Maksvela vienādojumi — Vikipēdija

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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Vietne"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Saturs" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Saturs</h2> <button class="vector-pinnable-header-toggle-button 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mw-ui-icon-wikimedia-expand"></span> <span>Pārslēgt Integrālie Maksvela vienādojumi apakšsadaļu</span> </button> <ul id="toc-Integrālie_Maksvela_vienādojumi-sublist" class="vector-toc-list"> <li id="toc-Vienādojumu_sistēmas_pāri" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vienādojumu_sistēmas_pāri"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Vienādojumu sistēmas pāri</span> </div> </a> <ul id="toc-Vienādojumu_sistēmas_pāri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maksvela_vienādojumu_fizikālais_saturs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maksvela_vienādojumu_fizikālais_saturs"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Maksvela vienādojumu fizikālais saturs</span> </div> </a> <ul id="toc-Maksvela_vienādojumu_fizikālais_saturs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maksvela_vienādojumu_empīriskie_fakti_vai_likumsakarības" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maksvela_vienādojumu_empīriskie_fakti_vai_likumsakarības"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Maksvela vienādojumu empīriskie fakti vai likumsakarības</span> </div> </a> <ul id="toc-Maksvela_vienādojumu_empīriskie_fakti_vai_likumsakarības-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Maksvela_diferenciālvienādojumi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Maksvela_diferenciālvienādojumi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Maksvela diferenciālvienādojumi</span> </div> </a> <button aria-controls="toc-Maksvela_diferenciālvienādojumi-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>Pārslēgt Maksvela diferenciālvienādojumi apakšsadaļu</span> </button> <ul id="toc-Maksvela_diferenciālvienādojumi-sublist" class="vector-toc-list"> <li id="toc-Pirmais_Maksvela_diferenciālvienādojums" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pirmais_Maksvela_diferenciālvienādojums"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Pirmais Maksvela diferenciālvienādojums</span> </div> </a> <ul id="toc-Pirmais_Maksvela_diferenciālvienādojums-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Otrais_Maksvela_diferenciālvienādojums" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Otrais_Maksvela_diferenciālvienādojums"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Otrais Maksvela diferenciālvienādojums</span> </div> </a> <ul id="toc-Otrais_Maksvela_diferenciālvienādojums-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trešais_Maksvela_diferenciālvienādojums" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trešais_Maksvela_diferenciālvienādojums"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Trešais Maksvela diferenciālvienādojums</span> </div> </a> <ul id="toc-Trešais_Maksvela_diferenciālvienādojums-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ceturtais_Maksvela_diferenciālvienādojums" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ceturtais_Maksvela_diferenciālvienādojums"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Ceturtais Maksvela diferenciālvienādojums</span> </div> </a> <ul id="toc-Ceturtais_Maksvela_diferenciālvienādojums-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maksvela_diferenciālvienādojumu_interpretācija_vektorlauka_teorijas_jēdzienos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maksvela_diferenciālvienādojumu_interpretācija_vektorlauka_teorijas_jēdzienos"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Maksvela diferenciālvienādojumu interpretācija vektorlauka teorijas jēdzienos</span> </div> </a> <ul id="toc-Maksvela_diferenciālvienādojumu_interpretācija_vektorlauka_teorijas_jēdzienos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maksvela_vienādojumi_koordinātās" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maksvela_vienādojumi_koordinātās"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Maksvela vienādojumi koordinātās</span> </div> </a> <ul id="toc-Maksvela_vienādojumi_koordinātās-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maksvela_vienādojumi_nav_jebkuru_elektromagnētisko_procesu_vienādojumi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maksvela_vienādojumi_nav_jebkuru_elektromagnētisko_procesu_vienādojumi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Maksvela vienādojumi nav jebkuru elektromagnētisko procesu vienādojumi</span> </div> </a> <ul id="toc-Maksvela_vienādojumi_nav_jebkuru_elektromagnētisko_procesu_vienādojumi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Papildu_literatūra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Papildu_literatūra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Papildu literatūra</span> </div> </a> <ul id="toc-Papildu_literatūra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ārējās_saites" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ārējās_saites"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ārējās saites</span> </div> </a> <ul id="toc-Ārējās_saites-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="Saturs" 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="Pārslēgt satura rādītāju" > <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">Pārslēgt satura rādītāju</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">Maksvela vienādojumi</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="Pāriet uz rakstu citā valodā. Pieejams 77 valodās" > <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-77" 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">77 valodas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Maxwell_se_vergelykings" title="Maxwell se vergelykings – afrikandu" lang="af" hreflang="af" data-title="Maxwell se vergelykings" data-language-autonym="Afrikaans" data-language-local-name="afrikandu" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Maxwell-Gleichungen" title="Maxwell-Gleichungen – Šveices vācu" lang="gsw" hreflang="gsw" data-title="Maxwell-Gleichungen" data-language-autonym="Alemannisch" data-language-local-name="Šveices vācu" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A7%D8%AA_%D9%85%D8%A7%D9%83%D8%B3%D9%88%D9%8A%D9%84" title="معادلات ماكسويل – arābu" lang="ar" hreflang="ar" data-title="معادلات ماكسويل" data-language-autonym="العربية" data-language-local-name="arābu" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Ecuaciones_de_Maxwell" title="Ecuaciones de Maxwell – astūriešu" lang="ast" hreflang="ast" data-title="Ecuaciones de Maxwell" data-language-autonym="Asturianu" data-language-local-name="astūriešu" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Maksvell_t%C9%99nlikl%C9%99ri" title="Maksvell tənlikləri – azerbaidžāņu" lang="az" hreflang="az" data-title="Maksvell tənlikləri" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaidžāņu" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%DA%A9%D8%B3%D9%88%D9%84_%D9%85%D9%88%D8%B9%D8%A7%D8%AF%DB%8C%D9%84%D9%87%E2%80%8C%D9%84%D8%B1%DB%8C" title="ماکسول موعادیله‌لری – South Azerbaijani" lang="azb" hreflang="azb" data-title="ماکسول موعادیله‌لری" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be badge-Q17437796 badge-featuredarticle mw-list-item" title="vērtīgs raksts"><a href="https://be.wikipedia.org/wiki/%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D1%96_%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%B0" title="Ураўненні Максвела – baltkrievu" lang="be" hreflang="be" data-title="Ураўненні Максвела" data-language-autonym="Беларуская" data-language-local-name="baltkrievu" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D0%B0%D1%9E%D0%BD%D0%B0%D0%BD%D1%8C%D0%BD%D1%96_%D0%9C%D0%B0%D0%BA%D1%81%D1%9E%D1%8D%D0%BB%D0%B0" title="Раўнаньні Максўэла – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Раўнаньні Максўэла" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%9C%D0%B0%D0%BA%D1%81%D1%83%D0%B5%D0%BB" title="Уравнения на Максуел – bulgāru" lang="bg" hreflang="bg" data-title="Уравнения на Максуел" data-language-autonym="Български" data-language-local-name="bulgāru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%95%E0%A7%8D%E0%A6%B8%E0%A6%93%E0%A6%AF%E0%A6%BC%E0%A7%87%E0%A6%B2%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A6%AE%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3%E0%A6%B8%E0%A6%AE%E0%A7%82%E0%A6%B9" title="ম্যাক্সওয়েলের সমীকরণসমূহ – bengāļu" lang="bn" hreflang="bn" data-title="ম্যাক্সওয়েলের সমীকরণসমূহ" data-language-autonym="বাংলা" data-language-local-name="bengāļu" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Maxwellove_jedna%C4%8Dine" title="Maxwellove jednačine – bosniešu" lang="bs" hreflang="bs" data-title="Maxwellove jednačine" data-language-autonym="Bosanski" data-language-local-name="bosniešu" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Equacions_de_Maxwell" title="Equacions de Maxwell – katalāņu" lang="ca" hreflang="ca" data-title="Equacions de Maxwell" data-language-autonym="Català" data-language-local-name="katalāņu" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Maxwellovy_rovnice" title="Maxwellovy rovnice – čehu" lang="cs" hreflang="cs" data-title="Maxwellovy rovnice" data-language-autonym="Čeština" data-language-local-name="čehu" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9Ca%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BB_%D1%82%D0%B0%D0%BD%D0%BB%C4%83%D1%85%C4%95%D1%81%D0%B5%D0%BC" title="Мaксвелл танлăхĕсем – čuvašu" lang="cv" hreflang="cv" data-title="Мaксвелл танлăхĕсем" data-language-autonym="Чӑвашла" data-language-local-name="čuvašu" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Maxwells_ligninger" title="Maxwells