</mi> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{\alpha }=(ct,x,y,z)\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bab85e96bc84ad54ff78ff841048b616398aff47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.077ex; height:2.843ex;" alt="{\displaystyle x^{\alpha }=(ct,x,y,z)\,.}"></span></dd></dl></dd></dl> <ul><li>Metre·saniye<sup>−1</sup> cinsinden, hız dört boyutlu vektörü (başka bir deyişle dört boyutlu hız vektörü)</li></ul> <dl><dd><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 u^{\alpha }=\gamma (c,\mathbf {u} )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>c</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u^{\alpha }=\gamma (c,\mathbf {u} )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0f84c4cf3fc5f566668b467495982fe76c12ad8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.697ex; height:2.843ex;" alt="{\displaystyle u^{\alpha }=\gamma (c,\mathbf {u} )\,}"></span></dd></dl></dd> <dd>γ(<b>u</b>) 'nin Lorentz çarpanı olduğu yerde üç boyutlu hız vektörü <b>u</b> 'dur.</dd></dl> <ul><li>kilogram·metre·saniye<sup>−1</sup> cinsinden, bir parçacığın dört boyutlu momentum vektörü (başka bir deyişle momentum dört boyutlu vektörü)</li></ul> <dl><dd><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 p_{\alpha }=(E/c,-\mathbf {p} )=mu_{\alpha }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> <mo>,</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>m</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\alpha }=(E/c,-\mathbf {p} )=mu_{\alpha }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fd690eb8c72f50f8ee64b6fadb8ea676ed27ca8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:23.863ex; height:2.843ex;" alt="{\displaystyle p_{\alpha }=(E/c,-\mathbf {p} )=mu_{\alpha }\,}"></span></dd></dl></dd> <dd><b>p</b> üç boyutlu momentum olduğu yerde, <i>E</i> kinetik enerjidir, ve<i>m</i> parçacığın durgun kütlesidir.</dd></dl> <ul><li>metre<sup>−1</sup> cinsinden the dört boyutlu eğim</li></ul> <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 \partial ^{\nu }={\frac {\partial }{\partial x_{\nu }}}=\left({\frac {1}{c}}{\frac {\partial }{\partial t}},-\mathbf {\nabla } \right)\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∇</mi> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial ^{\nu }={\frac {\partial }{\partial x_{\nu }}}=\left({\frac {1}{c}}{\frac {\partial }{\partial t}},-\mathbf {\nabla } \right)\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b993befa5535f71b712a244b9d26a4ee5df3dc09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.844ex; height:6.176ex;" alt="{\displaystyle \partial ^{\nu }={\frac {\partial }{\partial x_{\nu }}}=\left({\frac {1}{c}}{\frac {\partial }{\partial t}},-\mathbf {\nabla } \right)\,,}"></span></dd></dl> <ul><li>Metre cinsinden<sup>−2</sup> d'Alembertian operatörü: <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 \Box }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>◻</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Box }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/029b77f09ebeaf7528fc831fe57848be51f2240b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Box }"></span> şeklinde gösterilir.</li></ul> <p>Sıralanan tensör analizlerindeki işaretler tensörler için geleneksel bir kullanımdır. Buradaki geleneksel kullanım Minkowski tensörüne tekabül eden <tt>+---</tt> kullanımıdır: </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 \eta ^{\mu \nu }={\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta ^{\mu \nu }={\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7e714ab176f5fdc2e56da8333110d9f4afec50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:28.614ex; height:12.509ex;" alt="{\displaystyle \eta ^{\mu \nu }={\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}\,}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Elektromanyetik_tensör"><span id="Elektromanyetik_tens.C3.B6r"></span>Elektromanyetik tensör</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=3" title="Değiştirilen bölüm: Elektromanyetik tensör" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=3" title="Bölümün kaynak kodunu değiştir: Elektromanyetik tensör"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Elektromanyetik_tens%C3%B6r&action=edit&redlink=1" class="new" title="Elektromanyetik tensör (sayfa mevcut değil)">elektromanyetik tensör</a></div> <p>Elektro manyetik tensör manyetik ve elektrik alanların bir eşdeğişimli antisimetrikmetrik tensörün içindeki kombinasyonudur. volt·saniye·metre<sup>−2</sup> cinsinden, alan kuvvet tensörü alanlar cinsinden şu şekilde yazılır:<sup id="cite_ref-Vanderlinde_1-0" class="reference"><a href="#cite_note-Vanderlinde-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\alpha \beta }=\left({\begin{matrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\alpha \beta }=\left({\begin{matrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/609e7e6d418e823fbdb41e2595071f9a978d4fb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:40.734ex; height:13.509ex;" alt="{\displaystyle F_{\alpha \beta }=\left({\begin{matrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,}"></span></dd></dl> <p>ve dizinlerinin yükseltilmesinin sonucu </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F^{\mu \nu }\,{\stackrel {\mathrm {def} }{=}}\,\eta ^{\mu \alpha }\,F_{\alpha \beta }\,\eta ^{\beta \nu }=\left({\begin{matrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }\,{\stackrel {\mathrm {def} }{=}}\,\eta ^{\mu \alpha }\,F_{\alpha \beta }\,\eta ^{\beta \nu }=\left({\begin{matrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/accf053036b7936e6fb9861c89e4bfb532570d44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:59.766ex; height:13.509ex;" alt="{\displaystyle F^{\mu \nu }\,{\stackrel {\mathrm {def} }{=}}\,\eta ^{\mu \alpha }\,F_{\alpha \beta }\,\eta ^{\beta \nu }=\left({\begin{matrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{matrix}}\right)\,.}"></span> 'dur.</dd></dl> <p><b>E</b> 'nin enerjiyi gösterdiği yerde elektrik alan, <b>B</b> 'dir ve <i>c</i> ışık hızıdır. </p> <div class="mw-heading mw-heading3"><h3 id="dört_boyutlu_Akım_Vektörü"><span id="d.C3.B6rt_boyutlu_Ak.C4.B1m_Vekt.C3.B6r.C3.BC"></span>dört boyutlu Akım Vektörü</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=4" title="Değiştirilen bölüm: dört boyutlu Akım Vektörü" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=4" title="Bölümün kaynak kodunu değiştir: dört boyutlu Akım Vektörü"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=D%C3%B6rt_boyutlu_Ak%C4%B1m_Vekt%C3%B6r%C3%BC&action=edit&redlink=1" class="new" title="Dört boyutlu Akım Vektörü (sayfa mevcut değil)">dört boyutlu Akım Vektörü</a></div> <p>dört boyutlu akım vektörü elektrik akım yoğunluğu <b>J</b> ile elektrik yük yoğunluğunu ρ birleştiren kontravaryant dört boyutlu vektörüdür. amper·metre<sup>−2</sup> cinsinden, </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 J^{\alpha }=\,(c\rho ,\mathbf {J} )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>c</mi> <mi>ρ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J^{\alpha }=\,(c\rho ,\mathbf {J} )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa7cc06d975c792901400858ca3e53ed481a1239" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.115ex; height:2.843ex;" alt="{\displaystyle J^{\alpha }=\,(c\rho ,\mathbf {J} )\,}"></span></dd></dl> <p>şeklinde gösterilir. </p> <div class="mw-heading mw-heading3"><h3 id="dört_boyutlu_Potansiyel"><span id="d.C3.B6rt_boyutlu_Potansiyel"></span>dört boyutlu Potansiyel</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=5" title="Değiştirilen bölüm: dört boyutlu Potansiyel" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=5" title="Bölümün kaynak kodunu değiştir: dört boyutlu Potansiyel"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=D%C3%B6rt_boyutlu_potansiyel&action=edit&redlink=1" class="new" title="Dört boyutlu potansiyel (sayfa mevcut değil)">dört boyutlu potansiyel</a></div> <p>volt·saniye·metre<sup>−1</sup> cinsinden, elektromanyetik dört boyutlu potansiyel bir eşdeğişimli dört boyutlu vektördür ve elektriksel potansiyeli (başka bir deyişle skaler potansiyel) φ ve manyetik vektör potansiyeli (başka bir deyişle vektör potansiyeli) <b>A</b> içerir ve şu şekilde formüle edilir: </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 A_{\alpha }=\left(\phi /c,-\mathbf {A} \right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> <mo>,</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\alpha }=\left(\phi /c,-\mathbf {A} \right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e5b0804f02e2b7c6950811eddf11eb3e319ac7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.738ex; height:2.843ex;" alt="{\displaystyle A_{\alpha }=\left(\phi /c,-\mathbf {A} \right)\,}"></span></dd></dl> <p>Elektromanyetik alanla elektromanyetik ilişki arasındaki ilişki bu denklemle gösterilir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\alpha \beta }=\partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mo>−</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\alpha \beta }=\partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53561ed5c438af3dd5c0a2e17fd3402f5511773d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.918ex; height:2.843ex;" alt="{\displaystyle F_{\alpha \beta }=\partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }\,}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Elektromanyetik_gerilim–enerji_tensöru"><span id="Elektromanyetik_gerilim.E2.80.93enerji_tens.C3.B6ru"></span>Elektromanyetik gerilim–enerji tensöru</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=6" title="Değiştirilen bölüm: Elektromanyetik gerilim–enerji tensöru" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=6" title="Bölümün kaynak kodunu değiştir: Elektromanyetik gerilim–enerji tensöru"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Elektromanyetik_gerilim%E2%80%93enerji_tens%C3%B6r&action=edit&redlink=1" class="new" title="Elektromanyetik gerilim–enerji tensör (sayfa mevcut değil)">elektromanyetik gerilim–enerji tensör</a></div> <p>The elektromanyetik gerilim–enerji tensörü dört boyutlu mometum vektörünün akısı (yoğunluğu) olarak düşünülebilir ve elektromanyetik alanların toplam gerilim–enerji tensörüne katkısı olan bir kontravaryant si tensördür. joule·metre<sup>−3</sup> cinsinden şu şekilde gösterilir </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 T^{\alpha \beta }={\begin{pmatrix}\epsilon _{0}E^{2}/2+B^{2}/2\mu _{0}&S_{x}/c&S_{y}/c&S_{z}/c\\S_{x}/c&-\sigma _{xx}&-\sigma _{xy}&-\sigma _{xz}\\S_{y}/c&-\sigma _{yx}&-\sigma _{yy}&-\sigma _{yz}\\S_{z}/c&-\sigma _{zx}&-\sigma _{zy}&-\sigma _{zz}\end{pmatrix}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>ϵ</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 class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{\alpha \beta }={\begin{pmatrix}\epsilon _{0}E^{2}/2+B^{2}/2\mu _{0}&S_{x}/c&S_{y}/c&S_{z}/c\\S_{x}/c&-\sigma _{xx}&-\sigma _{xy}&-\sigma _{xz}\\S_{y}/c&-\sigma _{yx}&-\sigma _{yy}&-\sigma _{yz}\\S_{z}/c&-\sigma _{zx}&-\sigma _{zy}&-\sigma _{zz}\end{pmatrix}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2f523659027ed7720afe49e71b7d3e99a57fe0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; margin-top: -0.234ex; width:52.279ex; height:13.509ex;" alt="{\displaystyle T^{\alpha \beta }={\begin{pmatrix}\epsilon _{0}E^{2}/2+B^{2}/2\mu _{0}&S_{x}/c&S_{y}/c&S_{z}/c\\S_{x}/c&-\sigma _{xx}&-\sigma _{xy}&-\sigma _{xz}\\S_{y}/c&-\sigma _{yx}&-\sigma _{yy}&-\sigma _{yz}\\S_{z}/c&-\sigma _{zx}&-\sigma _{zy}&-\sigma _{zz}\end{pmatrix}}\,}"></span></dd></dl> <pre>ε<sub>0</sub> vakumlu ortamın elektrik geçirgenliği olduğu yerde, μ<sub>0</sub> da vakumlu ortamın manyetik geçirgenliğidir, Poynting vectorü watt·metre<sup>−2</sup> cinsinden </pre> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} ={\frac {1}{\mu _{0}}}\mathbf {E} \times \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} ={\frac {1}{\mu _{0}}}\mathbf {E} \times \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ac6532f39a4f6fbc482514fcf7b2b2a54f0f888" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.374ex; height:5.676ex;" alt="{\displaystyle \mathbf {S} ={\frac {1}{\mu _{0}}}\mathbf {E} \times \mathbf {B} }"></span> 'dir.</dd></dl> <p>ve Maxwell gerilim tensörü in joule·metre<sup>−3</sup> cinsinden şu şekilde gösterilir </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 \sigma _{ij}=\epsilon _{0}E_{i}E_{j}+{\frac {1}{\mu _{0}}}B_{i}B_{j}-\left({\frac {1}{2}}\epsilon _{0}E^{2}+{\frac {1}{2\mu _{0}}}B^{2}\right)\delta _{ij}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>ϵ</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> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{ij}=\epsilon _{0}E_{i}E_{j}+{\frac {1}{\mu _{0}}}B_{i}B_{j}-\left({\frac {1}{2}}\epsilon _{0}E^{2}+{\frac {1}{2\mu _{0}}}B^{2}\right)\delta _{ij}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66ed799fc325de35234f79f5b78fb11d0530042" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:51.561ex; height:6.176ex;" alt="{\displaystyle \sigma _{ij}=\epsilon _{0}E_{i}E_{j}+{\frac {1}{\mu _{0}}}B_{i}B_{j}-\left({\frac {1}{2}}\epsilon _{0}E^{2}+{\frac {1}{2\mu _{0}}}B^{2}\right)\delta _{ij}\,.}"></span></dd></dl> <p>The elektromanyetik alan tensörü <i>F</i> elektromanyetik gerilim–enerji tensörünü <i>T</i> aşağıdaki formülle oluşturur: </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 T^{\alpha \beta }={\frac {1}{\mu _{0}}}\left(\eta _{\gamma \nu }F^{\alpha \gamma }F^{\nu \beta }-{\frac {1}{4}}\eta ^{\alpha \beta }F_{\gamma \nu }F^{\gamma \nu }\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>γ</mi> </mrow> </msup> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>β</mi> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mi>ν</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{\alpha \beta }={\frac {1}{\mu _{0}}}\left(\eta _{\gamma \nu }F^{\alpha \gamma }F^{\nu \beta }-{\frac {1}{4}}\eta ^{\alpha \beta }F_{\gamma \nu }F^{\gamma \nu }\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d043a468de92d9e9a1436c87dafa948697231aa2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.688ex; height:6.176ex;" alt="{\displaystyle T^{\alpha \beta }={\frac {1}{\mu _{0}}}\left(\eta _{\gamma \nu }F^{\alpha \gamma }F^{\nu \beta }-{\frac {1}{4}}\eta ^{\alpha \beta }F_{\gamma \nu }F^{\gamma \nu }\right)}"></span></dd></dl> <p>η'nin Minkowski metrik tensörü olduğunu düşünürsek. Fark edilmesi gereken önemli bir nokta ise burada Maxwell denklemleri tarafından tahmin edilen </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 \epsilon _{0}\mu _{0}c^{2}=1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}\mu _{0}c^{2}=1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e2e037bc84767b34a4aba5d34345cf3dd85057b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.163ex; height:3.176ex;" alt="{\displaystyle \epsilon _{0}\mu _{0}c^{2}=1\,}"></span></dd></dl> <p>ilişkisini kullandığımızdır. </p> <div class="mw-heading mw-heading2"><h2 id="Vakum_koşullarında_Maxwell_denklemleri"><span id="Vakum_ko.C5.9Fullar.C4.B1nda_Maxwell_denklemleri"></span>Vakum koşullarında Maxwell denklemleri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=7" title="Değiştirilen bölüm: Vakum koşullarında Maxwell denklemleri" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=7" title="Bölümün kaynak kodunu değiştir: Vakum koşullarında Maxwell denklemleri"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Maxwell%27s_equations&action=edit&redlink=1" class="new" title="Maxwell's equations (sayfa mevcut değil)">Maxwell's equations</a></div> <p>Vkum koşullarında (yahut mikroskopik denklemler için, makroskopik materyal tanımlarını içermeyen) Maxwell denklemleri iki tensör denklemi olarak yazılabilir. </p><p>İki homojen olmayan Maxwell denklemi, Gauss yasası ve Amper yasası (Maxwell denklemlerinin düzeltmeleriyle) (+--- metriği ile) birleştiler :<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><a href="/w/index.php?title=%C5%9Eablon:Equation_box_1&action=edit&redlink=1" class="new" title="Şablon:Equation box 1 (sayfa mevcut değil)">Şablon:Equation box 1</a> </p><p>homojen denklemler – Faraday'ın indüksiyon yasası ve Gauss'un manyetizma yasaları şunları oluşturmak için birleşirken: </p><p><a href="/w/index.php?title=%C5%9Eablon:Equation_box_1&action=edit&redlink=1" class="new" title="Şablon:Equation box 1 (sayfa mevcut değil)">Şablon:Equation box 1</a> </p><p><i>F</i><sup>αβ</sup> 'nin elektromanyetik tensör olduğu yerde, <i>J</i><sup>α</sup> dört boyutlu akımdır, ε<sup>αβγδ</sup> Levi-Civita sembolüdür ve indeksler geleneksel Einstein toplamına göre davranır. </p><p>İlk tensör denklemi β'nin her değeri için bir tane olmak üzere dört skaler denkleme karsılık gelir. İkinci tensör denklemi aslında 4<sup>3</sup> = 64 farklı skaler denkleme karşılık gelir, fakat yalnızca dördü birbirinden bağımsızdır. elektromanyetik alanın antisimetrikmetrisini kullanarak hem bir tanımlamayı indirgenebilir (0 = 0) hem de λ, μ, ν = bunlardan herhangi biri 1,2,3 or 2,3,0 or 3,0,1 or 0,1,2 haricindeki tüm gereksiz denklemleri eleyebiliriz. </p><p>Kısmi türev için antisimetrikmetrik tensör notasyonunu ve virgül notasyonunu kullanarak f (Ricci kalkülüsüne bakın), daha uygun ikinci bir denklem şu şekilde yazılabilir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{[\alpha \beta ,\gamma ]}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>α</mi> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">]</mo> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{[\alpha \beta ,\gamma ]}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac1872f69d73faede8a76451030f2442b3d19f7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.246ex; height:3.009ex;" alt="{\displaystyle F_{[\alpha \beta ,\gamma ]}=0}"></span></dd></dl> <p>Kaynakların yetersizliğinde, Maxwell denklemleri suna indirgenir: </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 \partial ^{\nu }\partial _{\nu }F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ \,\Box F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ {1 \over c^{2}}{\partial ^{2}F^{\alpha \beta } \over {\partial t}^{2}}-\nabla ^{2}F^{\alpha \beta }=0\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mi>◻</mi> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial ^{\nu }\partial _{\nu }F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ \,\Box F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ {1 \over c^{2}}{\partial ^{2}F^{\alpha \beta } \over {\partial t}^{2}}-\nabla ^{2}F^{\alpha \beta }=0\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c03d708ae69dcd917bd82d109caa7231c926b762" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.008ex; height:6.343ex;" alt="{\displaystyle \partial ^{\nu }\partial _{\nu }F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ \,\Box F^{\alpha \beta }\,\ {\stackrel {\mathrm {def} }{=}}\ {1 \over c^{2}}{\partial ^{2}F^{\alpha \beta } \over {\partial t}^{2}}-\nabla ^{2}F^{\alpha \beta }=0\,,}"></span></dd></dl> <p>ve bu da alan kuvvet tensöründe yer alan elektromanyetik dalga denklemidir. </p> <div class="mw-heading mw-heading3"><h3 id="Lorenz_ölçüsünde_Maxwell_denklemleri"><span id="Lorenz_.C3.B6l.C3.A7.C3.BCs.C3.BCnde_Maxwell_denklemleri"></span>Lorenz ölçüsünde Maxwell denklemleri</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=8" title="Değiştirilen bölüm: Lorenz ölçüsünde Maxwell denklemleri" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=8" title="Bölümün kaynak kodunu değiştir: Lorenz ölçüsünde Maxwell denklemleri"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Lorenz_%C3%B6l%C3%A7%C3%BC_ko%C5%9Fullar%C4%B1&action=edit&redlink=1" class="new" title="Lorenz ölçü koşulları (sayfa mevcut değil)">Lorenz ölçü koşulları</a></div> <p>Lorenz ölçü koşulları Lorentz varyanssız ölçü koşullarıdır. (Bu diğer ölçü koşullarıyla karşılaştırılabilir Coulomb ölçü koşulları gibi; eğer bir eylemsiz referans sisteminde tutarsa genel olarak diğer eylemsiz referans sistemlerinde de tutar.)dört boyutlu potansiyel çinsinden aşağıdaki gibi gösterilir: </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 \partial _{\alpha }A^{\alpha }=\partial ^{\alpha }A_{\alpha }=0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\alpha }A^{\alpha }=\partial ^{\alpha }A_{\alpha }=0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f38d19654d51fc9f662194b1c69954bf70eadc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.594ex; height:2.676ex;" alt="{\displaystyle \partial _{\alpha }A^{\alpha }=\partial ^{\alpha }A_{\alpha }=0\,.}"></span></dd></dl> <pre>Lorenz ölçülerinde, mikroskopik Maxwell denklemleri şu şekilde gösterilir: </pre> <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 \Box A^{\sigma }=\mu _{0}\,J^{\sigma }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>◻</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Box A^{\sigma }=\mu _{0}\,J^{\sigma }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd6d46848670e84ff4912baf356451703b94019f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.751ex; height:2.843ex;" alt="{\displaystyle \Box A^{\sigma }=\mu _{0}\,J^{\sigma }\,}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Lorentz_kuvveti">Lorentz kuvveti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=9" title="Değiştirilen bölüm: Lorentz kuvveti" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=9" title="Bölümün kaynak kodunu değiştir: Lorentz kuvveti"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/wiki/Lorentz_kuvveti" title="Lorentz kuvveti">Lorentz kuvveti</a></div> <div class="mw-heading mw-heading3"><h3 id="Yüklü_parçacık"><span id="Y.C3.BCkl.C3.BC_par.C3.A7ac.C4.B1k"></span>Yüklü parçacık</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=10" title="Değiştirilen bölüm: Yüklü parçacık" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=10" title="Bölümün kaynak kodunu değiştir: Yüklü parçacık"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>q</i>yüklü hareket eden ve anlık hızı <b>v</b> olan bir parçacık üstündeki </p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Lorentz_force_particle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lorentz_force_particle.svg/200px-Lorentz_force_particle.svg.png" decoding="async" width="200" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lorentz_force_particle.svg/300px-Lorentz_force_particle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lorentz_force_particle.svg/400px-Lorentz_force_particle.svg.png 2x" data-file-width="325" data-file-height="345" /></a><figcaption><a href="/wiki/Lorentz_kuvveti" title="Lorentz kuvveti">Lorentz kuvveti</a> <b>f</b> </figcaption></figure><p>. The electric alan <b>E</b> ve manyetik alan <b>B</b> uzay ve zamanda değişir. </p><p>Lorentz kuvvetine göre elektromanyetik (EM) alan elektrik yüklü maddelerin hareketini etkiler.bu yolla, elektromanyetik alanlar tespit edilebilir (parçacık fiziğindeki uygulamalar ile ve doğal oluşumları ile Auroralarda olduğu gibi). Rölativistik formda, newton cinsinden Lorentz kuvvet alan kuvvet tensörünü şu şekilde kullanır.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Koordinat zamanı cinsinden ifade edilmiş <i>t</i> 'nin saniye cinsinden ölçüldüğü gösterim: </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 {dp_{\alpha } \over {dt}}=q\,F_{\alpha \beta }\,{\frac {dx^{\beta }}{dt}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>q</mi> <mspace width="thinmathspace" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {dp_{\alpha } \over {dt}}=q\,F_{\alpha \beta }\,{\frac {dx^{\beta }}{dt}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e1736e5967692c664510151ca5f16bbe68782c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.111ex; height:5.843ex;" alt="{\displaystyle {dp_{\alpha } \over {dt}}=q\,F_{\alpha \beta }\,{\frac {dx^{\beta }}{dt}}\,}"></span></dd></dl> <pre><i>p</i><sub>α</sub> 'nin yukarıda görüldüğü gibi dört boyutlu momentum olduğu koşulda, <i>q</i> coulomb cinsinden elktrik yüküdür, ve<i>x</i><sup>β</sup> metre cinsinden pozisyonu ifade eder. </pre> <p>Hareketli referans sisteminde, bu alanlar dört kuvvet olarak adlandırılır </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 {dp_{\alpha }}{d\tau }}\,=q\,F_{\alpha \beta }\,u^{\beta }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>τ</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mi>q</mi> <mspace width="thinmathspace" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dp_{\alpha }}{d\tau }}\,=q\,F_{\alpha \beta }\,u^{\beta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/523f1114332cac6d74f9fa4423d57b51332e6a9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.059ex; height:5.509ex;" alt="{\displaystyle {\frac {dp_{\alpha }}{d\tau }}\,=q\,F_{\alpha \beta }\,u^{\beta }}"></span></dd></dl> <pre>Yukarıda görüldüğü gibi <i>u</i><sup>β</sup> 'nun dört boyutlu hız olduğu yerde ve τ 'nin parçacığın koordinat zamanıyla <i>dt</i> = γ<i>d</i>τ bağıntısıyla bağlandığı zamanıdır. </pre> <div class="mw-heading mw-heading3"><h3 id="Yükün_devamlılığı"><span id="Y.C3.BCk.C3.BCn_devaml.C4.B1l.C4.B1.C4.9F.C4.B1"></span>Yükün devamlılığı</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=11" title="Değiştirilen bölüm: Yükün devamlılığı" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=11" title="Bölümün kaynak kodunu değiştir: Yükün devamlılığı"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Lorentz_force_continuum.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Lorentz_force_continuum.svg/200px-Lorentz_force_continuum.svg.png" decoding="async" width="200" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Lorentz_force_continuum.svg/300px-Lorentz_force_continuum.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Lorentz_force_continuum.svg/400px-Lorentz_force_continuum.svg.png 2x" data-file-width="348" data-file-height="437" /></a><figcaption> Hareket halindeki sürekli bir yük dağılımında (yük yoğunluğu ρ) Lorentz kuvvetini (her birim üç boyutlu hacimdeki) <b>f</b> olarak gösterelim. üç boyutlu akım yoğunluğu <b>J</b> yük elemanı <i>dq</i> 'nun hacim elemanı <i>dV</i> 'nın hareketine karşılık gelir ve devamlılık süresince değişir.</figcaption></figure> <div role="note" class="hatnote navigation-not-searchable">Ayrıca bakınız: <a href="/w/index.php?title=Continuum_mechanics&action=edit&redlink=1" class="new" title="Continuum mechanics (sayfa mevcut değil)">continuum mechanics</a></div> <p>Sürekli bir ortamda, üç boyutlu <i>kuvvet yoğunluğu</i> eşdeğişimli dört boyutlu vektörü oluşturmak için <i>güç yoğunluğuyla</i> birleşir, <i>f</i><sub>μ</sub>. Uzaysal kısım küçük hücreler (üç boyutlu uzayda) üstündeki kuvvetin hücrenin hacmiyle bölünmesinin sonucudur. Zaman bileşeni 1/<i>c</i> çarpı hücreye transfer edilen güçün hücrenin hacmine bölümüdür. Lorentz kuvvetinin yoğunluğu elektromanyetizmadan kaynaklanan kuvvet yoğunluğunun bir parçasıdır. Uzaysal bölümü şöyledir </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\mathbf {f} =-(\rho \mathbf {E} +\mathbf {J} \times \mathbf {B} )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\mathbf {f} =-(\rho \mathbf {E} +\mathbf {J} \times \mathbf {B} )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8539ea8db08a78df6e2efc1851e9fb86f2cd9ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.886ex; height:2.843ex;" alt="{\displaystyle -\mathbf {f} =-(\rho \mathbf {E} +\mathbf {J} \times \mathbf {B} )\,}"></span>.</dd></dl> <p>Açıkça eşdeğişimli notasyonu şu şekle gelir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\alpha }=F_{\alpha \beta }J^{\beta }.\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> <mo>.</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\alpha }=F_{\alpha \beta }J^{\beta }.\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aab4dbe1f9a4e4f96d6bab03a7a1c2147235a8ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.204ex; width:12.406ex; height:3.343ex;" alt="{\displaystyle f_{\alpha }=F_{\alpha \beta }J^{\beta }.\!