Elektromagnetvälja tensor

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class="vector-toc-numb">3</span> <span>Vaata ka</span> </div> </a> <ul id="toc-Vaata_ka-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="Sisukord" 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="Lülita sisukord ümber" > <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 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Saadaval 18 keeles" > <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-18" 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">18 keelt</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tensor_electromagn%C3%A8tic" title="Tensor electromagnètic – katalaani" lang="ca" hreflang="ca" data-title="Tensor electromagnètic" data-language-autonym="Català" data-language-local-name="katalaani" 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/Tenzor_intenzity_elektromagnetick%C3%A9ho_pole" title="Tenzor intenzity elektromagnetického pole – tšehhi" lang="cs" hreflang="cs" data-title="Tenzor intenzity elektromagnetického pole" data-language-autonym="Čeština" data-language-local-name="tšehhi" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elektromagnetischer_Feldst%C3%A4rketensor" title="Elektromagnetischer Feldstärketensor – saksa" lang="de" hreflang="de" data-title="Elektromagnetischer Feldstärketensor" data-language-autonym="Deutsch" data-language-local-name="saksa" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Electromagnetic_tensor" title="Electromagnetic tensor – inglise" lang="en" hreflang="en" data-title="Electromagnetic tensor" data-language-autonym="English" data-language-local-name="inglise" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tensor_de_campo_electromagn%C3%A9tico" title="Tensor de campo electromagnético – hispaania" lang="es" hreflang="es" data-title="Tensor de campo electromagnético" data-language-autonym="Español" data-language-local-name="hispaania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D9%86%D8%B3%D9%88%D8%B1_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%D9%88%D9%85%D8%BA%D9%86%D8%A7%D8%B7%DB%8C%D8%B3%DB%8C" title="تانسور الکترومغناطیسی – pärsia" lang="fa" hreflang="fa" data-title="تانسور الکترومغناطیسی" data-language-autonym="فارسی" data-language-local-name="pärsia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Tenseur_%C3%A9lectromagn%C3%A9tique" title="Tenseur électromagnétique – prantsuse" lang="fr" hreflang="fr" data-title="Tenseur électromagnétique" data-language-autonym="Français" data-language-local-name="prantsuse" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%84%EC%9E%90%EA%B8%B0%EC%9E%A5_%ED%85%90%EC%84%9C" title="전자기장 텐서 – korea" lang="ko" hreflang="ko" data-title="전자기장 텐서" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tensore_elettromagnetico" title="Tensore elettromagnetico – itaalia" lang="it" hreflang="it" data-title="Tensore elettromagnetico" data-language-autonym="Italiano" data-language-local-name="itaalia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%A0%D7%96%D7%95%D7%A8_%D7%94%D7%A9%D7%93%D7%94_%D7%94%D7%90%D7%9C%D7%A7%D7%98%D7%A8%D7%95%D7%9E%D7%92%D7%A0%D7%98%D7%99" title="טנזור השדה האלקטרומגנטי – heebrea" lang="he" hreflang="he" data-title="טנזור השדה האלקטרומגנטי" data-language-autonym="עברית" data-language-local-name="heebrea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elektromagnetische_veldtensor" title="Elektromagnetische veldtensor – hollandi" lang="nl" hreflang="nl" data-title="Elektromagnetische veldtensor" data-language-autonym="Nederlands" data-language-local-name="hollandi" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%BB%E7%A3%81%E5%A0%B4%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB" title="電磁場テンソル – jaapani" lang="ja" hreflang="ja" data-title="電磁場テンソル" data-language-autonym="日本語" data-language-local-name="jaapani" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tensor_pola_elektromagnetycznego" title="Tensor pola elektromagnetycznego – poola" lang="pl" hreflang="pl" data-title="Tensor pola elektromagnetycznego" data-language-autonym="Polski" data-language-local-name="poola" 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/Tensor_eletromagn%C3%A9tico" title="Tensor eletromagnético – portugali" lang="pt" hreflang="pt" data-title="Tensor