ligninger – dāņu" lang="da" hreflang="da" data-title="Maxwells ligninger" data-language-autonym="Dansk" data-language-local-name="dāņu" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Maxwell-Gleichungen" title="Maxwell-Gleichungen – vācu" lang="de" hreflang="de" data-title="Maxwell-Gleichungen" data-language-autonym="Deutsch" data-language-local-name="vācu" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BE%CE%B9%CF%83%CF%8E%CF%83%CE%B5%CE%B9%CF%82_%CE%9C%CE%AC%CE%BE%CE%B3%CE%BF%CF%85%CE%B5%CE%BB" title="Εξισώσεις Μάξγουελ – grieķu" lang="el" hreflang="el" data-title="Εξισώσεις Μάξγουελ" data-language-autonym="Ελληνικά" data-language-local-name="grieķu" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Maxwell%27s_equations" title="Maxwell's equations – angļu" lang="en" hreflang="en" data-title="Maxwell's equations" data-language-autonym="English" data-language-local-name="angļu" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ekvacioj_de_Maxwell" title="Ekvacioj de Maxwell – esperanto" lang="eo" hreflang="eo" data-title="Ekvacioj de Maxwell" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es badge-Q17437798 badge-goodarticle mw-list-item" title="labs raksts"><a href="https://es.wikipedia.org/wiki/Ecuaciones_de_Maxwell" title="Ecuaciones de Maxwell – spāņu" lang="es" hreflang="es" data-title="Ecuaciones de Maxwell" data-language-autonym="Español" data-language-local-name="spāņu" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Maxwelli_v%C3%B5rrandid" title="Maxwelli võrrandid – igauņu" lang="et" hreflang="et" data-title="Maxwelli võrrandid" data-language-autonym="Eesti" data-language-local-name="igauņu" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Maxwellen_ekuazioak" title="Maxwellen ekuazioak – basku" lang="eu" hreflang="eu" data-title="Maxwellen ekuazioak" data-language-autonym="Euskara" data-language-local-name="basku" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A7%D8%AA_%D9%85%D8%A7%DA%A9%D8%B3%D9%88%D9%84" title="معادلات ماکسول – persiešu" lang="fa" hreflang="fa" data-title="معادلات ماکسول" data-language-autonym="فارسی" data-language-local-name="persiešu" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Maxwellin_yht%C3%A4l%C3%B6t" title="Maxwellin yhtälöt – somu" lang="fi" hreflang="fi" data-title="Maxwellin yhtälöt" data-language-autonym="Suomi" data-language-local-name="somu" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89quations_de_Maxwell" title="Équations de Maxwell – franču" lang="fr" hreflang="fr" data-title="Équations de Maxwell" data-language-autonym="Français" data-language-local-name="franču" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Ecuaci%C3%B3ns_de_Maxwell" title="Ecuacións de Maxwell – galisiešu" lang="gl" hreflang="gl" data-title="Ecuacións de Maxwell" data-language-autonym="Galego" data-language-local-name="galisiešu" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%95%D7%AA_%D7%9E%D7%A7%D7%A1%D7%95%D7%95%D7%9C" title="משוואות מקסוול – ivrits" lang="he" hreflang="he" data-title="משוואות מקסוול" data-language-autonym="עברית" data-language-local-name="ivrits" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A5%88%E0%A4%95%E0%A5%8D%E0%A4%B8%E0%A4%B5%E0%A5%87%E0%A4%B2_%E0%A4%95%E0%A5%87_%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3" title="मैक्सवेल के समीकरण – hindi" lang="hi" hreflang="hi" data-title="मैक्सवेल के समीकरण" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Maxwellove_jednad%C5%BEbe" title="Maxwellove jednadžbe – horvātu" lang="hr" hreflang="hr" data-title="Maxwellove jednadžbe" data-language-autonym="Hrvatski" data-language-local-name="horvātu" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Ekwasyon_Maxwell" title="Ekwasyon Maxwell – haitiešu" lang="ht" hreflang="ht" data-title="Ekwasyon Maxwell" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiešu" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Maxwell-egyenletek" title="Maxwell-egyenletek – ungāru" lang="hu" hreflang="hu" data-title="Maxwell-egyenletek" data-language-autonym="Magyar" data-language-local-name="ungāru" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D6%84%D5%BD%D5%BE%D5%A5%D5%AC%D5%AB_%D5%B0%D5%A1%D5%BE%D5%A1%D5%BD%D5%A1%D6%80%D5%B8%D6%82%D5%B4%D5%B6%D5%A5%D6%80" title="Մաքսվելի հավասարումներ – armēņu" lang="hy" hreflang="hy" data-title="Մաքսվելի հավասարումներ" data-language-autonym="Հայերեն" data-language-local-name="armēņu" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Equationes_de_Maxwell" title="Equationes de Maxwell – interlingva" lang="ia" hreflang="ia" data-title="Equationes de Maxwell" data-language-autonym="Interlingua" data-language-local-name="interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Persamaan_Maxwell" title="Persamaan Maxwell – indonēziešu" lang="id" hreflang="id" data-title="Persamaan Maxwell" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonēziešu" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/J%C3%B6fnur_Maxwells" title="Jöfnur Maxwells – islandiešu" lang="is" hreflang="is" data-title="Jöfnur Maxwells" data-language-autonym="Íslenska" data-language-local-name="islandiešu" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Equazioni_di_Maxwell" title="Equazioni di Maxwell – itāļu" lang="it" hreflang="it" data-title="Equazioni di Maxwell" data-language-autonym="Italiano" data-language-local-name="itāļu" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9E%E3%82%AF%E3%82%B9%E3%82%A6%E3%82%A7%E3%83%AB%E3%81%AE%E6%96%B9%E7%A8%8B%E5%BC%8F" title="マクスウェルの方程式 – japāņu" lang="ja" hreflang="ja" data-title="マクスウェルの方程式" data-language-autonym="日本語" data-language-local-name="japāņu" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%A5%E1%83%A1%E1%83%95%E1%83%94%E1%83%9A%E1%83%98%E1%83%A1_%E1%83%92%E1%83%90%E1%83%9C%E1%83%A2%E1%83%9D%E1%83%9A%E1%83%94%E1%83%91%E1%83%94%E1%83%91%E1%83%98" title="მაქსველის განტოლებები – gruzīnu" lang="ka" hreflang="ka" data-title="მაქსველის განტოლებები" data-language-autonym="ქართული" data-language-local-name="gruzīnu" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BB_%D1%82%D0%B5%D2%A3%D0%B4%D0%B5%D1%83%D1%96" title="Максвелл теңдеуі – kazahu" lang="kk" hreflang="kk" data-title="Максвелл теңдеуі" data-language-autonym="Қазақша" data-language-local-name="kazahu" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AE%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%95%E0%B3%8D%E0%B2%B8%E0%B3%8D%E2%80%8C%E0%B2%B5%E0%B3%86%E0%B2%B2%E0%B3%8D%E2%80%8C%E0%B2%A8_%E0%B2%B8%E0%B2%AE%E0%B3%80%E0%B2%95%E0%B2%B0%E0%B2%A3%E0%B2%97%E0%B2%B3%E0%B3%81" title="ಮ್ಯಾಕ್ಸ್‌ವೆಲ್‌ನ ಸಮೀಕರಣಗಳು – kannadu" lang="kn" hreflang="kn" data-title="ಮ್ಯಾಕ್ಸ್‌ವೆಲ್‌ನ ಸಮೀಕರಣಗಳು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannadu" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%A5%EC%8A%A4%EC%9B%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="맥스웰 방정식 – korejiešu" lang="ko" hreflang="ko" data-title="맥스웰 방정식" data-language-autonym="한국어" data-language-local-name="korejiešu" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Aequationes_Maxwellianae" title="Aequationes Maxwellianae – latīņu" lang="la" hreflang="la" data-title="Aequationes Maxwellianae" data-language-autonym="Latina" data-language-local-name="latīņu" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/W%C3%A8tte_van_Maxwell" title="Wètte van Maxwell – limburgiešu" lang="li" hreflang="li" data-title="Wètte van Maxwell" data-language-autonym="Limburgs" data-language-local-name="limburgiešu" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Maksvelo_lygtys" title="Maksvelo lygtys – lietuviešu" lang="lt" hreflang="lt" data-title="Maksvelo lygtys" data-language-autonym="Lietuvių" data-language-local-name="lietuviešu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437798 badge-goodarticle mw-list-item" title="labs raksts"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BE%D0%B2%D0%B8_%D1%80%D0%B0%D0%B2%D0%B5%D0%BD%D0%BA%D0%B8" title="Максвелови равенки – maķedoniešu" lang="mk" hreflang="mk" data-title="Максвелови равенки" data-language-autonym="Македонски" data-language-local-name="maķedoniešu" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AE%E0%A5%85%E0%A4%95%E0%A5%8D%E0%A4%B8%E0%A4%B5%E0%A5%87%E0%A4%B2%E0%A4%9A%E0%A5%80_%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A5%87" title="मॅक्सवेलची समीकरणे – marathu" lang="mr" hreflang="mr" data-title="मॅक्सवेलची समीकरणे" data-language-autonym="मराठी" data-language-local-name="marathu" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Persamaan_Maxwell" title="Persamaan Maxwell – malajiešu" lang="ms" hreflang="ms" data-title="Persamaan Maxwell" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiešu" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%95%E0%A5%8D%E0%A4%B8%E0%A4%B5%E0%A5%87%E0%A4%B2_%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3" title="माक्सवेल समीकरण – nepāliešu" lang="ne" hreflang="ne" data-title="माक्सवेल समीकरण" data-language-autonym="नेपाली" data-language-local-name="nepāliešu" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wetten_van_Maxwell" title="Wetten van Maxwell – holandiešu" lang="nl" hreflang="nl" data-title="Wetten van Maxwell" data-language-autonym="Nederlands" data-language-local-name="holandiešu" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Maxwells_likningar" title="Maxwells likningar – jaunnorvēģu" lang="nn" hreflang="nn" data-title="Maxwells likningar" data-language-autonym="Norsk nynorsk" data-language-local-name="jaunnorvēģu" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Maxwells_likninger" title="Maxwells likninger – norvēģu bukmols" lang="nb" hreflang="nb" data-title="Maxwells likninger" data-language-autonym="Norsk bokmål" data-language-local-name="norvēģu