}"></span></dd></dl> <p>Lorent kuvveti ve elektromanyetik enerji-gerilim tensörü arasındaki ilişki şöyledir </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f^{\alpha }=-{T^{\alpha \beta }}_{,\beta }\equiv -{\frac {\partial T^{\alpha \beta }}{\partial x^{\beta }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mo>≡</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{\alpha }=-{T^{\alpha \beta }}_{,\beta }\equiv -{\frac {\partial T^{\alpha \beta }}{\partial x^{\beta }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48ca280ec80b64e1602912f5ea2e7076c84d2519" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:24.742ex; height:6.009ex;" alt="{\displaystyle f^{\alpha }=-{T^{\alpha \beta }}_{,\beta }\equiv -{\frac {\partial T^{\alpha \beta }}{\partial x^{\beta }}}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Korunum_yasaları"><span id="Korunum_yasalar.C4.B1"></span>Korunum yasaları</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=12" title="Değiştirilen bölüm: Korunum yasaları" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=12" title="Bölümün kaynak kodunu değiştir: Korunum yasaları"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Elektrik_yükü"><span id="Elektrik_y.C3.BCk.C3.BC"></span>Elektrik yükü</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=13" title="Değiştirilen bölüm: Elektrik yükü" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=13" title="Bölümün kaynak kodunu değiştir: Elektrik yükü"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Devamlılık denklemi: </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 {J^{\alpha }}_{,\alpha }\,{\stackrel {\mathrm {def} }{=}}\,\partial _{\alpha }J^{\alpha }\,=\,0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {J^{\alpha }}_{,\alpha }\,{\stackrel {\mathrm {def} }{=}}\,\partial _{\alpha }J^{\alpha }\,=\,0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c4b93cd0759a6a2e4e0498f1ab469f73bf04ee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.979ex; height:4.009ex;" alt="{\displaystyle {J^{\alpha }}_{,\alpha }\,{\stackrel {\mathrm {def} }{=}}\,\partial _{\alpha }J^{\alpha }\,=\,0\,.}"></span></dd></dl> <p>toplam yükün korunumunu açıklar. </p> <div class="mw-heading mw-heading3"><h3 id="elektromanyetik_enerji–momentum"><span id="elektromanyetik_enerji.E2.80.93momentum"></span>elektromanyetik enerji–momentum</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=14" title="Değiştirilen bölüm: elektromanyetik enerji–momentum" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=14" title="Bölümün kaynak kodunu değiştir: elektromanyetik enerji–momentum"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Maxwell denklemlerini kullanarak, sıradaki elektromanyetik tensörü ve dört boyutlu akım vektörünü ilişkilendiren diferansiyel denklemi sağlayan gerilim–enerji tensörlerini görebilir (yukarıda tanımlandığı gibi) </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 {T^{\alpha \beta }}_{,\beta }+F^{\alpha \beta }J_{\beta }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {T^{\alpha \beta }}_{,\beta }+F^{\alpha \beta }J_{\beta }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68aae8eaa85e340c1f06fa1dd57b4e6c3715d367" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.184ex; height:3.343ex;" alt="{\displaystyle {T^{\alpha \beta }}_{,\beta }+F^{\alpha \beta }J_{\beta }=0}"></span></dd></dl> <p>yahut </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 \eta _{\alpha \nu }{T^{\nu \beta }}_{,\beta }+F_{\alpha \beta }J^{\beta }=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>ν</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>β</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{\alpha \nu }{T^{\nu \beta }}_{,\beta }+F_{\alpha \beta }J^{\beta }=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed3fa108f2ec15e0eae6a28fa1c176571725e3c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.877ex; height:3.343ex;" alt="{\displaystyle \eta _{\alpha \nu }{T^{\nu \beta }}_{,\beta }+F_{\alpha \beta }J^{\beta }=0,}"></span></dd></dl> <p>Bu da lineer momentumun ve enerjini elektromanyetik etkileşimlerde korunduğunu ifade eder. </p> <div class="mw-heading mw-heading2"><h2 id="Madde_içimdeki_eşdeğişimli_objeler"><span id="Madde_i.C3.A7imdeki_e.C5.9Fde.C4.9Fi.C5.9Fimli_objeler"></span>Madde içimdeki eşdeğişimli objeler</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=15" title="Değiştirilen bölüm: Madde içimdeki eşdeğişimli objeler" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=15" title="Bölümün kaynak kodunu değiştir: Madde içimdeki eşdeğişimli objeler"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Serbest_ve_bağlı_dörtlü_akımları"><span id="Serbest_ve_ba.C4.9Fl.C4.B1_d.C3.B6rtl.C3.BC_ak.C4.B1mlar.C4.B1"></span>Serbest ve bağlı dörtlü akımları</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=16" title="Değiştirilen bölüm: Serbest ve bağlı dörtlü akımları" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=16" title="Bölümün kaynak kodunu değiştir: Serbest ve bağlı dörtlü akımları"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Burada verilen elektromanyetizma denklemlerini çözmek için, elektrik akımının nasıl hesaplandığıyla ilgili ek bilgiye ihtiyaç vardır, <i>J</i><sup>ν</sup> Çoğunlukla, akımı farklı denklemlerle modellenen iki parçaya ayırmak gelenekselleşmiştir, serbest akım ve bağlı akım; </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 J^{\nu }={J^{\nu }}_{\text{free}}+{J^{\nu }}_{\text{bound}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J^{\nu }={J^{\nu }}_{\text{free}}+{J^{\nu }}_{\text{bound}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbf42efdf955f3403b3942d54096b91206cfa6a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.411ex; height:2.676ex;" alt="{\displaystyle J^{\nu }={J^{\nu }}_{\text{free}}+{J^{\nu }}_{\text{bound}}\,,}"></span></dd></dl> <p>olduğu zaman </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 {J^{\nu }}_{\text{free}}=(c\rho _{\text{free}},\mathbf {J} _{\text{free}})=\left(c\nabla \cdot \mathbf {D} ,-\ {\frac {\partial \mathbf {D} }{\partial t}}+\nabla \times \mathbf {H} \right)\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>c</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>c</mi> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>,</mo> <mo>−</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {J^{\nu }}_{\text{free}}=(c\rho _{\text{free}},\mathbf {J} _{\text{free}})=\left(c\nabla \cdot \mathbf {D} ,-\ {\frac {\partial \mathbf {D} }{\partial t}}+\nabla \times \mathbf {H} \right)\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e10d47f1fec9103e217281eaf57bc33615b90b37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:52.628ex; height:6.176ex;" alt="{\displaystyle {J^{\nu }}_{\text{free}}=(c\rho _{\text{free}},\mathbf {J} _{\text{free}})=\left(c\nabla \cdot \mathbf {D} ,-\ {\frac {\partial \mathbf {D} }{\partial t}}+\nabla \times \mathbf {H} \right)\,,}"></span></dd> <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 {J^{\nu }}_{\text{bound}}=(c\rho _{\text{bound}},\mathbf {J} _{\text{bound}})=\left(-\ c\nabla \cdot \mathbf {P} ,{\frac {\partial \mathbf {P} }{\partial t}}+\nabla \times \mathbf {M} \right)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>c</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mtext> </mtext> <mi>c</mi> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {J^{\nu }}_{\text{bound}}=(c\rho _{\text{bound}},\mathbf {J} _{\text{bound}})=\left(-\ c\nabla \cdot \mathbf {P} ,{\frac {\partial \mathbf {P} }{\partial t}}+\nabla \times \mathbf {M} \right)\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adf112c75fafc39eeeaf27899edd0847d0eab50c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:58.238ex; height:6.176ex;" alt="{\displaystyle {J^{\nu }}_{\text{bound}}=(c\rho _{\text{bound}},\mathbf {J} _{\text{bound}})=\left(-\ c\nabla \cdot \mathbf {P} ,{\frac {\partial \mathbf {P} }{\partial t}}+\nabla \times \mathbf {M} \right)\,.}"></span></dd></dl> <p>Maxwell's makroskopik denklemleri kullanılmıştır, ek olarak elektriksel yerdeğiştirmenin <b>D</b> (coloumb·metre<sup>−1</sup> cinsinden) tanımları the definitions of the <a href="/w/index.php?title=Electric_displacement&action=edit&redlink=1" class="new" title="Electric displacement (sayfa mevcut değil)">electric displacement</a> ve manyetik şiddet <b>H</b> (amper·metre<sup>−1</sup> cinsinden): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {D} =\epsilon _{0}\mathbf {E} +\mathbf {P} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {D} =\epsilon _{0}\mathbf {E} +\mathbf {P} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab3f9bf34260602c3c8a0445bca8982992c9a3f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.958ex; height:2.509ex;" alt="{\displaystyle \mathbf {D} =\epsilon _{0}\mathbf {E} +\mathbf {P} \,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {H} ={\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} \,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {H} ={\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} \,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/737bc6c6c9568ac6ad04450048abc2ea14171bec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.795ex; height:5.676ex;" alt="{\displaystyle \mathbf {H} ={\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} \,.