eletromagnético" data-language-autonym="Português" data-language-local-name="portugali" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%BC%D0%B0%D0%B3%D0%BD%D0%B8%D1%82%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BF%D0%BE%D0%BB%D1%8F" title="Тензор электромагнитного поля – vene" lang="ru" hreflang="ru" data-title="Тензор электромагнитного поля" data-language-autonym="Русский" data-language-local-name="vene" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Tensori_elektromagnetik" title="Tensori elektromagnetik – albaania" lang="sq" hreflang="sq" data-title="Tensori elektromagnetik" data-language-autonym="Shqip" data-language-local-name="albaania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%BC%D0%B0%D0%B3%D0%BD%D1%96%D1%82%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BF%D0%BE%D0%BB%D1%8F" title="Тензор електромагнітного поля – ukraina" lang="uk" hreflang="uk" data-title="Тензор електромагнітного поля" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9B%BB%E7%A3%81%E5%BC%B5%E9%87%8F" title="電磁張量 – hiina" lang="zh" hreflang="zh" data-title="電磁張量" data-language-autonym="中文" data-language-local-name="hiina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1076013#sitelinks-wikipedia" title="Muuda keelelinke" 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.hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"> <ul><li><a href="/wiki/Elektrilaeng" title="Elektrilaeng">Elektrilaeng</a></li> <li><a href="/wiki/Staatiline_elekter" title="Staatiline elekter">Staatiline elekter</a></li> <li><a href="/wiki/Coulomb%27i_seadus" title="Coulomb'i seadus">Coulomb'i seadus</a></li> <li><a href="/wiki/Elektriv%C3%A4lja_tugevus" title="Elektrivälja tugevus">Elektrivälja tugevus</a></li> <li><a href="/wiki/Elektriline_induktsioon" class="mw-redirect" title="Elektriline induktsioon">Elektriline induktsioon</a></li> <li><a href="/wiki/Gaussi_seadus_elektriv%C3%A4lja_jaoks" title="Gaussi seadus elektrivälja jaoks">Gaussi seadus 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class="sidebar-list-title" style=";"><a href="/wiki/Elektrod%C3%BCnaamika" title="Elektrodünaamika">Elektrodünaamika</a></div> <div class="mw-collapsible-content" style=""> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5492003"><div class="hlist"> <ul><li><a href="/wiki/Lorentzi_j%C3%B5ud" title="Lorentzi jõud">Lorentzi jõud</a></li> <li><a href="/wiki/Elektromotoorj%C3%B5ud" title="Elektromotoorjõud">Elektromotoorjõud</a></li> <li><a href="/wiki/Elektromagnetiline_induktsioon" title="Elektromagnetiline induktsioon">Elektromagnetiline induktsioon</a></li> <li><a href="/wiki/Faraday_seadus" title="Faraday seadus">Faraday seadus</a></li> <li><a href="/wiki/Lenzi_reegel" title="Lenzi reegel">Lenzi reegel</a></li> <li><a href="/wiki/Nihkevool" title="Nihkevool">Nihkevool</a></li> <li><a href="/wiki/Maxwelli_v%C3%B5rrandid" title="Maxwelli võrrandid">Maxwelli võrrandid</a></li> <li><a href="/wiki/Elektromagnetv%C3%A4li" class="mw-redirect" title="Elektromagnetväli">Elektromagnetväli</a></li> <li><a href="/wiki/Elektromagnetiline_kiirgus" title="Elektromagnetiline kiirgus">Elektromagnetiline kiirgus</a></li> <li><a href="/w/index.php?title=Li%C3%A9nardi-Wiecherti_potentsiaal&action=edit&redlink=1" class="new" title="Liénardi-Wiecherti potentsiaal (pole veel kirjutatud)">Liénardi-Wiecherti potentsiaal</a></li> <li><a href="/w/index.php?title=Maxwelli_tensor&action=edit&redlink=1" class="new" title="Maxwelli tensor (pole veel kirjutatud)">Maxwelli tensor</a></li> <li><a href="/w/index.php?title=Poyntingi_vector&action=edit&redlink=1" class="new" title="Poyntingi vector (pole veel kirjutatud)">Poyntingi vector</a></li> <li><a href="/wiki/P%C3%B6%C3%B6risvool" title="Pöörisvool">Pöörisvool</a></li></ul> </div> </div> </div></td> </tr><tr> <td class="sidebar-content" style=";"> <div class="mw-collapsible mw-collapsed" style=""> <div class="sidebar-list-title" style=";"><a href="/wiki/Vooluahel" class="mw-redirect" title="Vooluahel">Vooluahelad</a></div> <div class="mw-collapsible-content" style=""> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5492003"><div class="hlist"> <ul><li><a href="/wiki/Elektrivool" title="Elektrivool">Elektrivool</a></li> <li><a href="/wiki/Pinge_(elekter)" title="Pinge (elekter)">Pinge</a></li> <li><a href="/wiki/Elektromotoorj%C3%B5ud" title="Elektromotoorjõud">Elektromotoorjõud</a></li> <li><a href="/wiki/Ohmi_seadus" title="Ohmi seadus">Ohmi seadus</a></li> <li><a href="/wiki/Kirchhoffi_seadused" title="Kirchhoffi seadused">Kirchhoffi seadused</a></li> <li><a href="/wiki/Alalisvool" title="Alalisvool">Alalisvool</a></li> <li><a href="/wiki/Vahelduvvool" title="Vahelduvvool">Vahelduvvool</a></li> <li><a href="/wiki/Elektritakistus" class="mw-redirect" title="Elektritakistus">Elektritakistus</a></li> <li><a href="/wiki/Elektrijuhtivus" title="Elektrijuhtivus">Elektrijuhtivus</a></li> <li><a href="/wiki/Mahtuvus" title="Mahtuvus">Mahtuvus</a></li> <li><a href="/wiki/Induktiivsus" title="Induktiivsus">Induktiivsus</a></li> <li><a href="/wiki/Memristiivsus" class="mw-redirect" title="Memristiivsus">Memristiivsus</a></li> <li><a href="/wiki/N%C3%A4ivtakistus" title="Näivtakistus">Näivtakistus</a></li> <li><a href="/wiki/Resonaator" title="Resonaator">Resonaator</a></li> <li><a href="/wiki/Lainejuht" class="mw-redirect" title="Lainejuht">Lainejuht</a></li></ul> </div> </div> </div></td> </tr><tr> <td class="sidebar-content" style=";"> <div class="mw-collapsible mw-collapsed" style=""> <div class="sidebar-list-title" style=";"><a href="/wiki/Klassikalise_elektromagnetismi_kovariantne_formuleering" title="Klassikalise elektromagnetismi kovariantne formuleering">Kovariantne formuleering</a></div> <div class="mw-collapsible-content" style=""> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5492003"><div class="hlist"> <ul><li><a class="mw-selflink selflink">Elektromagnetvälja tensor</a></li> <li><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_energia-impulsi_tensor&action=edit&redlink=1" class="new" title="Elektromagnetvälja energia-impulsi tensor (pole veel kirjutatud)">Elektromagnetvälja energia-impulsi tensor</a></li> <li><a href="/w/index.php?title=Neli-vool&action=edit&redlink=1" class="new" title="Neli-vool (pole veel kirjutatud)">Neli-vool</a></li> <li><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_neli-potentsiaal&action=edit&redlink=1" class="new" title="Elektromagnetvälja neli-potentsiaal (pole veel kirjutatud)">Elektromagnetvälja neli-potentsiaal</a></li></ul> </div> </div> </div></td> </tr><tr> <td class="sidebar-content" style=";"> <div class="mw-collapsible mw-collapsed" style=""> <div class="sidebar-list-title" style=";">Teadlased</div> <div class="mw-collapsible-content" style=""> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5492003"><div class="hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" class="mw-redirect" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" class="mw-redirect" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li></ul> </div> </div> </div></td> </tr><tr> <td class="sidebar-navbar" style="padding-top: 0.6em;"><style data-mw-deduplicate="TemplateStyles:r6347537">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar ul{margin:0;display:inline-block;line-height:inherit}.mw-parser-output .navbar li{white-space:nowrap;word-spacing:-0.125em;display:inline}.mw-parser-output .navbar li:not(:last-child):after{content:" · ";font-weight:bold}.mw-parser-output .navbar.mini li abbr[title]{border-bottom:none;text-decoration:none;cursor:inherit}</style><div class="navbar mini"><ul><li class="nv-view"><a href="/wiki/Mall:Elektromagnetism" title="Mall:Elektromagnetism"><abbr title="Vaata seda malli">v</abbr></a></li><li class="nv-edit"><a href="/wiki/Eri:EditPage/Mall:Elektromagnetism" title="Eri:EditPage/Mall:Elektromagnetism"><abbr title="Redigeeri seda malli">r</abbr></a></li></ul></div></td> </tr> </tbody></table></div> <p><b>Elektromagnetvälja tensor</b> on <a href="/wiki/F%C3%BC%C3%BCsikaline_suurus" title="Füüsikaline suurus">füüsikaline suurus</a>, mis võimaldab <a href="/wiki/Elektromagnetv%C3%A4li" class="mw-redirect" title="Elektromagnetväli">elektromagnetvälja</a> <a href="/w/index.php?title=Kovariantsus&action=edit&redlink=1" class="new" title="Kovariantsus (pole veel kirjutatud)">kovariantselt</a> kirjeldada. Elektromagnetvälja tensor on <a href="/wiki/Neljam%C3%B5%C3%B5tmelisus" title="Neljamõõtmelisus">neljamõõtmeline</a> tensor, mida hakkas kasutama <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a> enda loodud <a href="/wiki/Erirelatiivsusteooria" title="Erirelatiivsusteooria">erirelatiivsusteooria</a> formalismis. Elektromagnetvälja tensor võimaldab mõningaid füüsikaseadusi väga kompaktselt kirja panna. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Detailid">Detailid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&veaction=edit&section=1" title="Muuda alaosa "Detailid"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&action=edit&section=1" title="Muuda alaosa "Detailid" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><i>Matemaatiline märkus: selles artiklis kasutatakse <a href="/w/index.php?title=Abstraktne_indeksinotatsioon&action=edit&redlink=1" class="new" title="Abstraktne indeksinotatsioon (pole veel kirjutatud)">abstraktset indeksinotatsiooni</a>.</i></dd></dl> <p>Elektromagnetvälja tensor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270a5daa364616f695db1f470f3d341755df881a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.909ex; height:2.343ex;" alt="{\displaystyle F^{\mu \nu }}"></span> esitatakse tavaliselt maatriksina: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F^{\mu \nu }={\begin{pmatrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }={\begin{pmatrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d43a17292775e392800cb94cd08629e34da9cd7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:44.152ex; height:13.509ex;" alt="{\displaystyle F^{\mu \nu }={\begin{pmatrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&-B_{z}&B_{y}\\E_{y}/c&B_{z}&0&-B_{x}\\E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}"></span></dd></dl></dd></dl> <p>või </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mu \nu }={\begin{pmatrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mu \nu }={\begin{pmatrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e449e0ab8b83f2e76beceded7ed4294bf8be3d69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.171ex; width:40.216ex; height:13.509ex;" alt="{\displaystyle F_{\mu \nu }={\begin{pmatrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&-B_{z}&B_{y}\\-E_{y}/c&B_{z}&0&-B_{x}\\-E_{z}/c&-B_{y}&B_{x}&0\end{pmatrix}}}"></span></dd></dl></dd> <dd>kus <dl><dd><i><b>E</b></i> on <a href="/wiki/Elektriv%C3%A4li" title="Elektriväli">elektriväli</a>,</dd> <dd><i><b>B</b></i> on <a href="/wiki/Magnetv%C3%A4li" title="Magnetväli">magnetväli</a> ja</dd> <dd><i><b>c</b></i> on <a href="/wiki/Valguse_kiirus" title="Valguse kiirus">valguse kiirus</a>.</dd></dl></dd> <dd>Ülaltoodud märgid sõltuvad aegruumi <a href="/w/index.php?title=Meetriline_tensor&action=edit&redlink=1" class="new" title="Meetriline tensor (pole veel kirjutatud)">meetrilise tensori</a> valikust. Siin kasutatakse <a href="/w/index.php?title=M%C3%A4rgikokkulepe&action=edit&redlink=1" class="new" title="Märgikokkulepe (pole veel kirjutatud)">märgikokkulepet</a> <tt>+---</tt>, millele vastab meetriline tensor</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0c95c230eb61399b8b00a052f590838a539493" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:21.86ex; height:12.509ex;" alt="{\displaystyle {\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Omadused">Omadused</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&veaction=edit&section=2" title="Muuda alaosa "Omadused"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&action=edit&section=2" title="Muuda alaosa "Omadused" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Väljatensori maatrikskujust ilmnevad järgmised omadused: </p> <ul><li><a href="/w/index.php?title=Antis%C3%BCmmeetriline_tensor&action=edit&redlink=1" class="new" title="Antisümmeetriline tensor (pole veel kirjutatud)">antisümmeetria</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 F^{\mu \nu }\,=-F^{\nu \mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mo>−</mo> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>μ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }\,=-F^{\nu \mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b8f7dde75caeea98213e58e2bb19857e57a5619" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.113ex; height:2.509ex;" alt="{\displaystyle F^{\mu \nu }\,=-F^{\nu \mu }}"></span> (millest ka nimi <a href="/w/index.php?title=Bivektor&action=edit&redlink=1" class="new" title="Bivektor (pole veel kirjutatud)">bivektor</a>).