bukmols" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AE%E0%A9%88%E0%A8%95%E0%A8%B8%E0%A8%B5%E0%A9%88%E0%A9%B1%E0%A8%B2_%E0%A8%A6%E0%A9%80%E0%A8%86%E0%A8%82_%E0%A8%B8%E0%A8%AE%E0%A9%80%E0%A8%95%E0%A8%B0%E0%A8%A8%E0%A8%BE%E0%A8%82" title="ਮੈਕਸਵੈੱਲ ਦੀਆਂ ਸਮੀਕਰਨਾਂ – pandžabu" lang="pa" hreflang="pa" data-title="ਮੈਕਸਵੈੱਲ ਦੀਆਂ ਸਮੀਕਰਨਾਂ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžabu" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/R%C3%B3wnania_Maxwella" title="Równania Maxwella – poļu" lang="pl" hreflang="pl" data-title="Równania Maxwella" data-language-autonym="Polski" data-language-local-name="poļu" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Equa%C3%A7%C3%B5es_de_Maxwell" title="Equações de Maxwell – portugāļu" lang="pt" hreflang="pt" data-title="Equações de Maxwell" data-language-autonym="Português" data-language-local-name="portugāļu" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ecua%C8%9Biile_lui_Maxwell" title="Ecuațiile lui Maxwell – rumāņu" lang="ro" hreflang="ro" data-title="Ecuațiile lui Maxwell" data-language-autonym="Română" data-language-local-name="rumāņu" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="vērtīgs raksts"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BB%D0%B0" title="Уравнения Максвелла – krievu" lang="ru" hreflang="ru" data-title="Уравнения Максвелла" data-language-autonym="Русский" data-language-local-name="krievu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Maxwellove_jednad%C5%BEbe" title="Maxwellove jednadžbe – serbu–horvātu" lang="sh" hreflang="sh" data-title="Maxwellove jednadžbe" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbu–horvātu" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Maxwell%27s_equations" title="Maxwell's equations – Simple English" lang="en-simple" hreflang="en-simple" data-title="Maxwell's equations" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Maxwellove_rovnice" title="Maxwellove rovnice – slovāku" lang="sk" hreflang="sk" data-title="Maxwellove rovnice" data-language-autonym="Slovenčina" data-language-local-name="slovāku" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Maxwellove_ena%C4%8Dbe" title="Maxwellove enačbe – slovēņu" lang="sl" hreflang="sl" data-title="Maxwellove enačbe" data-language-autonym="Slovenščina" data-language-local-name="slovēņu" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ekuacionet_e_Maksuellit" title="Ekuacionet e Maksuellit – albāņu" lang="sq" hreflang="sq" data-title="Ekuacionet e Maksuellit" data-language-autonym="Shqip" data-language-local-name="albāņu" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BE%D0%B2%D0%B5_%D1%98%D0%B5%D0%B4%D0%BD%D0%B0%D1%87%D0%B8%D0%BD%D0%B5" title="Максвелове једначине – serbu" lang="sr" hreflang="sr" data-title="Максвелове једначине" data-language-autonym="Српски / srpski" data-language-local-name="serbu" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Maxwells_ekvationer" title="Maxwells ekvationer – zviedru" lang="sv" hreflang="sv" data-title="Maxwells ekvationer" data-language-autonym="Svenska" data-language-local-name="zviedru" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BE%E0%AE%95%E0%AF%8D%E0%AE%9A%E0%AF%81%E0%AE%B5%E0%AF%86%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%9A%E0%AE%AE%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AE%B3%E0%AF%8D" title="மாக்சுவெல்லின் சமன்பாடுகள் – tamilu" lang="ta" hreflang="ta" data-title="மாக்சுவெல்லின் சமன்பாடுகள்" data-language-autonym="தமிழ்" data-language-local-name="tamilu" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AE%E0%B0%BE%E0%B0%95%E0%B1%8D%E0%B0%B8%E0%B1%8D%E0%B0%B5%E0%B1%86%E0%B0%B2%E0%B1%8D_%E0%B0%B8%E0%B0%AE%E0%B1%80%E0%B0%95%E0%B0%B0%E0%B0%A3%E0%B0%BE%E0%B0%B2%E0%B1%81" title="మాక్స్వెల్ సమీకరణాలు – telugu" lang="te" hreflang="te" data-title="మాక్స్వెల్ సమీకరణాలు" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%81%E0%B8%A1%E0%B8%81%E0%B8%8B%E0%B9%8C%E0%B9%80%E0%B8%A7%E0%B8%A5%E0%B8%A5%E0%B9%8C" title="สมการของแมกซ์เวลล์ – taju" lang="th" hreflang="th" data-title="สมการของแมกซ์เวลล์" data-language-autonym="ไทย" data-language-local-name="taju" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Mga_ekwasyon_ni_Maxwell" title="Mga ekwasyon ni Maxwell – tagalu" lang="tl" hreflang="tl" data-title="Mga ekwasyon ni Maxwell" data-language-autonym="Tagalog" data-language-local-name="tagalu" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Maxwell_denklemleri" title="Maxwell denklemleri – turku" lang="tr" hreflang="tr" data-title="Maxwell denklemleri" data-language-autonym="Türkçe" data-language-local-name="turku" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Makswell_tigezl%C3%A4m%C3%A4l%C3%A4re" title="Makswell tigezlämäläre – tatāru" lang="tt" hreflang="tt" data-title="Makswell tigezlämäläre" data-language-autonym="Татарча / tatarça" data-language-local-name="tatāru" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D0%BD%D1%8F_%D0%9C%D0%B0%D0%BA%D1%81%D0%B2%D0%B5%D0%BB%D0%BB%D0%B0" title="Рівняння Максвелла – ukraiņu" lang="uk" hreflang="uk" data-title="Рівняння Максвелла" data-language-autonym="Українська" data-language-local-name="ukraiņu" class="interlanguage-link-target"><span>Українська</span></a></li><li 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data-language-autonym="Tiếng Việt" data-language-local-name="vjetnamiešu" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6%E6%96%B9%E7%A8%8B%E7%BB%84" title="麦克斯韦方程组 – vu ķīniešu" lang="wuu" hreflang="wuu" data-title="麦克斯韦方程组" data-language-autonym="吴语" data-language-local-name="vu ķīniešu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9E%D7%90%D7%A7%D7%A1%D7%95%D7%95%D7%A2%D7%9C%D7%A1_%D7%92%D7%9C%D7%B2%D7%9B%D7%95%D7%A0%D7%92%D7%A2%D7%9F" title="מאקסוועלס גלײכונגען – jidišs" lang="yi" hreflang="yi" data-title="מאקסוועלס גלײכונגען" data-language-autonym="ייִדיש" data-language-local-name="jidišs" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh badge-Q17437798 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.sidebar-navbar{text-align:right;font-size:115%}.mw-parser-output .sidebar-collapse .sidebar-navbar{padding-top:0.6em}.mw-parser-output .sidebar-list-title{text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{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 nomobile"><caption class="sidebar-outer-title">Elektrodinamika</caption><tbody><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Maksvela_diferenci%C4%81lvien%C4%81dojumi" class="mw-redirect" title="Maksvela diferenciālvienādojumi">Maksvela diferenciālvienādojumi</a></th></tr><tr><td class="sidebar-content"> <div class="plainlist"><ul><li><a href="/wiki/Integr%C4%81lie_Maksvela_vien%C4%81dojumi" class="mw-redirect" title="Integrālie Maksvela vienādojumi">Integrālie Maksvela vienādojumi</a></li></ul></div></td> </tr><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Elektriskais_lauks" title="Elektriskais lauks">Elektriskais lauks</a></th></tr><tr><td class="sidebar-content"> <div class="plainlist"><ul><li><a href="/wiki/Gausa_teor%C4%93ma" title="Gausa teorēma">Gausa teorēma</a> (elektriskā lauka plūsma)</li><li><a href="/wiki/Elektrisk%C4%81_lauka_cirkul%C4%81cija" title="Elektriskā lauka cirkulācija">Elektriskā lauka cirkulācija</a></li><li><a href="/wiki/Kulona_likums" title="Kulona likums">Kulona likums</a></li><li><a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">Elektriskā strāva</a></li><li><a href="/wiki/Str%C4%81vas_nep%C4%81rtraukt%C4%ABbas_vien%C4%81dojums" title="Strāvas nepārtrauktības vienādojums">Strāvas nepārtrauktības vienādojums</a></li><li><a href="/wiki/Piln%C4%81s_str%C4%81vas_nep%C4%81rtraukt%C4%ABbas_vien%C4%81dojums" title="Pilnās strāvas nepārtrauktības vienādojums">Pilnās strāvas nepārtrauktības vienādojums</a></li><li><a href="/wiki/Nob%C4%ABdes_str%C4%81va" title="Nobīdes strāva">Nobīdes strāva</a></li><li><a href="/wiki/Elektrisk%C4%81_l%C4%81di%C5%86a_nez%C5%ABdam%C4%ABbas_likums" title="Elektriskā lādiņa nezūdamības likums">Elektriskā lādiņa nezūdamības likums</a></li><li><a href="/wiki/Elektromagn%C4%93tisk%C4%81s_indukcijas_likums" class="mw-redirect" title="Elektromagnētiskās indukcijas likums">Elektromagnētiskās indukcijas likums</a></li></ul></div></td> </tr><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">Magnētiskais lauks</a></th></tr><tr><td class="sidebar-content"> <div class="plainlist"><ul><li><a href="/wiki/Magn%C4%93tisk%C4%81s_indukcijas_pl%C5%ABsma" title="Magnētiskās indukcijas plūsma">Magnētiskās indukcijas plūsma</a></li><li><a href="/wiki/Magn%C4%93tisk%C4%81s_indukcijas_cirkul%C4%81cija" title="Magnētiskās indukcijas cirkulācija">Magnētiskās indukcijas cirkulācija</a></li><li><a href="/wiki/Lorenca_sp%C4%93ks" title="Lorenca spēks">Lorenca spēks</a></li></ul></div></td> </tr><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_avoti" title="Elektromagnētiskā lauka avoti">Elektromagnētiskā lauka avoti</a></th></tr><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_ener%C4%A3ija" title="Elektromagnētiskā lauka enerģija">Elektromagnētiskā lauka enerģija</a></th></tr><tr><th class="sidebar-heading" style="background-color:#D3D3D3"> <a href="/wiki/Delta_funkcija" title="Delta funkcija">Delta funkcija</a></th></tr><tr><td class="sidebar-navbar"><div class="plainlinks hlist navbar mini"><ul><li class="nv-skatīt"><a href="/wiki/Veidne:Elektrodinamika" title="Veidne:Elektrodinamika"><abbr title="Skatīt šo veidni" style=";">s</abbr></a></li><li class="nv-diskusija"><a href="/w/index.php?title=Veidnes_diskusija:Elektrodinamika&action=edit&redlink=1" class="new" title="Veidnes diskusija:Elektrodinamika (vēl nav uzrakstīts)"><abbr title="Diskusija par šo veidni" style="color:#002bb8;;">d</abbr></a></li><li class="nv-labot"><a class="external text" href="https://lv.wikipedia.org/w/index.php?title=Veidne:Elektrodinamika&action=edit"><abbr title="Labot šo