}"></span></dd></dl> <p><b>M</b> manyetizasyon (ampere·metre<sup>−2</sup> cinsinden) ve<b>P</b> electriksel polarizasyon (coulomb·metre<sup>−2</sup> cinsinden) olduğu. </p> <div class="mw-heading mw-heading3"><h3 id="Manyetizasyon-polarizasyon_tensörü"><span id="Manyetizasyon-polarizasyon_tens.C3.B6r.C3.BC"></span>Manyetizasyon-polarizasyon tensörü</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=17" title="Değiştirilen bölüm: Manyetizasyon-polarizasyon tensörü" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=17" title="Bölümün kaynak kodunu değiştir: Manyetizasyon-polarizasyon tensörü"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bağılı akım antikontravaryant manyetizasyon-polarizasyon tensörü (amper·metre<sup>2</sup>) oluşturan <b>P</b> ve<b>M</b> alanlarından türetilmiştir <sup id="cite_ref-Vanderlinde_1-1" class="reference"><a href="#cite_note-Vanderlinde-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {M}}^{\mu \nu }={\begin{pmatrix}0&P_{x}c&P_{y}c&P_{z}c\\-P_{x}c&0&-M_{z}&M_{y}\\-P_{y}c&M_{z}&0&-M_{x}\\-P_{z}c&-M_{y}&M_{x}&0\end{pmatrix}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}^{\mu \nu }={\begin{pmatrix}0&P_{x}c&P_{y}c&P_{z}c\\-P_{x}c&0&-M_{z}&M_{y}\\-P_{y}c&M_{z}&0&-M_{x}\\-P_{z}c&-M_{y}&M_{x}&0\end{pmatrix}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36218bded205b71e30dfd2d35ca2297cebf24641" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:41.306ex; height:13.509ex;" alt="{\displaystyle {\mathcal {M}}^{\mu \nu }={\begin{pmatrix}0&P_{x}c&P_{y}c&P_{z}c\\-P_{x}c&0&-M_{z}&M_{y}\\-P_{y}c&M_{z}&0&-M_{x}\\-P_{z}c&-M_{y}&M_{x}&0\end{pmatrix}},}"></span></dd></dl> <p>ve bağlı akım su sekilde belirlenir </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 {J^{\nu }}_{\text{bound}}=\partial _{\mu }{\mathcal {M}}^{\mu \nu }\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {J^{\nu }}_{\text{bound}}=\partial _{\mu }{\mathcal {M}}^{\mu \nu }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad8892c7afad2ad878c97d8634793ea3cc732d12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.815ex; height:3.009ex;" alt="{\displaystyle {J^{\nu }}_{\text{bound}}=\partial _{\mu }{\mathcal {M}}^{\mu \nu }\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Elektriksel_yerdeğiştirme_tensörü"><span id="Elektriksel_yerde.C4.9Fi.C5.9Ftirme_tens.C3.B6r.C3.BC"></span>Elektriksel yerdeğiştirme tensörü</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=18" title="Değiştirilen bölüm: Elektriksel yerdeğiştirme tensörü" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=18" title="Bölümün kaynak kodunu değiştir: Elektriksel yerdeğiştirme tensörü"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eğer elektriksel yerdeğiştirme tensörü <i>F</i><sup>μν</sup> birleşirse <b>D</b> ve<b>H</b> alanlarını aşağıda olduğu gibi birleştiren antisimetrikmetrik kontravaryant elektromanyetik yerdeğiştirme tensörü elde edilir (amper·metre<sup>−1</sup> cinsinden) : </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 {\mathcal {D}}^{\mu \nu }={\begin{pmatrix}0&-D_{x}c&-D_{y}c&-D_{z}c\\D_{x}c&0&-H_{z}&H_{y}\\D_{y}c&H_{z}&0&-H_{x}\\D_{z}c&-H_{y}&H_{x}&0\end{pmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mu \nu }={\begin{pmatrix}0&-D_{x}c&-D_{y}c&-D_{z}c\\D_{x}c&0&-H_{z}&H_{y}\\D_{y}c&H_{z}&0&-H_{x}\\D_{z}c&-H_{y}&H_{x}&0\end{pmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64a53fa0bcf41d30ec6f62439a3a702d7364dbbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:40.963ex; height:13.509ex;" alt="{\displaystyle {\mathcal {D}}^{\mu \nu }={\begin{pmatrix}0&-D_{x}c&-D_{y}c&-D_{z}c\\D_{x}c&0&-H_{z}&H_{y}\\D_{y}c&H_{z}&0&-H_{x}\\D_{z}c&-H_{y}&H_{x}&0\end{pmatrix}}.}"></span></dd></dl> <p>Üç alan tensörü şu şekilde ilişkilendirilmiştir: </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 {\mathcal {D}}^{\mu \nu }={\frac {1}{\mu _{0}}}F^{\mu \nu }-{\mathcal {M}}^{\mu \nu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mu \nu }={\frac {1}{\mu _{0}}}F^{\mu \nu }-{\mathcal {M}}^{\mu \nu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08fd67503630a8b5f51b6eb5b33f45f332ef784" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.299ex; height:5.676ex;" alt="{\displaystyle {\mathcal {D}}^{\mu \nu }={\frac {1}{\mu _{0}}}F^{\mu \nu }-{\mathcal {M}}^{\mu \nu }\,}"></span></dd></dl> <p>Bu da <b>D</b> ve<b>H</b> alanlarının yukarıda verilen tanımlarına denktir. </p> <div class="mw-heading mw-heading2"><h2 id="Madde_içinde_Maxwell_denklemleri"><span id="Madde_i.C3.A7inde_Maxwell_denklemleri"></span>Madde içinde Maxwell denklemleri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=19" title="Değiştirilen bölüm: Madde içinde Maxwell denklemleri" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=19" title="Bölümün kaynak kodunu değiştir: Madde içinde Maxwell denklemleri"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sonuç Amper yasası, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\nabla } \times \mathbf {H} =\mathbf {J} _{\text{free}}+{\frac {\partial \mathbf {D} }{\partial t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∇</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\nabla } \times \mathbf {H} =\mathbf {J} _{\text{free}}+{\frac {\partial \mathbf {D} }{\partial t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e43f8adfd6855a1baae175dfdf05356eec2b42ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.232ex; height:5.509ex;" alt="{\displaystyle \mathbf {\nabla } \times \mathbf {H} =\mathbf {J} _{\text{free}}+{\frac {\partial \mathbf {D} }{\partial t}}}"></span>,</dd></dl> <p>ve Gauss's yasası, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\nabla } \cdot \mathbf {D} =\rho _{\text{free}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∇</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\nabla } \cdot \mathbf {D} =\rho _{\text{free}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fa96cfe692c3753a71a9c84cba791b709669c02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.805ex; height:2.676ex;" alt="{\displaystyle \mathbf {\nabla } \cdot \mathbf {D} =\rho _{\text{free}}}"></span>,</dd></dl> <p>bir denklemde birleştirirsek: </p><p><a href="/w/index.php?title=%C5%9Eablon:Equation_box_1&action=edit&redlink=1" class="new" title="Şablon:Equation box 1 (sayfa mevcut değil)">Şablon:Equation box 1</a> </p><p>The bound current vefree current as defined above are automatically veseparately conserved </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 \partial _{\nu }{J^{\nu }}_{\text{bound}}=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>bound</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\nu }{J^{\nu }}_{\text{bound}}=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14515359613dade8b9028cfa4a3890444350bf69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.325ex; height:2.676ex;" alt="{\displaystyle \partial _{\nu }{J^{\nu }}_{\text{bound}}=0\,}"></span></dd> <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 \partial _{\nu }{J^{\nu }}_{\text{free}}=0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\nu }{J^{\nu }}_{\text{free}}=0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/258a73b5146e5c8b49c733b42a188812ba6bf8c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.102ex; height:2.676ex;" alt="{\displaystyle \partial _{\nu }{J^{\nu }}_{\text{free}}=0\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Geleneksel_Denklemler">Geleneksel Denklemler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=20" title="Değiştirilen bölüm: Geleneksel Denklemler" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=20" title="Bölümün kaynak kodunu değiştir: Geleneksel Denklemler"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Geleneksel_denklemler&action=edit&redlink=1" class="new" title="Geleneksel denklemler (sayfa mevcut değil)">Geleneksel denklemler</a></div> <div class="mw-heading mw-heading4"><h4 id="Vakum">Vakum</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=21" title="Değiştirilen bölüm: Vakum" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=21" title="Bölümün kaynak kodunu değiştir: Vakum"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vakumlu bir ortamda alan ve yerdeğiştirme tensörleri arasındaki geleneksel ilişki şöyledir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{0}{\mathcal {D}}^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>α</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{0}{\mathcal {D}}^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06ac0c2c77da4ff455cd5a83d9cd2b9ec916129b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.864ex; height:3.343ex;" alt="{\displaystyle \mu _{0}{\mathcal {D}}^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,.}"></span></dd></dl> <p>Antisimetri 16 denklemi sadece 6 bağımsız denkleme indirger. Çünkü <i>F</i><sup>μν</sup> ifadesini </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>α</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4af403f5b7ee21f6461db3d8e9060181803e0876" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.784ex; height:3.343ex;" alt="{\displaystyle F^{\mu \nu }=\eta ^{\mu \alpha }F_{\alpha \beta }\eta ^{\beta \nu }\,}"></span> ile ifade etmek gelenekseldir.</dd></dl> <p>Vakum koşullarında geleneksel denklemler Gauss-Ampère yasasıyla birleştirildiğinde şu sonuç açığa çıkar: </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 \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }.\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>.</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }.\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34e2028a19370f38003350478f5f0ecac08890f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.204ex; width:15.277ex; height:3.343ex;" alt="{\displaystyle \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }.\!}"></span></dd></dl> <p>Elektromanyetik gerilim–enerji tensörü yerdeğiştirme cinsinden: </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 T_{\alpha }^{\pi }=F_{\alpha \beta }{\mathcal {D}}^{\pi \beta }-{\frac {1}{4}}\delta _{\alpha }^{\pi }F_{\mu \nu }{\mathcal {D}}^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mi>β</mi> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msubsup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\alpha }^{\pi }=F_{\alpha \beta }{\mathcal {D}}^{\pi \beta }-{\frac {1}{4}}\delta _{\alpha }^{\pi }F_{\mu \nu }{\mathcal {D}}^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a901f6009b03401861848ceda9c5aa72b3f015" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.252ex; height:5.176ex;" alt="{\displaystyle T_{\alpha }^{\pi }=F_{\alpha \beta }{\mathcal {D}}^{\pi \beta }-{\frac {1}{4}}\delta _{\alpha }^{\pi }F_{\mu \nu }{\mathcal {D}}^{\mu \nu }}"></span></dd></dl> <p>δ<sub>α</sub><sup>π</sup> Kronecker delta olduğu yerde. Üst indeks η ile düşürüldüğü zaman, simetrik olur ve yerçekimi alanı kaynağının bir parçası olur. </p> <div class="mw-heading mw-heading4"><h4 id="Madde">Madde</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=22" title="Değiştirilen bölüm: Madde" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=22" title="Bölümün kaynak kodunu değiştir: Madde"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Böylece akımı modelleme işini ikiye indirdik, <i>J</i><sup>ν</sup> daha kolay modeller — serbest akımı modellemek, <i>J</i><sup>ν</sup><sub>free</sub> ve manyetizasyonla polarizasyonu, <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 {M}}^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5069928634b055692ef43851f2fe32439596f0b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.885ex; height:2.343ex;" alt="{\displaystyle {\mathcal {M}}^{\mu \nu }}"></span>. Örnek olarak, düşük frekanslı en basit malzemelerden anlık hareketli referans sisteminde yer alan bir tanesi buna sahip; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{\text{free}}=\sigma \mathbf {E} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>=</mo> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{\text{free}}=\sigma \mathbf {E} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89ca5835d7dddd4675f0b0aee5f7cbe86a0b6142" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.793ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{\text{free}}=\sigma \mathbf {E} \,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} =\epsilon _{0}\chi _{e}\mathbf {E} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} =\epsilon _{0}\chi _{e}\mathbf {E} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9880e142cb5d0c258279a4386d8b3fd6c15eb8e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.521ex; height:2.509ex;" alt="{\displaystyle \mathbf {P} =\epsilon _{0}\chi _{e}\mathbf {E} \,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {M} =\chi _{m}\mathbf {H} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mo>=</mo> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {M} =\chi _{m}\mathbf {H} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ec8fceff21e6ab3e6b4929ba1d367be14b7ffb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.245ex; height:2.509ex;" alt="{\displaystyle \mathbf {M} =\chi _{m}\mathbf {H} \,}"></span></dd></dl> <pre>σ onun elektrik iletkenliği, χ<sub>e</sub> onun elektrik hassalığı ve χ<sub>m</sub> onun manyetik hassaslığıdır. </pre> <pre><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 {D}}}"> <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">D</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3277962e1959c3241fb1b70c7f0ac6dcefebd966" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}"></span> ve <i>F</i> tensörleri arasındaki geleneksel ilişki, Hermann Minkowski tarafından lineer malzemeler için ortaya konmuştur (yani, <b>E</b> ile <b>D</b> doğru orantılı ve<b>B</b> de <b>H</b> ile doğru orantılı),:<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> </pre> <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 {\mathcal {D}}^{\mu \nu }u_{\nu }=c^{2}\epsilon F^{\mu \nu }u_{\nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ϵ</mi> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mu \nu }u_{\nu }=c^{2}\epsilon F^{\mu \nu }u_{\nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d13c77cd745d4292a86189d227bb4855cbb6a78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.766ex; height:3.009ex;" alt="{\displaystyle {\mathcal {D}}^{\mu \nu }u_{\nu }=c^{2}\epsilon F^{\mu \nu }u_{\nu }}"></span></dd> <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 {\star {\mathcal {D}}^{\mu \nu }}u_{\nu }={\frac {1}{\mu }}{\star F^{\mu \nu }}u_{\nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mrow> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>μ</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆</mo> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mrow> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\star {\mathcal {D}}^{\mu \nu }}u_{\nu }={\frac {1}{\mu }}{\star F^{\mu \nu }}u_{\nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7eddac21325103ebeebc0b7b20dac8741d58c60c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.323ex; height:5.676ex;" alt="{\displaystyle {\star {\mathcal {D}}^{\mu \nu }}u_{\nu }={\frac {1}{\mu }}{\star F^{\mu \nu }}u_{\nu }}"></span></dd></dl> <p><i>u</i> 'nun maddenin dört boyutlu hızı olduğu yerde, ε ve μ maddenin geçirgenliğidir </p> <pre>(i.e. in rest frame of material), <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 \star }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋆</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \star }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd316a21eeb5079a850f223b1d096a06bfa788c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.035ex; margin-bottom: -0.206ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \star }"></span> vedenotes the <a href="/w/index.php?title=Hodge_dual&action=edit&redlink=1" class="new" title="Hodge dual (sayfa mevcut değil)">Hodge dual</a>. </pre> <div class="mw-heading mw-heading2"><h2 id="Klasik_elektrodinamik_için_Lagrangian"><span id="Klasik_elektrodinamik_i.C3.A7in_Lagrangian"></span>Klasik elektrodinamik için Lagrangian</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=23" title="Değiştirilen bölüm: Klasik elektrodinamik için Lagrangian" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=23" title="Bölümün kaynak kodunu değiştir: Klasik elektrodinamik için Lagrangian"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Vakum_2">Vakum</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=24" title="Değiştirilen bölüm: Vakum" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=24" title="Bölümün kaynak kodunu değiştir: Vakum"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Klasik elektrodinamik için Lagrangia (Lagrangian yoğunluğu) (joule·metre<sup>−3</sup> cinsinden) şöyledir; </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 {\mathcal {L}}\,=\,{\mathcal {L}}_{\mathrm {alan} }+{\mathcal {L}}_{\mathrm {int} }=-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J^{\alpha }\,.}"> <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">L</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}\,=\,{\mathcal {L}}_{\mathrm {alan} }+{\mathcal {L}}_{\mathrm {int} }=-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J^{\alpha }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/937fba9f5ed7f4f22a14eded475cc7738d8e297e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:43.849ex; height:5.676ex;" alt="{\displaystyle {\mathcal {L}}\,=\,{\mathcal {L}}_{\mathrm {alan} }+{\mathcal {L}}_{\mathrm {int} }=-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J^{\alpha }\,.}"></span></dd></dl> <p>Etkileşim cinsinden, dört boyutlu akım diğer yüklü alanların elektrik akımlarını kendi değişkenleri cinsinden ifade eden pek çok terimin kısaltılması olarak anlasılmalıdır, dört boyutlu akımın kendisi temel bir alan değildir. </p><p>Elektromanyetik Lagrangian yoğunluğu için Euler–Lagrange denklemi <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 {L}}(A_{\alpha },\partial _{\beta }A_{\alpha })\,}"> <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">L</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}(A_{\alpha },\partial _{\beta }A_{\alpha })\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14d7b23d0fe8793006cdb2ed3480441a6fdb5b2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.297ex; height:3.009ex;" alt="{\displaystyle {\mathcal {L}}(A_{\alpha },\partial _{\beta }A_{\alpha })\,}"></span> ilerleyen basamaklarda olduğu gibi gösterilebilir: </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 \partial _{\beta }\left[{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}\right]-{\frac {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mrow> <mo>[</mo> <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">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mo>−</mo> <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">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\beta }\left[{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}\right]-{\frac {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=0\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a02d4079bf5859ef0b36a4e5e5b7b01d98f1dcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:27.967ex; height:6.343ex;" alt="{\displaystyle \partial _{\beta }\left[{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}\right]-{\frac {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=0\,.