</li> <li>elektrivälja tensoril on kuus sõltumatut komponenti.</li></ul> <p>Et tegemist on tensoriga, siis moodustub kontraktsioonidel <a href="/w/index.php?title=Lorentzi_invariant&action=edit&redlink=1" class="new" title="Lorentzi invariant (pole veel kirjutatud)">Lorentzi invariant</a>: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mu \nu }F^{\mu \nu }=\ 2\left(B^{2}-{\frac {E^{2}}{c^{2}}}\right)=\mathrm {invariant} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mtext> </mtext> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mu \nu }F^{\mu \nu }=\ 2\left(B^{2}-{\frac {E^{2}}{c^{2}}}\right)=\mathrm {invariant} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68f9fb78f9f0f66d3b3705e4eb30a3a9b8a96c4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.837ex; height:6.343ex;" alt="{\displaystyle F_{\mu \nu }F^{\mu \nu }=\ 2\left(B^{2}-{\frac {E^{2}}{c^{2}}}\right)=\mathrm {invariant} }"></span></dd></dl></dd></dl> <p>Tensori <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F^{\mu \nu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu \nu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97ef295d39589e5d76b67299e4b51601615a191a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.297ex; height:2.343ex;" alt="{\displaystyle F^{\mu \nu }\,}"></span> korrutis oma duaalse tensoriga annab <a href="/w/index.php?title=Pseudoskalaar&action=edit&redlink=1" class="new" title="Pseudoskalaar (pole veel kirjutatud)">pseudoskalaarse</a> invariandi: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\alpha \beta \gamma \delta }F^{\alpha \beta }F^{\gamma \delta }={\frac {4}{c}}\left({\vec {B}}\cdot {\vec {E}}\right)=\mathrm {invariant} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> <mi>γ</mi> <mi>δ</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mi>δ</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{\alpha \beta \gamma \delta }F^{\alpha \beta }F^{\gamma \delta }={\frac {4}{c}}\left({\vec {B}}\cdot {\vec {E}}\right)=\mathrm {invariant} \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d391a1d077655a4eca5f3cb1b07c62611783b31d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.738ex; height:5.176ex;" alt="{\displaystyle \epsilon _{\alpha \beta \gamma \delta }F^{\alpha \beta }F^{\gamma \delta }={\frac {4}{c}}\left({\vec {B}}\cdot {\vec {E}}\right)=\mathrm {invariant} \,}"></span></dd></dl></dd></dl> <p>kus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \epsilon _{\alpha \beta \gamma \delta }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> <mi>γ</mi> <mi>δ</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \epsilon _{\alpha \beta \gamma \delta }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/899b89e0e614d2b88a3825b0418b6fcfbe33b057" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.772ex; height:2.343ex;" alt="{\displaystyle \ \epsilon _{\alpha \beta \gamma \delta }\,}"></span> on neljandat järku täielikult antisümmeetiline pseudotensor ehk <a href="/wiki/Levi-Civita_s%C3%BCmbol" title="Levi-Civita sümbol">Levi-Civita sümbol</a>. </p><p>Märkus: ülalasuva avaldise märk sõltub Levi-Civita sümboli jaoks kasutatavast märgikokkuleppest. Siin kasutatud kokkulepe on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \epsilon _{0123}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0123</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \epsilon _{0123}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1abdf02ee1375272250f1f197e461fbb4b96207d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.432ex; height:2.009ex;" alt="{\displaystyle \ \epsilon _{0123}\,}"></span> = +1. </p><p>Elektromagnetvälja tensori <a href="/wiki/Determinant" title="Determinant">determinant</a> on </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \det \left(F\right)={\frac {1}{c^{2}}}\left({\vec {B}}\cdot {\vec {E}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">det</mo> <mrow> <mo>(</mo> <mi>F</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \det \left(F\right)={\frac {1}{c^{2}}}\left({\vec {B}}\cdot {\vec {E}}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da91ccfac775267ca5e909cf8891cc832e935440" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.211ex; height:5.509ex;" alt="{\displaystyle \det \left(F\right)={\frac {1}{c^{2}}}\left({\vec {B}}\cdot {\vec {E}}\right)^{2}}"></span>.