veidni" style=";">l</abbr></a></li></ul></div></td></tr></tbody></table> <p><a href="/wiki/Fizika" title="Fizika">Fizikā</a> <b>Maksvela vienādojumi</b> ir četru <a href="/wiki/Diferenci%C4%81lvien%C4%81dojums" title="Diferenciālvienādojums">diferenciālvienādojumu</a> sistēma, kas apraksta <a href="/wiki/Elektromagn%C4%93tiskais_lauks" title="Elektromagnētiskais lauks">elektromagnētisko lauku</a> <a href="/wiki/Vakuums" title="Vakuums">vakuumā</a>. Tie raksturo <a href="/wiki/Elektriskais_lauks" title="Elektriskais lauks">elektriskā</a> un <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">magnētiskā</a> lauka savstarpējo mijiedarbību, kā arī to saistību ar <a href="/wiki/Elektriskais_l%C4%81di%C5%86%C5%A1" title="Elektriskais lādiņš">elektrisko lādiņu</a> un <a href="/w/index.php?title=Str%C4%81vas_bl%C4%ABvums&action=edit&redlink=1" class="new" title="Strāvas blīvums (vēl nav uzrakstīts)">strāvas blīvumu</a>. Šos vienādojumus <a href="/wiki/1861" class="mw-redirect" title="1861">1861</a>. gadā atklāja skotu fiziķis un matemātiķis <a href="/wiki/D%C5%BEeimss_Maksvels" title="Džeimss Maksvels">Džeimss Maksvels</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Integrālie_Maksvela_vienādojumi"><span id="Integr.C4.81lie_Maksvela_vien.C4.81dojumi"></span>Integrālie Maksvela vienādojumi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=1" title="Labot sadaļu: Integrālie Maksvela vienādojumi" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=1" title="Labot sadaļas vikikodu: Integrālie Maksvela vienādojumi"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Integrālie Maksvela vienādojumi</b> ir <a href="/wiki/Elektromagn%C4%93tiskais_lauks" title="Elektromagnētiskais lauks">elektromagnētiskā lauka</a> teorijas postulāti. </p> <ol><li><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 \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4be7f21e18d1146a6092f00ce3a7edf3609852d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.045ex; height:5.843ex;" alt="{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01b211daf224ec47f1538416fa49149f37579192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.924ex; height:5.676ex;" alt="{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }"></span></li> <li><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 \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e035188961c1bf317aaf0e2e0f32bd60dca4192c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.409ex; height:5.676ex;" alt="{\displaystyle \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }"></span></li> <li><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 \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>I</mi> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b000b5d153990055a646b63ee750b9f375884d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.312ex; height:5.676ex;" alt="{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f10891b54ded1b96ed7c2479f37799a51ef88378" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.321ex; height:5.676ex;" alt="{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }"></span></li> <li><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 \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3224585dc768c0cb087d2f7ac4be382a729cea0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.512ex; height:5.676ex;" alt="{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}}"></span></li></ol> <p>Šiem integrālajiem <a href="/wiki/Vien%C4%81dojums" title="Vienādojums">vienādojumiem</a> mēdz pievienot vēl arī <a href="/wiki/Elektrisk%C4%81_l%C4%81di%C5%86a_nez%C5%ABdam%C4%ABbas_likums" title="Elektriskā lādiņa nezūdamības likums">elektriskā lādiņa nezūdamības likumu</a> </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=-{\frac {\mathrm {d} q}{\mathrm {d} t}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=-{\frac {\mathrm {d} q}{\mathrm {d} t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc352425444684ab4c92e66997d1fd73aa86147" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.857ex; height:5.509ex;" alt="{\displaystyle I=-{\frac {\mathrm {d} q}{\mathrm {d} t}}\ }"></span></li></ol> <div class="mw-heading mw-heading3"><h3 id="Vienādojumu_sistēmas_pāri"><span id="Vien.C4.81dojumu_sist.C4.93mas_p.C4.81ri"></span>Vienādojumu sistēmas pāri</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=2" title="Labot sadaļu: Vienādojumu sistēmas pāri" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=2" title="Labot sadaļas vikikodu: Vienādojumu sistēmas pāri"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vienādojumu sistēma sastāv no diviem vienādojumu pāriem. </p> <ul><li>Pirmais vienādojumu pāris (1. un 2.) ir <a href="/w/index.php?title=Homog%C4%93ns&action=edit&redlink=1" class="new" title="Homogēns (vēl nav uzrakstīts)">homogēni</a> vienādojumi <a href="/wiki/Vektors" title="Vektors">vektoriem</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span>. Šie vienādojumi ir spēkā visiem <a href="/wiki/Elektromagn%C4%93tiskais_lauks" title="Elektromagnētiskais lauks">elektromagnētiskajiem laukiem</a> neatkarīgi no tā, kādi ir to <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_avoti" title="Elektromagnētiskā lauka avoti">avoti</a> (t.i., <a href="/wiki/L%C4%81di%C5%86%C5%A1" class="mw-redirect" title="Lādiņš">lādiņi</a> un <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāvas</a>)</li> <li>Otrs vienādojumu pāris (3. un 4.) ir nehomogēni vienādojumi: tie satur lauka avotus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a03bbeca27dabf60c0a27bf72cf03c5c46063d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.65ex; height:2.009ex;" alt="{\displaystyle q\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b93e901cc5457934e99cf908de005cf0eb593d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.752ex; height:2.176ex;" alt="{\displaystyle I\ }"></span>, kurus savstarpēji saista <a href="/wiki/Elektrisk%C4%81_l%C4%81di%C5%86a_nez%C5%ABdam%C4%ABbas_likums" title="Elektriskā lādiņa nezūdamības likums">lādiņa nezūdamības likums</a> (5.).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Maksvela_vienādojumu_fizikālais_saturs"><span id="Maksvela_vien.C4.81dojumu_fizik.C4.81lais_saturs"></span>Maksvela vienādojumu fizikālais saturs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=3" title="Labot sadaļu: Maksvela vienādojumu fizikālais saturs" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=3" title="Labot sadaļas vikikodu: Maksvela vienādojumu fizikālais saturs"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Pirmajā un trešajā vienādojumā <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span> cirkulāciju aprēķina pa jebkuru patvaļīgu slēgtu <a href="/w/index.php?title=Kont%C5%ABrs&action=edit&redlink=1" class="new" title="Kontūrs (vēl nav uzrakstīts)">kontūru</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97175dc1bb837de64dab2c74db334f7ced4f7ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.274ex; height:2.176ex;" alt="{\displaystyle l\ }"></span>, bet <a href="/wiki/Magn%C4%93tisk%C4%81s_indukcijas_pl%C5%ABsma" title="Magnētiskās indukcijas plūsma">magnētiskās indukcijas plūsmu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a925b493413fdf9a3b499ada79ec3edadd236186" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.259ex; height:2.176ex;" alt="{\displaystyle \Phi \ }"></span>, <a href="/wiki/Gausa_teor%C4%93ma" title="Gausa teorēma">elektriskās intensitātes plūsmu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da0c6861e044bf881b9271a7f2559501012cc19c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.644ex; height:2.176ex;" alt="{\displaystyle N\ }"></span> un <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">lādiņnesēju plūsmu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b93e901cc5457934e99cf908de005cf0eb593d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.752ex; height:2.176ex;" alt="{\displaystyle I\ }"></span> aprēķina pa atvērtu <a href="/wiki/Virsma" title="Virsma">virsmu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span>.</li> <li>Otrajā un ceturtajā vienādojumā ir aprēķināts <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">magnētiskās indukcijas</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span> un <a href="/wiki/Elektriskais_lauks" title="Elektriskais lauks">elektriskās intensitātes</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span> plūsmas caur jebkuru slēgtu viensakarīgu virsmu <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span>, bet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a03bbeca27dabf60c0a27bf72cf03c5c46063d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.65ex; height:2.009ex;" alt="{\displaystyle q\ }"></span> ir pilnais <a href="/wiki/Elektriskais_l%C4%81di%C5%86%C5%A1" title="Elektriskais lādiņš">elektriskais lādiņš</a> virsmas <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span> ierobežotajā <a href="/wiki/Tilpums" title="Tilpums">tilpumā</a>. (Šī virsma <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span> tātad nav un nevar būt tā pati, kas pirmajā un trešajā vienādojumā!)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Maksvela_vienādojumu_empīriskie_fakti_vai_likumsakarības"><span id="Maksvela_vien.C4.81dojumu_emp.C4.ABriskie_fakti_vai_likumsakar.C4.ABbas"></span>Maksvela vienādojumu empīriskie fakti vai likumsakarības</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=4" title="Labot sadaļu: Maksvela vienādojumu empīriskie fakti vai likumsakarības" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=4" title="Labot sadaļas vikikodu: Maksvela vienādojumu empīriskie fakti vai likumsakarības"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Katrs no postulētajiem integrālajiem vienādojumiem atbilst konkrētam empīriskajam faktam vai likumsakarībai, kurus apstiprina <a href="/wiki/Eksperiments" title="Eksperiments">eksperimenti</a>. </p> <ul><li>Pirmais vienādojums izsaka <a href="/wiki/Elektromagn%C4%93tisk%C4%81s_indukcijas_likums" class="mw-redirect" title="Elektromagnētiskās indukcijas likums">elektromagnētiskās indukcijas likumu</a>.