}"></span></dd></dl> <p>Not </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>−</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0dfcb492a61bde526660a0abfd4d439d0423003" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.524ex; height:2.843ex;" alt="{\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }\,}"></span>,</dd></dl> <p>kare parantezlerin içindeki ifade </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 {\begin{aligned}{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}&=-\ {\frac {1}{4\mu _{0}}}\ {\frac {\partial (F_{\mu \nu }\eta ^{\mu \lambda }\eta ^{\nu \sigma }F_{\lambda \sigma })}{\partial (\partial _{\beta }A_{\alpha })}}\\&=-\ {\frac {1}{4\mu _{0}}}\ \eta ^{\mu \lambda }\eta ^{\nu \sigma }\left(F_{\lambda \sigma }(\delta _{\mu }^{\beta }\delta _{\nu }^{\alpha }-\delta _{\nu }^{\beta }\delta _{\mu }^{\alpha })+F_{\mu \nu }(\delta _{\lambda }^{\beta }\delta _{\sigma }^{\alpha }-\delta _{\sigma }^{\beta }\delta _{\lambda }^{\alpha })\right)\\&=-\ {\frac {F^{\beta \alpha }}{\mu _{0}}}\,.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <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">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>λ</mi> </mrow> </msup> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>σ</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mi>σ</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mtext> </mtext> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>λ</mi> </mrow> </msup> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>σ</mi> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mi>σ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msubsup> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msubsup> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msubsup> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msubsup> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>α</mi> </mrow> </msup> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}&=-\ {\frac {1}{4\mu _{0}}}\ {\frac {\partial (F_{\mu \nu }\eta ^{\mu \lambda }\eta ^{\nu \sigma }F_{\lambda \sigma })}{\partial (\partial _{\beta }A_{\alpha })}}\\&=-\ {\frac {1}{4\mu _{0}}}\ \eta ^{\mu \lambda }\eta ^{\nu \sigma }\left(F_{\lambda \sigma }(\delta _{\mu }^{\beta }\delta _{\nu }^{\alpha }-\delta _{\nu }^{\beta }\delta _{\mu }^{\alpha })+F_{\mu \nu }(\delta _{\lambda }^{\beta }\delta _{\sigma }^{\alpha }-\delta _{\sigma }^{\beta }\delta _{\lambda }^{\alpha })\right)\\&=-\ {\frac {F^{\beta \alpha }}{\mu _{0}}}\,.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79dcdc780a2ca6e555806831b61b8618f867d189" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.005ex; width:68.053ex; height:19.176ex;" alt="{\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {L}}}{\partial (\partial _{\beta }A_{\alpha })}}&=-\ {\frac {1}{4\mu _{0}}}\ {\frac {\partial (F_{\mu \nu }\eta ^{\mu \lambda }\eta ^{\nu \sigma }F_{\lambda \sigma })}{\partial (\partial _{\beta }A_{\alpha })}}\\&=-\ {\frac {1}{4\mu _{0}}}\ \eta ^{\mu \lambda }\eta ^{\nu \sigma }\left(F_{\lambda \sigma }(\delta _{\mu }^{\beta }\delta _{\nu }^{\alpha }-\delta _{\nu }^{\beta }\delta _{\mu }^{\alpha })+F_{\mu \nu }(\delta _{\lambda }^{\beta }\delta _{\sigma }^{\alpha }-\delta _{\sigma }^{\beta }\delta _{\lambda }^{\alpha })\right)\\&=-\ {\frac {F^{\beta \alpha }}{\mu _{0}}}\,.\end{aligned}}}"></span></dd></dl> <p>İkinci terim </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 {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=-J^{\alpha }\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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">L</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=-J^{\alpha }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31a66325cdb11480faca80e9c6395d1ce8ee6e71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.932ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial {\mathcal {L}}}{\partial A_{\alpha }}}=-J^{\alpha }\,.}"></span></dd></dl> <p>Bununla birlikte, hareketin elektromanyetik alan denklemi budur; </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 {\partial F^{\beta \alpha }}{\partial x^{\beta }}}=\mu _{0}J^{\alpha }\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>α</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial F^{\beta \alpha }}{\partial x^{\beta }}}=\mu _{0}J^{\alpha }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2731a23ba6b17cea4cd78b16f0d0790157947c79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.593ex; height:6.009ex;" alt="{\displaystyle {\frac {\partial F^{\beta \alpha }}{\partial x^{\beta }}}=\mu _{0}J^{\alpha }\,.}"></span></dd></dl> <p>Görüldüğü üzere bu da yukarıdaki Maxwell denklemlerinden bir tanesidir. </p> <div class="mw-heading mw-heading3"><h3 id="Madde_2">Madde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=25" title="Değiştirilen bölüm: Madde" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=25" title="Bölümün kaynak kodunu değiştir: Madde"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Serbest akımları bağlı akımlardan ayırmak, başka bir deyişle Lagrangian yoğunluğunu yazmanın bir başka yolu aşağıdaki gibidir: </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 {\mathcal {L}}\,=\,-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J_{\text{free}}^{\alpha }+{\frac {1}{2}}F_{\alpha \beta }{\mathcal {M}}^{\alpha \beta }\,.}"> <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">L</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msubsup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msubsup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}\,=\,-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J_{\text{free}}^{\alpha }+{\frac {1}{2}}F_{\alpha \beta }{\mathcal {M}}^{\alpha \beta }\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ec1178b720a3d85ab98a9f3c514ae1ddd692a6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.109ex; height:5.676ex;" alt="{\displaystyle {\mathcal {L}}\,=\,-{\frac {1}{4\mu _{0}}}F^{\alpha \beta }F_{\alpha \beta }-A_{\alpha }J_{\text{free}}^{\alpha }+{\frac {1}{2}}F_{\alpha \beta }{\mathcal {M}}^{\alpha \beta }\,.}"></span></dd></dl> <p>Euler–Lagrange denklemini kullanarak, hareket denklemleri için <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 {D}}^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e27f21dca496b1ae1e4187eaa769efc363da5e63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.887ex; height:2.343ex;" alt="{\displaystyle {\mathcal {D}}^{\mu \nu }}"></span> ifadesi türetilebilir. </p><p>Rölativistik olmayan vektör notasyonunda denk ifade </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 {\mathcal {L}}\,=\,{\frac {1}{2}}\left(\epsilon _{0}E^{2}-{\frac {1}{\mu _{0}}}B^{2}\right)-\phi \,\rho _{\text{free}}+\mathbf {A} \cdot \mathbf {J} _{\text{free}}+\mathbf {E} \cdot \mathbf {P} +\mathbf {B} \cdot \mathbf {M} \,.}"> <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">L</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ϵ</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> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>ϕ</mi> <mspace width="thinmathspace" /> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>free</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}\,=\,{\frac {1}{2}}\left(\epsilon _{0}E^{2}-{\frac {1}{\mu _{0}}}B^{2}\right)-\phi \,\rho _{\text{free}}+\mathbf {A} \cdot \mathbf {J} _{\text{free}}+\mathbf {E} \cdot \mathbf {P} +\mathbf {B} \cdot \mathbf {M} \,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce44ef33bc81bf982563c8a942cd43d13c3a0fdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:62.591ex; height:6.176ex;" alt="{\displaystyle {\mathcal {L}}\,=\,{\frac {1}{2}}\left(\epsilon _{0}E^{2}-{\frac {1}{\mu _{0}}}B^{2}\right)-\phi \,\rho _{\text{free}}+\mathbf {A} \cdot \mathbf {J} _{\text{free}}+\mathbf {E} \cdot \mathbf {P} +\mathbf {B} \cdot \mathbf {M} \,.