</dd></dl></dd></dl> <p>Elektromagnetvälja tensori saab kirja panna <a href="/w/index.php?title=Elektromagnetv%C3%A4lja_nelipotentsiaal&action=edit&redlink=1" class="new" title="Elektromagnetvälja nelipotentsiaal (pole veel kirjutatud)">4-vektorpotentsiaali</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 A^{\alpha }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\alpha }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee20bc816128af3514b466ce4ed6be6e29540158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.414ex; height:2.343ex;" alt="{\displaystyle A^{\alpha }\,}"></span> kaudu: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\alpha \beta }\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\partial A_{\beta }}{\partial x^{\alpha }}}-{\frac {\partial A_{\alpha }}{\partial x^{\beta }}}\ {\stackrel {\mathrm {def} }{=}}\ \partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mo>−</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\alpha \beta }\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\partial A_{\beta }}{\partial x^{\alpha }}}-{\frac {\partial A_{\alpha }}{\partial x^{\beta }}}\ {\stackrel {\mathrm {def} }{=}}\ \partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76cbcfcf54448a5188cc199294545be663e03423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:37.36ex; height:6.009ex;" alt="{\displaystyle F_{\alpha \beta }\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\partial A_{\beta }}{\partial x^{\alpha }}}-{\frac {\partial A_{\alpha }}{\partial x^{\beta }}}\ {\stackrel {\mathrm {def} }{=}}\ \partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha }}"></span></dd></dl></dd></dl> <p>Kus nelivektorpotentsiaal on moodustatud magnetvälja vektorpotentsiaalist ja elektrivälja (skalaarsest) potentsiaalist: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{\mu }=\left({\frac {\phi }{c}},{\vec {A}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ϕ</mi> <mi>c</mi> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\mu }=\left({\frac {\phi }{c}},{\vec {A}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e11e75f069441b52fdbdee8ef3e5a517d03219b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.485ex; height:6.176ex;" alt="{\displaystyle A^{\mu }=\left({\frac {\phi }{c}},{\vec {A}}\right)}"></span></dd></dl></dd></dl> <p>ja selle <a href="/w/index.php?title=Kovariantsus&action=edit&redlink=1" class="new" title="Kovariantsus (pole veel kirjutatud)">kovariantne</a> kuju leitakse korrutamisel <a href="/w/index.php?title=Minkowski_meetrika&action=edit&redlink=1" class="new" title="Minkowski meetrika (pole veel kirjutatud)">Minkowski meetrikaga</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 \eta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41724238aa62aeef8fd437347731c787721cfd04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.557ex; height:2.176ex;" alt="{\displaystyle \eta \,}"></span> : </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\mu }\,=\eta _{\mu \nu }A^{\nu }=\left(-{\frac {\phi }{c}},{\vec {A}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ϕ</mi> <mi>c</mi> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\mu }\,=\eta _{\mu \nu }A^{\nu }=\left(-{\frac {\phi }{c}},{\vec {A}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3995596f45b47c1ee437926ba06fb26777d15c35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.875ex; height:6.176ex;" alt="{\displaystyle A_{\mu }\,=\eta _{\mu \nu }A^{\nu }=\left(-{\frac {\phi }{c}},{\vec {A}}\right)}"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Maxwelli_võrrandid"><span id="Maxwelli_v.C3.B5rrandid"></span>Maxwelli võrrandid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&veaction=edit&section=3" title="Muuda alaosa "Maxwelli võrrandid"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&action=edit&section=3" title="Muuda alaosa "Maxwelli võrrandid" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Next.svg/12px-Next.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Next.svg/18px-Next.