</li> <li>Otrais vienādojums izsaka apgalvojumu, ka <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">magnētiskās indukcijas</a> līnijas vienmēr ir noslēgtas.</li> <li>Trešais vienādojums saista <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">magnētisko lauku</a> ar tā iespējamiem <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_avoti" title="Elektromagnētiskā lauka avoti">avotiem</a> - <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāvu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b93e901cc5457934e99cf908de005cf0eb593d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.752ex; height:2.176ex;" alt="{\displaystyle I\ }"></span> un <a href="/wiki/Nob%C4%ABdes_str%C4%81va" title="Nobīdes strāva">nobīdes strāvu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{D}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{D}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afa51fbc62311bfcdda9ef82f6db43a725feb1de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.197ex; height:2.509ex;" alt="{\displaystyle I_{D}\ }"></span>.</li> <li>Ceturtais vienādojums ir <a href="/wiki/Gausa_teor%C4%93ma" title="Gausa teorēma">Gausa teorēma</a> <a href="/wiki/Elektriskais_lauks" title="Elektriskais lauks">elektriskajam laukam</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Maksvela_diferenciālvienādojumi"><span id="Maksvela_diferenci.C4.81lvien.C4.81dojumi"></span>Maksvela diferenciālvienādojumi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=5" title="Labot sadaļu: Maksvela diferenciālvienādojumi" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=5" title="Labot sadaļas vikikodu: Maksvela diferenciālvienādojumi"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>No <a href="/wiki/Integr%C4%81lie_Maksvela_vien%C4%81dojumi" class="mw-redirect" title="Integrālie Maksvela vienādojumi">Maksvela integrālajiem vienādojumiem</a>, kuri ir spēkā galīgam <a href="/wiki/Tilpums" title="Tilpums">tilpumam</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6425b77be88d43f9ce49c55f49537b4b3d90c19f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.368ex; height:2.176ex;" alt="{\displaystyle V\ }"></span>, <a href="/wiki/Virsma" title="Virsma">virsmai</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span> un <a href="/w/index.php?title=Kont%C5%ABrs&action=edit&redlink=1" class="new" title="Kontūrs (vēl nav uzrakstīts)">kontūram</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97175dc1bb837de64dab2c74db334f7ced4f7ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.274ex; height:2.176ex;" alt="{\displaystyle l\ }"></span> var iegūt atbilstošus <a href="/wiki/Diferenci%C4%81lvien%C4%81dojums" title="Diferenciālvienādojums">diferenciālvienādojumus</a>. Tie saista <a href="/wiki/Vektors" title="Vektors">vektorus</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span> katrā <a href="/wiki/Telpa" title="Telpa">telpas</a> punktā, jebkurā <a href="/wiki/Laiks" title="Laiks">laika</a> momentā un tāpēc ir noteiktā nozīmē <i>vispārīgāki</i> nekā integrālie vienādojumi. </p><p>Lai iegūtu Maksvela diferenciālvienādojumus <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{cases}\ rot{\vec {E}}=-\mu _{0}\epsilon _{0}{\frac {\partial {\vec {B}}}{\partial t}}\\\ div{\vec {B}}=0\end{cases}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mtext> </mtext> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}\ rot{\vec {E}}=-\mu _{0}\epsilon _{0}{\frac {\partial {\vec {B}}}{\partial t}}\\\ div{\vec {B}}=0\end{cases}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41281eafdfd24cde0878fe2dc3680c881ebcc2f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:20.954ex; height:7.509ex;" alt="{\displaystyle {\begin{cases}\ rot{\vec {E}}=-\mu _{0}\epsilon _{0}{\frac {\partial {\vec {B}}}{\partial t}}\\\ div{\vec {B}}=0\end{cases}}\ }"></span> <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{cases}\ rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\\\ div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\end{cases}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mtext> </mtext> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}\ rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\\\ div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\end{cases}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d7a2369dd2fd3d77be9e7c81f426ed8c87420ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:25.725ex; height:8.176ex;" alt="{\displaystyle {\begin{cases}\ rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\\\ div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\end{cases}}\ }"></span> , integrālie vienādojumi jāpārveido tā, lai to abās pusēs būtu <a href="/wiki/Integr%C4%81lis" title="Integrālis">integrāļi</a> pa vienu un to pašu apgabalu - virsmu vai tilpumu. Šādi pārveidotām zemintegrāļa izteiksmēm integrālo vienādojumu kreisajā un labajā pusē jābūt vienādām, jo integrēšanas apgabals ir patvaļīgs. Zemintegrāļu izteiksmju vienādības ir meklētie diferenciālvienādojumi. Integrālo vienādojumu pārveidošanai izmanto <a href="/w/index.php?title=Stoksa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Stoksa teorēma (vēl nav uzrakstīts)">Stoksa</a> un <a href="/w/index.php?title=Ostrogradska_-_Gausa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Ostrogradska - Gausa teorēma (vēl nav uzrakstīts)">Ostrogradska - Gausa teorēmas</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Pirmais_Maksvela_diferenciālvienādojums"><span id="Pirmais_Maksvela_diferenci.C4.81lvien.C4.81dojums"></span>Pirmais Maksvela diferenciālvienādojums</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=6" title="Labot sadaļu: Pirmais Maksvela diferenciālvienādojums" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=6" title="Labot sadaļas vikikodu: Pirmais Maksvela diferenciālvienādojums"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pirmo Maksvela diferenciālvienādojumu iegūst no <a href="/wiki/Integr%C4%81lie_Maksvela_vien%C4%81dojumi" class="mw-redirect" title="Integrālie Maksvela vienādojumi">integrālā vienādojuma</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4be7f21e18d1146a6092f00ce3a7edf3609852d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.045ex; height:5.843ex;" alt="{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}\ }"></span>. Šeit <a href="/wiki/Magn%C4%93tisk%C4%81s_indukcijas_pl%C5%ABsma" title="Magnētiskās indukcijas plūsma">plūsma</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01b211daf224ec47f1538416fa49149f37579192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.924ex; height:5.676ex;" alt="{\displaystyle \Phi =\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}\ }"></span> ir aprēķināta virsmai <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span>, kuru aptver noslēgts kontūrs <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 l\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97175dc1bb837de64dab2c74db334f7ced4f7ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.274ex; height:2.176ex;" alt="{\displaystyle l\ }"></span>. Vienādojuma kreiso pusi pārveido , izmantojot <a href="/w/index.php?title=Stoksa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Stoksa teorēma (vēl nav uzrakstīts)">Stoksa teorēmu</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b51d779e9f549dc3ca3b0ae5943e276f9ab1a6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.025ex; height:5.676ex;" alt="{\displaystyle \oint _{l}{\vec {E}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}\ }"></span> Labajā pusē mainam <a href="/wiki/Atvasin%C4%81%C5%A1ana" class="mw-redirect" title="Atvasināšana">atvasināšanas</a> un <a href="/wiki/Integr%C4%93%C5%A1ana" class="mw-redirect" title="Integrēšana">integrēšanas</a> secību, <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 {\mathrm {d} }{\mathrm {d} t}}\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}=\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}=\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dc70f16d42b6578616fe75631286042ec0f0702" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.323ex; height:6.509ex;" alt="{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\int _{S}{\vec {B}}\mathrm {d} {\vec {S}}=\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"></span>. Šo pārveidojumu rezultātā iegūstam, ka <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 \int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}=-\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}=-\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/916e3b15af6c6158631cdb8316c19d12b19d6fc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.19ex; height:6.509ex;" alt="{\displaystyle \int _{S}rot{\vec {E}}\mathrm {d} {\vec {S}}=-\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"></span> </p><p>Pielīdzinot zemintegrāļa izteiksmes vienu otrai, iegūst <b>pirmo Maksvela diferenciālvienādojumu</b> <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 rot{\vec {E}}=-{\frac {\partial {\vec {B}}}{\partial t}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle rot{\vec {E}}=-{\frac {\partial {\vec {B}}}{\partial t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc8aa0c6f38d3f9be7170c303235e809bde9ce2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.197ex; height:6.176ex;" alt="{\displaystyle rot{\vec {E}}=-{\frac {\partial {\vec {B}}}{\partial t}}\ }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Otrais_Maksvela_diferenciālvienādojums"><span id="Otrais_Maksvela_diferenci.C4.81lvien.C4.81dojums"></span>Otrais Maksvela