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Aynı_zamanda_bunlara_da_bakmanız_yararlı_olacaktır_(Kaynaklar_İngilizcedir)"><span id="Ayn.C4.B1_zamanda_bunlara_da_bakman.C4.B1z_yararl.C4.B1_olacakt.C4.B1r_.28Kaynaklar_.C4.B0ngilizcedir.29"></span>Aynı zamanda bunlara da bakmanız yararlı olacaktır (Kaynaklar İngilizcedir)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=26" title="Değiştirilen bölüm: Aynı zamanda bunlara da bakmanız yararlı olacaktır (Kaynaklar İngilizcedir)" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=26" title="Bölümün kaynak kodunu değiştir: Aynı zamanda bunlara da bakmanız yararlı olacaktır (Kaynaklar İngilizcedir)"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&redlink=1" class="new" title="Relativistic electromagnetism (sayfa mevcut değil)">Relativistic electromagnetism</a></li> <li><a href="/w/index.php?title=Elektromanyetik_wave_equation&action=edit&redlink=1" class="new" title="Elektromanyetik wave equation (sayfa mevcut değil)">elektromanyetik wave equation</a></li> <li><a href="/w/index.php?title=Li%C3%A9nard%E2%80%93Wiechert_potential&action=edit&redlink=1" class="new" title="Liénard–Wiechert potential (sayfa mevcut değil)">Liénard–Wiechert potential</a> for a charge in arbitrary motion</li> <li><a href="/w/index.php?title=Nonhomogeneous_elektromanyetik_wave_equation&action=edit&redlink=1" class="new" title="Nonhomogeneous elektromanyetik wave equation (sayfa mevcut değil)">Nonhomogeneous elektromanyetik wave equation</a></li> <li><a href="/w/index.php?title=Moving_magnet_veconductor_problem&action=edit&redlink=1" class="new" title="Moving magnet veconductor problem (sayfa mevcut değil)">Moving magnet veconductor problem</a></li> <li><a href="/w/index.php?title=Elektromanyetik_tens%C3%B6r&action=edit&redlink=1" class="new" title="Elektromanyetik tensör (sayfa mevcut değil)">elektromanyetik tensör</a></li> <li><a href="/w/index.php?title=Proca_action&action=edit&redlink=1" class="new" title="Proca action (sayfa mevcut değil)">Proca action</a></li> <li><a href="/w/index.php?title=Stueckelberg_action&action=edit&redlink=1" class="new" title="Stueckelberg action (sayfa mevcut değil)">Stueckelberg action</a></li> <li><a href="/w/index.php?title=Quantum_electrodynamics&action=edit&redlink=1" class="new" title="Quantum electrodynamics (sayfa mevcut değil)">Quantum electrodynamics</a></li> <li><a href="/w/index.php?title=Wheeler%E2%80%93Feynman_absorber_theory&action=edit&redlink=1" class="new" title="Wheeler–Feynman absorber theory (sayfa mevcut değil)">Wheeler–Feynman absorber theory</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Kaynakça"><span id="Kaynak.C3.A7a"></span>Kaynakça</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=27" title="Değiştirilen bölüm: Kaynakça" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=27" title="Bölümün kaynak kodunu değiştir: Kaynakça"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r32805677">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-count:2}.mw-parser-output .reflist-columns-3{column-count:3}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Vanderlinde-1"><strong>^</strong> <a href="#cite_ref-Vanderlinde_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Vanderlinde_1-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><cite id="CITEREFVanderlinde2004" class="kaynak">Vanderlinde, Jack (2004), <a rel="nofollow" class="external text" href="http://books.google.com/books?id=HWrMET9_VpUC&pg=PA316&dq=electromagnetic+alan+tensör+vanderlinde"><i>classical elektromanyetik theory</i></a>, Springer, ss. 313-328, <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/9781402026997" title="Özel:KitapKaynakları/9781402026997">9781402026997</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=classical+elektromanyetik+theory&rft.pages=313-328&rft.pub=Springer&rft.date=2004&rft.isbn=9781402026997&rft.aulast=Vanderlinde&rft.aufirst=Jack&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHWrMET9_VpUC%26pg%3DPA316%26dq%3Delectromagnetic%2Balan%2Btens%C3%B6r%2Bvanderlinde&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><strong><a href="#cite_ref-2">^</a></strong> <span class="reference-text">Classical Electrodynamics by Jackson, 3rd Edition, Chapter 11 Special Theory of Relativity</span> </li> <li id="cite_note-3"><strong><a href="#cite_ref-3">^</a></strong> <span class="reference-text"><b>E</b> ve<b>B</b> 'den oluşan kuvvetler haricinde başka hiçbir kuvvetin olmadığı varsayımı yapılmıştır, yani, hiçbir yerçekimi, zayıf yahut güç boyutlu kuvvet bulunmamaktadır.</span> </li> <li id="cite_note-4"><strong><a href="#cite_ref-4">^</a></strong> <span class="reference-text"><cite class="kaynak kitap"><i>Introduction to Electrodynamics</i> (3.3yazar=D.J. Griffiths bas.). Dorling Kindersley. 2007. s. 563. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/81-7758-293-3" title="Özel:KitapKaynakları/81-7758-293-3">81-7758-293-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Electrodynamics&rft.pages=563&rft.edition=3.3yazar%3DD.J.+Griffiths&rft.pub=Dorling+Kindersley&rft.date=2007&rft.isbn=81-7758-293-3&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Konuyla_ilgili_yayınlar"><span id="Konuyla_ilgili_yay.C4.B1nlar"></span>Konuyla ilgili yayınlar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&veaction=edit&section=28" title="Değiştirilen bölüm: Konuyla ilgili yayınlar" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromanyetizman%C4%B1n_e%C5%9Fde%C4%9Fi%C5%9Fim_form%C3%BClasyonu&action=edit&section=28" title="Bölümün kaynak kodunu değiştir: Konuyla ilgili yayınlar"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="kaynak kitap">Einstein, A. (1961). <a rel="nofollow" class="external text" href="https://archive.org/details/relativityspecia00eins_0"><i>Relativity: The Special veGeneral Theory</i></a>. New York: Crown. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0-517-02961-8" title="Özel:KitapKaynakları/0-517-02961-8">0-517-02961-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity%3A+The+Special+veGeneral+Theory&rft.place=New+York&rft.pub=Crown&rft.date=1961&rft.isbn=0-517-02961-8&rft.au=Einstein%2C+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Frelativityspecia00eins_0&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="kaynak kitap">Misner, Charles; Thorne, Kip S. & Wheeler, John Archibald (1973). <i>Gravitation</i>. San Francisco: W. H. Freeman. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0-7167-0344-0" title="Özel:KitapKaynakları/0-7167-0344-0">0-7167-0344-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitation&rft.place=San+Francisco&rft.pub=W.+H.+Freeman&rft.date=1973&rft.isbn=0-7167-0344-0&rft.au=Misner%2C+Charles%3B+Thorne%2C+Kip+S.+%26+Wheeler%2C+John+Archibald&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">KB1 bakım: Birden fazla ad: yazar listesi (<a href="/wiki/Kategori:KB1_bak%C4%B1m:_Birden_fazla_ad:_yazar_listesi" title="Kategori:KB1 bakım: Birden fazla ad: yazar listesi">link</a>) </span></li> <li><cite class="kaynak kitap">Landau, L. D. veLifshitz, E. M. (1975). <a rel="nofollow" class="external text" href="https://archive.org/details/classicaltheoryo0000land_k6k2"><i>Classical Theory of alans (Fourth Revised English Edition)</i></a>. Oxford: Pergamon. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0-08-018176-7" title="Özel:KitapKaynakları/0-08-018176-7">0-08-018176-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Theory+of+alans+%28Fourth+Revised+English+Edition%29&rft.place=Oxford&rft.pub=Pergamon&rft.date=1975&rft.isbn=0-08-018176-7&rft.au=Landau%2C+L.+D.+veLifshitz%2C+E.+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fclassicaltheoryo0000land_k6k2&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">KB1 bakım: Birden fazla ad: yazar listesi (<a href="/wiki/Kategori:KB1_bak%C4%B1m:_Birden_fazla_ad:_yazar_listesi" title="Kategori:KB1 bakım: Birden fazla ad: yazar listesi">link</a>) </span></li> <li><cite class="kaynak kitap">R. P. Feynman, F. B. Moringo, veW. G. Wagner (1995). <a rel="nofollow" class="external text" href="https://archive.org/details/feynmanlectureso0000feyn_g4q1"><i>Feynman Lectures on Gravitation</i></a>. Addison-Wesley. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0-201-62734-5" title="Özel:KitapKaynakları/0-201-62734-5">0-201-62734-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Feynman+Lectures+on+Gravitation&rft.pub=Addison-Wesley&rft.date=1995&rft.isbn=0-201-62734-5&rft.au=R.+P.+Feynman%2C+F.+B.+Moringo%2C+veW.+G.+Wagner&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffeynmanlectureso0000feyn_g4q1&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AElektromanyetizman%C4%B1n+e%C5%9Fde%C4%9Fi%C5%9Fim+form%C3%BClasyonu" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">KB1 bakım: Birden fazla ad: yazar listesi (<a href="/wiki/Kategori:KB1_bak%C4%B1m:_Birden_fazla_ad:_yazar_listesi" title="Kategori:KB1 bakım: Birden fazla ad: yazar listesi">link</a>) </span></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://tr.wikipedia.org/w/index.php?title=Elektromanyetizmanın_eşdeğişim_formülasyonu&oldid=34005384">https://tr.wikipedia.org/w/index.php?title=Elektromanyetizmanın_eşdeğişim_formülasyonu&oldid=34005384</a>" sayfasından alınmıştır</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C3%96zel:Kategoriler" title="Özel:Kategoriler">Kategori</a>: <ul><li><a href="/wiki/Kategori:Elektromanyetizma" title="Kategori:Elektromanyetizma">Elektromanyetizma</a></li><li><a href="/wiki/Kategori:%C3%96zel_g%C3%B6relilik" title="Kategori:Özel görelilik">Özel görelilik</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Gizli kategoriler: <ul><li><a href="/wiki/Kategori:K%C4%B1rm%C4%B1z%C4%B1_ba%C4%9Flant%C4%B1ya_sahip_ana_madde_%C5%9Fablonu_i%C3%A7eren_maddeler" title="Kategori:Kırmızı bağlantıya sahip ana madde şablonu içeren maddeler">Kırmızı bağlantıya sahip ana madde şablonu içeren maddeler</a></li><li><a href="/wiki/Kategori:KB1_bak%C4%B1m:_Birden_fazla_ad:_yazar_listesi" title="Kategori:KB1 bakım: Birden fazla ad: yazar listesi">KB1 bakım: Birden fazla ad: yazar listesi</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sayfa en son 18.17, 16 Ekim 2024 tarihinde değiştirildi.</li> <li id="footer-info-copyright">Metin <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.tr">Creative Commons Atıf-AynıLisanslaPaylaş Lisansı</a> altındadır ve ek koşullar uygulanabilir. 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