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Next.svg/24px-Next.svg.png 2x" data-file-width="160" data-file-height="160" /></span></span> <i>Pikemalt artiklis <a href="/wiki/Maxwelli_v%C3%B5rrandid" title="Maxwelli võrrandid">Maxwelli võrrandid</a></i></dd></dl> <p><a href="/wiki/Maxwelli_v%C3%B5rrandid" title="Maxwelli võrrandid">Maxwelli võrrandid</a> võtavad elektromagnetilise tensori kaudu väljendudes võrdlemisi kompaktse kuju. Elektrivälja jaoks kehtib </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da74849fd89ec90b2a3fe968247e8b291fc49ce9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.201ex; height:3.343ex;" alt="{\displaystyle \partial _{\beta }F^{\alpha \beta }=\mu _{0}J^{\alpha }\,}"></span></dd></dl></dd></dl> <p>kus </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J^{\alpha }=(c\,\rho ,{\vec {J}})\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>c</mi> <mspace width="thinmathspace" /> <mi>ρ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>J</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J^{\alpha }=(c\,\rho ,{\vec {J}})\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac754110fad6734bfae20bc627c951edfee11dd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.523ex; height:3.343ex;" alt="{\displaystyle J^{\alpha }=(c\,\rho ,{\vec {J}})\,}"></span></dd></dl></dd></dl> <p>on <a href="/wiki/Elektrilaeng" title="Elektrilaeng">elektrilaengu</a> <a href="/w/index.php?title=4-vool&action=edit&redlink=1" class="new" title="4-vool (pole veel kirjutatud)">4-vool</a>. </p><p>Võrrandid magnetismi jaoks taanduvad kujule </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\alpha \beta ,\gamma }+F_{\beta \gamma ,\alpha }+F_{\gamma \alpha ,\beta }=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> <mo>,</mo> <mi>γ</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi>γ</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\alpha \beta ,\gamma }+F_{\beta \gamma ,\alpha }+F_{\gamma \alpha ,\beta }=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/289cda33b711c74d410cda3606b8784a92aecf99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.541ex; height:2.843ex;" alt="{\displaystyle F_{\alpha \beta ,\gamma }+F_{\beta \gamma ,\alpha }+F_{\gamma \alpha ,\beta }=0\,}"></span></dd></dl></dd></dl> <p>kus koma tähistab <a href="/wiki/Osatuletis" title="Osatuletis">osatuletist</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\partial f \over \partial x^{\gamma }}\equiv \partial _{\gamma }f\equiv {f}_{,\gamma }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>≡</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mi>f</mi> <mo>≡</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> <mi>γ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\partial f \over \partial x^{\gamma }}\equiv \partial _{\gamma }f\equiv {f}_{,\gamma }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/688829f80f6cffca1d37c87199562fd9f4de9bb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.165ex; height:5.676ex;" alt="{\displaystyle {\partial f \over \partial x^{\gamma }}\equiv \partial _{\gamma }f\equiv {f}_{,\gamma }}"></span>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Vaata_ka">Vaata ka</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&veaction=edit&section=4" title="Muuda alaosa "Vaata ka"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektromagnetv%C3%A4lja_tensor&action=edit&section=4" title="Muuda alaosa "Vaata ka" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elektromagnetism" title="Elektromagnetism">Elektromagnetism</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Pärit leheküljelt "<a dir="ltr" href="https://et.wikipedia.org/w/index.php?title=Elektromagnetvälja_tensor&oldid=5285624">https://et.wikipedia.org/w/index.php?title=Elektromagnetvälja_tensor&oldid=5285624</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Eri:Kategooriad" title="Eri:Kategooriad">Kategooriad</a>: <ul><li><a href="/wiki/Kategooria:Elektromagnetism" title="Kategooria:Elektromagnetism">Elektromagnetism</a></li><li><a href="/wiki/Kategooria:Relatiivsusteooria" title="Kategooria:Relatiivsusteooria">Relatiivsusteooria</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Selle lehekülje viimane muutmine: 07:50, 20. aprill 2019.</li> <li id="footer-info-copyright">Tekst on kasutatav vastavalt Creative Commonsi litsentsile "<a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.et">Autorile viitamine + jagamine samadel tingimustel</a>"; 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