diferenciālvienādojums</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=7" title="Labot sadaļu: Otrais Maksvela diferenciālvienādojums" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=7" title="Labot sadaļas vikikodu: Otrais Maksvela diferenciālvienādojums"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Otrā Maksvela diferenciālvienādojuma uzrakstīšanai izmanto <a href="/w/index.php?title=Ostrogradska_-_Gausa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Ostrogradska - Gausa teorēma (vēl nav uzrakstīts)">Ostrogradska - Gausa teorēmu</a> <a href="/wiki/Integr%C4%81lie_Maksvela_vien%C4%81dojumi" class="mw-redirect" title="Integrālie Maksvela vienādojumi">integrālam vienādojumam</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e035188961c1bf317aaf0e2e0f32bd60dca4192c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.409ex; height:5.676ex;" alt="{\displaystyle \oint _{S}{\vec {B}}\mathrm {d} {\vec {S}}=0\ }"></span>, proti, nosacījumam, ka <a href="/wiki/Magn%C4%93tisk%C4%81_pl%C5%ABsma" class="mw-redirect" title="Magnētiskā plūsma">magnētiskā plūsma</a> caur jebkuru noslēgtu virsmu <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span> ir vienāda ar <a href="/wiki/Nulle" title="Nulle">nulli</a>. Patvaļīgam tilpumam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6425b77be88d43f9ce49c55f49537b4b3d90c19f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.368ex; height:2.176ex;" alt="{\displaystyle V\ }"></span> <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 \int _{V}div{\vec {B}}\mathrm {d} V=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{V}div{\vec {B}}\mathrm {d} V=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efa39785132e7ffc69d63a91678a15af5b02e57b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.007ex; height:5.676ex;" alt="{\displaystyle \int _{V}div{\vec {B}}\mathrm {d} V=0\ }"></span>. No tā izriet <b>otrais Maksvela diferenciālvienādojums</b> </p><p><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 div{\vec {B}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle div{\vec {B}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00e92d3516080880004c360692591c661b34201c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.752ex; height:2.843ex;" alt="{\displaystyle div{\vec {B}}=0\ }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Trešais_Maksvela_diferenciālvienādojums"><span id="Tre.C5.A1ais_Maksvela_diferenci.C4.81lvien.C4.81dojums"></span>Trešais Maksvela diferenciālvienādojums</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=8" title="Labot sadaļu: Trešais Maksvela diferenciālvienādojums" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=8" title="Labot sadaļas vikikodu: Trešais Maksvela diferenciālvienādojums"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trešo Maksvela diferenciālvienādojumu iegūst analogi pirmā diferenciālvienādojuma pārveidošanai <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 \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>I</mi> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b000b5d153990055a646b63ee750b9f375884d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.312ex; height:5.676ex;" alt="{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\mu _{0}(I+I_{D})\ }"></span>, kur <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāva</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87c23c871ad9800edde1c90f04057c471e30c1b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.748ex; height:5.676ex;" alt="{\displaystyle I=\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}\ }"></span> un vektora <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span> <a href="/wiki/Gausa_teor%C4%93ma" title="Gausa teorēma">plūsma</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f10891b54ded1b96ed7c2479f37799a51ef88378" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.321ex; height:5.676ex;" alt="{\displaystyle N=\int _{S}{\vec {E}}\mathrm {d} {\vec {S}}\ }"></span> ir saķēdēta ar kontūru <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 l\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97175dc1bb837de64dab2c74db334f7ced4f7ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.274ex; height:2.176ex;" alt="{\displaystyle l\ }"></span>, kas savukārt ietver virsmu <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span>. Izmantojot <a href="/w/index.php?title=Stoksa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Stoksa teorēma (vēl nav uzrakstīts)">Stoksa teorēmu</a> <a href="/wiki/Magn%C4%93tisk%C4%81s_indukcijas_cirkul%C4%81cija" title="Magnētiskās indukcijas cirkulācija">magnētiskās indukcijas cirkulācijai</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363970e0a240d41d720ed14824e7e1107b9e67c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.421ex; height:5.676ex;" alt="{\displaystyle \oint _{l}{\vec {B}}\mathrm {d} {\boldsymbol {\ell }}=\int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}}"></span>. Lietojot <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāvas tilpuma blīvuma</a> formulu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {j}}=\rho {\vec {v}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {j}}=\rho {\vec {v}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d87d500e8c3e13a260f64d9ddf13177ac7719ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.15ex; height:3.343ex;" alt="{\displaystyle {\vec {j}}=\rho {\vec {v}}\ }"></span>, strāvu var uzskatīt par lādiņnesēju plūsmu caur virsmu <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 S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span>, kuras robežkontūrs <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 l\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97175dc1bb837de64dab2c74db334f7ced4f7ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.274ex; height:2.176ex;" alt="{\displaystyle l\ }"></span>. Mainot atvasināšanas un integrēšanas secību vienādojuma labās puses otrajā saskaitāmajā, var atrast, ka <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 \int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}=\mu _{0}\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}+\epsilon _{0}\mu _{0}\int _{S}{\frac {\partial {\vec {E}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <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> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}=\mu _{0}\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}+\epsilon _{0}\mu _{0}\int _{S}{\frac {\partial {\vec {E}}}{\partial t}}\mathrm {d} {\vec {S}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31b4afbe30a69159c183068b9b3d08176a274f00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.416ex; height:6.509ex;" alt="{\displaystyle \int _{S}rot{\vec {B}}\mathrm {d} {\vec {S}}=\mu _{0}\int _{S}{\vec {j}}\mathrm {d} {\vec {S}}+\epsilon _{0}\mu _{0}\int _{S}{\frac {\partial {\vec {E}}}{\partial t}}\mathrm {d} {\vec {S}}\ }"></span> un tātad iegūstam <b>trešo Maksvela diferenciālvienādojumu</b> </p><p><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 rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65f96bd115104a197fec544bab9bc501c78a66df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.233ex; height:6.176ex;" alt="{\displaystyle rot{\vec {B}}=\mu _{0}{\vec {j}}+\epsilon _{0}\mu _{0}{\frac {\partial {\vec {E}}}{\partial t}}\ }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Ceturtais_Maksvela_diferenciālvienādojums"><span id="Ceturtais_Maksvela_diferenci.C4.81lvien.C4.81dojums"></span>Ceturtais Maksvela diferenciālvienādojums</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=9" title="Labot sadaļu: Ceturtais Maksvela diferenciālvienādojums" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=9" title="Labot sadaļas vikikodu: Ceturtais Maksvela diferenciālvienādojums"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ceturto Maksvela diferenciālvienādojumu uzraksta, izmantojot <a href="/wiki/Gausa_teor%C4%93ma" title="Gausa teorēma">Gausa teorēmu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d04b2bc79c4803741717460c32487fb28bd47b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.092ex; height:5.676ex;" alt="{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}={\frac {q}{\epsilon _{0}}}\ }"></span>. Noslēgtas <a href="/wiki/Virsma" title="Virsma">virsmas</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ad6ca2966c9c927edc8c46cb6ee2d9637bfc2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.08ex; height:2.176ex;" alt="{\displaystyle S\ }"></span> ierobežotā <a href="/wiki/Tilpums" title="Tilpums">tilpumā</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6425b77be88d43f9ce49c55f49537b4b3d90c19f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.368ex; height:2.176ex;" alt="{\displaystyle V\ }"></span> <a href="/wiki/L%C4%81di%C5%86%C5%A1" class="mw-redirect" title="Lādiņš">lādiņš</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q=\int _{V}\rho \mathrm {d} V\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q=\int _{V}\rho \mathrm {d} V\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e52d41ece5c92276631ff830ad7795b328117f3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.206ex; height:5.676ex;" alt="{\displaystyle q=\int _{V}\rho \mathrm {d} V\ }"></span> (<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 \rho \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3ebd6a737acd6be86d8aa1eeb671550885db7b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle \rho \ }"></span> ir tilpuma <a href="/w/index.php?title=L%C4%81di%C5%86a_bl%C4%ABvums&action=edit&redlink=1" class="new" title="Lādiņa blīvums (vēl nav uzrakstīts)">lādiņa blīvums</a>). Pārveidojot <a href="/wiki/Elektrisk%C4%81_intensit%C4%81te" class="mw-redirect" title="Elektriskā intensitāte">elektriskās intensitātes</a> plūsmu pēc <a href="/w/index.php?title=Ostrogradska-Gausa_teor%C4%93ma&action=edit&redlink=1" class="new" title="Ostrogradska-Gausa teorēma (vēl nav uzrakstīts)">Ostrogradska-Gausa teorēmas</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}=\int _{V}div{\vec {E}}\mathrm {d} V\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}=\int _{V}div{\vec {E}}\mathrm {d} V\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86c0e4f77c9744d0f3f6f49de5b4be528d3621d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.435ex; height:5.676ex;" alt="{\displaystyle \oint _{S}{\vec {E}}\mathrm {d} {\vec {S}}=\int _{V}div{\vec {E}}\mathrm {d} V\ }"></span>, varam uzrakstīt, ka <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 \int _{V}div{\vec {E}}\mathrm {d} V=\int _{V}{\frac {\rho \mathrm {d} V}{\epsilon _{0}}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mrow> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{V}div{\vec {E}}\mathrm {d} V=\int _{V}{\frac {\rho \mathrm {d} V}{\epsilon _{0}}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c020b676ce8be1f10b0c3632aeea5d2cf0a4449" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.15ex; height:5.843ex;" alt="{\displaystyle \int _{V}div{\vec {E}}\mathrm {d} V=\int _{V}{\frac {\rho \mathrm {d} V}{\epsilon _{0}}}\ }"></span>. </p><p>Tātad, rezultātā iegūstam pēdējo, <b>ceturto Maksvela diferenciālvienādojumu</b>: <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 div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00df5fb90a21d1c49c1a1d55e6b8b9524c60fb66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.435ex; height:5.176ex;" alt="{\displaystyle div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Maksvela_diferenciālvienādojumu_interpretācija_vektorlauka_teorijas_jēdzienos"><span id="Maksvela_diferenci.C4.81lvien.C4.81dojumu_interpret.C4.81cija_vektorlauka_teorijas_j.C4.93dzienos"></span>Maksvela diferenciālvienādojumu interpretācija vektorlauka teorijas jēdzienos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=10" title="Labot sadaļu: Maksvela diferenciālvienādojumu interpretācija vektorlauka teorijas jēdzienos" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=10" title="Labot sadaļas vikikodu: Maksvela diferenciālvienādojumu interpretācija vektorlauka teorijas jēdzienos"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Pirmais <a href="/wiki/Vien%C4%81dojums" title="Vienādojums">vienādojums</a> elektriskā lauka intensitātes <a href="/w/index.php?title=Rotors&action=edit&redlink=1" class="new" title="Rotors (vēl nav uzrakstīts)">rotoram</a> ir <a href="/wiki/Elektromagn%C4%93tisk%C4%81s_indukcijas_likums" class="mw-redirect" title="Elektromagnētiskās indukcijas likums">elektromagnētiskās indukcijas likums</a> diferenciālā formā: <a href="/wiki/Laiks" title="Laiks">laikā</a> mainīgs <a href="/wiki/Magn%C4%93tiskais_lauks" title="Magnētiskais lauks">magnētiskais lauks</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span> inducē elektrisko <a href="/w/index.php?title=Virpu%C4%BClauks&action=edit&redlink=1" class="new" title="Virpuļlauks (vēl nav uzrakstīts)">virpuļlauku</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52f4cb6818924a5daf2f129cf08178ff58a4de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}\ }"></span>. Ja magnētiskā lauka nav vai arī ja tas ir <a href="/wiki/Stacion%C4%81rs" class="mw-redirect" title="Stacionārs">stacionārs</a>, tad <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 rot{\vec {E}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle rot{\vec {E}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d448e6acccc867f9ae4e45f5b6fa8ba482a5cb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.633ex; height:2.843ex;" alt="{\displaystyle rot{\vec {E}}=0\ }"></span> un <a href="/wiki/Elektriskais_lauks" title="Elektriskais lauks">elektriskais lauks</a> ir <a href="/w/index.php?title=Potenci%C4%81ls_lauks&action=edit&redlink=1" class="new" title="Potenciāls lauks (vēl nav uzrakstīts)">potenciāls lauks</a>. Potenciālu elektrisko lauku rada nekustīgi <a href="/wiki/Elektriskais_l%C4%81di%C5%86%C5%A1" title="Elektriskais lādiņš">elektriskie lādiņi</a>. Ja tie izvietoti tilpumā tā, ka to <a href="/wiki/Bl%C4%ABvums" title="Blīvums">blīvums</a> ir <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 \rho \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3ebd6a737acd6be86d8aa1eeb671550885db7b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle \rho \ }"></span>, elektriskā lauka intensitāti nosaka ceturtais Maksvela vienādojums, <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 div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00df5fb90a21d1c49c1a1d55e6b8b9524c60fb66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.435ex; height:5.176ex;" alt="{\displaystyle div{\vec {E}}={\frac {\rho }{\epsilon _{0}}}\ }"></span>. Saskaņā ar šo vienādojumu intensitātes līnijas izplūst no <a href="/wiki/Telpa" title="Telpa">telpas</a> punktiem, kuros lādiņa blīvums ir pozitīvs (<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 \rho >0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>></mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho >0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdc753bc57964248cd889726e9d736f5f2e96e07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.044ex; height:2.676ex;" alt="{\displaystyle \rho >0\ }"></span>), bet ieplūst punktos, kuros tas ir negatīvs (<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 \rho <0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo><</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho <0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e62d01b7b51e94e196b7f12a354f2e2dfd4c83b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.044ex; height:2.676ex;" alt="{\displaystyle \rho <0\ }"></span>).</li> <li>Otrais Maksvela vienādojums, <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 div{\vec {B}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle div{\vec {B}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00e92d3516080880004c360692591c661b34201c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.752ex; height:2.843ex;" alt="{\displaystyle div{\vec {B}}=0\ }"></span>, ir magnētiskā lauka <a href="/w/index.php?title=Solenoidalit%C4%81tes_nosac%C4%ABjums&action=edit&redlink=1" class="new" title="Solenoidalitātes nosacījums (vēl nav uzrakstīts)">solenoidalitātes nosacījums</a>; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d650a60b9249a2120a31b215f26e7ecddac894bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}\ }"></span> līnijas <i>vienmēr</i> ir noslēgtas: tām nav izteču un noteču.</li> <li>Trešais Maksvela vienādojums saista magnētisko lauku ar tā <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_avoti" title="Elektromagnētiskā lauka avoti">avotiem</a>: 1) <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāvu</a>, kuras blīvums ir <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {j}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>j</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {j}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b87ad171595b2b65aa6d62fc2967069bb3dd13f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.675ex; height:3.176ex;" alt="{\displaystyle {\vec {j}}\ }"></span>, un 2) laikā mainīga elektriskā lauka <a href="/wiki/Atvasin%C4%81jums" title="Atvasinājums">atvasinājumu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial {\vec {E}}}{\partial t}}\ }"> <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"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial {\vec {E}}}{\partial t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82abf41504bf0bae4a5d84bf0a879bb35f0d69e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.51ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial {\vec {E}}}{\partial t}}\ }"></span>.</li> <li>Ceturtā Maksvela vienādojumu interpretāciju skatīt pie pirmā Maksvela vienādojuma interpretācijas.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Maksvela_vienādojumi_koordinātās"><span id="Maksvela_vien.C4.81dojumi_koordin.C4.81t.C4.81s"></span>Maksvela vienādojumi koordinātās</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=11" title="Labot sadaļu: Maksvela vienādojumi koordinātās" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=11" title="Labot sadaļas vikikodu: Maksvela vienādojumi koordinātās"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Maksvela vienādojumus var uzrakstīt arī koordinātās. Piemēram, <a href="/wiki/Dekarta_koordin%C4%81tu_sist%C4%93ma" title="Dekarta koordinātu sistēma">Dekarta koordinātās</a> iegūstam astoņus <a href="/w/index.php?title=Parci%C4%81lais_diferenci%C4%81lvien%C4%81dojums&action=edit&redlink=1" class="new" title="Parciālais diferenciālvienādojums (vēl nav uzrakstīts)">parciālos diferenciālvienādojumus</a> trim <a href="/wiki/Elektrisk%C4%81_intensit%C4%81te" class="mw-redirect" title="Elektriskā intensitāte">elektriskās intensitātes</a> koordinātām <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{x}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{x}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6973f10ccea0906886b1716e79c61758f4f382fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.468ex; height:2.509ex;" alt="{\displaystyle E_{x}\ }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{y}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b574b6be6f57ddcf24131ddfbffcb39b724df9c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.345ex; height:2.843ex;" alt="{\displaystyle E_{y}\ }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{z}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{z}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1332b1d21b2892ba1642fd55a1019f9371d9e104" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.298ex; height:2.509ex;" alt="{\displaystyle E_{z}\ }"></span> un trim <a href="/wiki/Magn%C4%93tisk%C4%81_indukcija" class="mw-redirect" title="Magnētiskā indukcija">magnētiskās indukcijas</a> koordinātām <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 B_{x}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{x}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae4ab32b3713202292918d2536f563102cef925d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.517ex; height:2.509ex;" alt="{\displaystyle B_{x}\ }"></span>, <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 B_{y}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{y}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632b11ba1e8e0c66f53bede8f92fe6974924c6dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.394ex; height:2.843ex;" alt="{\displaystyle B_{y}\ }"></span>, <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 B_{z}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{z}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d25c1adb245c6f4d1397f43907a9cf5c23778ad1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.346ex; height:2.509ex;" alt="{\displaystyle B_{z}\ }"></span>: </p><p><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{cases}\ {\frac {\partial E_{z}}{\partial y}}-{\frac {\partial E_{y}}{\partial z}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{x}}{\partial t}}\\\ {\frac {\partial E_{x}}{\partial z}}-{\frac {\partial E_{z}}{\partial x}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{y}}{\partial t}}\\\ {\frac {\partial E_{y}}{\partial x}}-{\frac {\partial E_{x}}{\partial y}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{z}}{\partial t}}\end{cases}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}\ {\frac {\partial E_{z}}{\partial y}}-{\frac {\partial E_{y}}{\partial z}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{x}}{\partial t}}\\\ {\frac {\partial E_{x}}{\partial z}}-{\frac {\partial E_{z}}{\partial x}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{y}}{\partial t}}\\\ {\frac {\partial E_{y}}{\partial x}}-{\frac {\partial E_{x}}{\partial y}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{z}}{\partial t}}\end{cases}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/169cbf64e6b4b6814788f3b069f05d282fcf764b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:27.702ex; height:13.509ex;" alt="{\displaystyle {\begin{cases}\ {\frac {\partial E_{z}}{\partial y}}-{\frac {\partial E_{y}}{\partial z}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{x}}{\partial t}}\\\ {\frac {\partial E_{x}}{\partial z}}-{\frac {\partial E_{z}}{\partial x}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{y}}{\partial t}}\\\ {\frac {\partial E_{y}}{\partial x}}-{\frac {\partial E_{x}}{\partial y}}=-\epsilon _{0}\mu _{0}{\frac {\partial B_{z}}{\partial t}}\end{cases}}\ }"></span> </p><p><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 B_{x}}{\partial x}}+{\frac {\partial B_{y}}{\partial y}}+{\frac {\partial B_{z}}{\partial z}}=0\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial B_{x}}{\partial x}}+{\frac {\partial B_{y}}{\partial y}}+{\frac {\partial B_{z}}{\partial z}}=0\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ae7c7f13dd7c1c23a195c6b98321f96502b50e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.5ex; height:6.343ex;" alt="{\displaystyle {\frac {\partial B_{x}}{\partial x}}+{\frac {\partial B_{y}}{\partial y}}+{\frac {\partial B_{z}}{\partial z}}=0\ }"></span> </p><p><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{cases}\ {\frac {\partial B_{z}}{\partial y}}-{\frac {\partial B_{y}}{\partial z}}=\mu _{0}j_{x}+\epsilon _{0}\mu _{0}{\frac {\partial E_{x}}{\partial t}}\\\ {\frac {\partial B_{x}}{\partial z}}-{\frac {\partial B_{z}}{\partial x}}=\mu _{0}j_{y}+\epsilon _{0}\mu _{0}{\frac {\partial E_{y}}{\partial t}}\\\ {\frac {\partial B_{y}}{\partial x}}-{\frac {\partial B_{x}}{\partial y}}=\mu _{0}j_{z}+\epsilon _{0}\mu _{0}{\frac {\partial E_{z}}{\partial t}}\end{cases}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>+</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>+</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>+</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}\ {\frac {\partial B_{z}}{\partial y}}-{\frac {\partial B_{y}}{\partial z}}=\mu _{0}j_{x}+\epsilon _{0}\mu _{0}{\frac {\partial E_{x}}{\partial t}}\\\ {\frac {\partial B_{x}}{\partial z}}-{\frac {\partial B_{z}}{\partial x}}=\mu _{0}j_{y}+\epsilon _{0}\mu _{0}{\frac {\partial E_{y}}{\partial t}}\\\ {\frac {\partial B_{y}}{\partial x}}-{\frac {\partial B_{x}}{\partial y}}=\mu _{0}j_{z}+\epsilon _{0}\mu _{0}{\frac {\partial E_{z}}{\partial t}}\end{cases}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bfdf381870ee8328144494226854fc1f7483e08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:33.355ex; height:13.509ex;" alt="{\displaystyle {\begin{cases}\ {\frac {\partial B_{z}}{\partial y}}-{\frac {\partial B_{y}}{\partial z}}=\mu _{0}j_{x}+\epsilon _{0}\mu _{0}{\frac {\partial E_{x}}{\partial t}}\\\ {\frac {\partial B_{x}}{\partial z}}-{\frac {\partial B_{z}}{\partial x}}=\mu _{0}j_{y}+\epsilon _{0}\mu _{0}{\frac {\partial E_{y}}{\partial t}}\\\ {\frac {\partial B_{y}}{\partial x}}-{\frac {\partial B_{x}}{\partial y}}=\mu _{0}j_{z}+\epsilon _{0}\mu _{0}{\frac {\partial E_{z}}{\partial t}}\end{cases}}\ }"></span> </p><p><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 E_{x}}{\partial x}}+{\frac {\partial E_{y}}{\partial y}}+{\frac {\partial E_{z}}{\partial z}}={\frac {\rho }{\epsilon _{0}}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial E_{x}}{\partial x}}+{\frac {\partial E_{y}}{\partial y}}+{\frac {\partial E_{z}}{\partial z}}={\frac {\rho }{\epsilon _{0}}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41965c6311c37661b1ccd824a1aeacae863ad125" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.026ex; height:6.343ex;" alt="{\displaystyle {\frac {\partial E_{x}}{\partial x}}+{\frac {\partial E_{y}}{\partial y}}+{\frac {\partial E_{z}}{\partial z}}={\frac {\rho }{\epsilon _{0}}}\ }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Maksvela_vienādojumi_nav_jebkuru_elektromagnētisko_procesu_vienādojumi"><span id="Maksvela_vien.C4.81dojumi_nav_jebkuru_elektromagn.C4.93tisko_procesu_vien.C4.81dojumi"></span>Maksvela vienādojumi nav jebkuru elektromagnētisko procesu vienādojumi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=12" title="Labot sadaļu: Maksvela vienādojumi nav jebkuru elektromagnētisko procesu vienādojumi" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=12" title="Labot sadaļas vikikodu: Maksvela vienādojumi nav jebkuru elektromagnētisko procesu vienādojumi"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Maksvela vienādojumi ir elektromagnētiskā lauka dinamikas vienādojumi. Tomēr tie nav <i>jebkuru</i> elektromagnētisko vai elektrodinamisko procesu vienādojumi, un, piemēram, no tiem neizriet <a href="/wiki/Elektromagn%C4%93tisk%C4%81_lauka_avoti" title="Elektromagnētiskā lauka avoti">lauka avotu</a> - <a href="/wiki/L%C4%81di%C5%86%C5%A1" class="mw-redirect" title="Lādiņš">lādiņu</a> (vai, precīzāk sakot, lādiņnesēju) <a href="/wiki/Kust%C4%ABba" class="mw-disambig" title="Kustība">kustības</a> likumi elektriskajā un magnētiskajā laukā. Tie jāformulē īpaši, iepriekš noskaidrojot, kādi ir <a href="/wiki/Sp%C4%93ks" title="Spēks">spēki</a> un <a href="/w/index.php?title=Moments&action=edit&redlink=1" class="new" title="Moments (vēl nav uzrakstīts)">momenti</a>, kuri uz lādiņnesējiem un <a href="/wiki/Elektrisk%C4%81_str%C4%81va" title="Elektriskā strāva">strāvas</a> vadītājiem darbojas elektriskajā un magnētiskajā laukā. </p> <div class="mw-heading mw-heading2"><h2 id="Papildu_literatūra"><span id="Papildu_literat.C5.ABra"></span>Papildu literatūra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=13" title="Labot sadaļu: Papildu literatūra" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=13" title="Labot sadaļas vikikodu: Papildu literatūra"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation">Platacis, Jānis (1974), Elektrība, Zvaigzne</span>.</li> <li><span class="citation">Fleisch, Daniel A. (2008), A student's guide to Maxwell's equations, Cambridge University Press, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Special:BookSources/978-0-52-170147-1" title="Special:BookSources/978-0-52-170147-1">978-0-52-170147-1</a></span>.</li> <li><span class="citation">Huray, Paul G. (2009), Maxwell's Equations, John Wiley & Sons, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47-054276-7" title="Special:BookSources/978-0-47-054276-7">978-0-47-054276-7</a></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Ārējās_saites"><span id=".C4.80r.C4.93j.C4.81s_saites"></span>Ārējās saites</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&veaction=edit&section=14" title="Labot sadaļu: Ārējās saites" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Maksvela_vien%C4%81dojumi&action=edit&section=14" title="Labot sadaļas vikikodu: Ārējās saites"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/MaxwellEquations.html">Maxwell Equations</a>, scienceworld.wolfram.com <span style="font-size:0.95em; color:#555;">(angliski)</span></li> <li><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html">Maxwell's Equations</a>, Hyperphysics <span style="font-size:0.95em; color:#555;">(angliski)</span></li></ul> <table cellspacing="0" class="navbox" style="border-spacing:0;"><tbody><tr><td style="padding:2px;"><table cellspacing="0" class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit;"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-skatīt"><a href="/wiki/Veidne:Relativit%C4%81te" title="Veidne:Relativitāte"><abbr title="Skatīt šo veidni" style=";;;background:none 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