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id="toc-Definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spænding" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Spænding"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Spænding</span> </div> </a> <ul id="toc-Spænding-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksempel:_Punktladning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksempel:_Punktladning"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Eksempel: Punktladning</span> </div> </a> <ul id="toc-Eksempel:_Punktladning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Litteraturhenvisninger" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Litteraturhenvisninger"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> 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mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vis/skjul indholdsfortegnelsen</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">Elektrisk potential</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="Gå til en artikel på et andet sprog. Tilgængelig på 64 sprog" > <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-64" 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">64 sprog</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/Elektriese_potensiaal" title="Elektriese potensiaal – afrikaans" lang="af" hreflang="af" data-title="Elektriese potensiaal" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8A%A4%E1%88%8C%E1%8A%AD%E1%89%B5%E1%88%AA%E1%8A%AD_%E1%8A%A5%E1%88%9D%E1%89%85" title="የኤሌክትሪክ እምቅ – amharisk" lang="am" hreflang="am" data-title="የኤሌክትሪክ እምቅ" data-language-autonym="አማርኛ" data-language-local-name="amharisk" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D9%85%D9%88%D9%86_%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A" title="كمون كهربائي – arabisk" lang="ar" hreflang="ar" data-title="كمون كهربائي" data-language-autonym="العربية" data-language-local-name="arabisk" 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/Potencial_ll%C3%A9tricu" title="Potencial llétricu – asturisk" lang="ast" hreflang="ast" data-title="Potencial llétricu" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Elektrisches_Potenzi%C3%A4u" title="Elektrisches Potenziäu – Bavarian" lang="bar" hreflang="bar" data-title="Elektrisches Potenziäu" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%8B%D1%87%D0%BD%D1%8B_%D0%BF%D0%B0%D1%82%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB" title="Электрычны патэнцыял – belarusisk" lang="be" hreflang="be" data-title="Электрычны патэнцыял" data-language-autonym="Беларуская" data-language-local-name="belarusisk" 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%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%8B%D1%87%D0%BD%D1%8B_%D0%BF%D0%B0%D1%82%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB" title="Электрычны патэнцыял – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Электрычны патэнцыял" 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%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D0%BD_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="Електричен потенциал – bulgarsk" lang="bg" hreflang="bg" data-title="Електричен потенциал" data-language-autonym="Български" data-language-local-name="bulgarsk" 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%A4%E0%A6%A1%E0%A6%BC%E0%A6%BF%E0%A7%8E_%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%AC" title="তড়িৎ বিভব – bengali" lang="bn" hreflang="bn" data-title="তড়িৎ বিভব" data-language-autonym="বাংলা" data-language-local-name="bengali" 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/Elektri%C4%8Dni_potencijal" title="Električni potencijal – bosnisk" lang="bs" hreflang="bs" data-title="Električni potencijal" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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/Potencial_el%C3%A8ctric" title="Potencial elèctric – catalansk" lang="ca" hreflang="ca" data-title="Potencial elèctric" data-language-autonym="Català" data-language-local-name="catalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%DB%86%D8%AA%DB%95%D9%86%D8%B4%DA%B5%DB%8C_%DA%A9%D8%A7%D8%B1%DB%95%D8%A8%D8%A7%DB%8C%DB%8C" title="پۆتەنشڵی کارەبایی – sorani" lang="ckb" hreflang="ckb" data-title="پۆتەنشڵی کارەبایی" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Elektrick%C3%BD_potenci%C3%A1l" title="Elektrický potenciál – tjekkisk" lang="cs" hreflang="cs" data-title="Elektrický potenciál" data-language-autonym="Čeština" data-language-local-name="tjekkisk" 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%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="Электростатикăлла потенциал – tjuvasjisk" lang="cv" hreflang="cv" data-title="Электростатикăлла потенциал" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elektrisches_Potential" title="Elektrisches Potential – tysk" lang="de" hreflang="de" data-title="Elektrisches Potential" data-language-autonym="Deutsch" data-language-local-name="tysk" 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%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CF%8C_%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CF%8C" title="Ηλεκτρικό δυναμικό – græsk" lang="el" hreflang="el" data-title="Ηλεκτρικό δυναμικό" data-language-autonym="Ελληνικά" data-language-local-name="græsk" 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/Electric_potential" title="Electric potential – engelsk" lang="en" hreflang="en" data-title="Electric potential" data-language-autonym="English" data-language-local-name="engelsk" 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/Elektra_potencialo" title="Elektra potencialo – esperanto" lang="eo" hreflang="eo" data-title="Elektra potencialo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico" title="Potencial eléctrico – spansk" lang="es" hreflang="es" data-title="Potencial eléctrico" data-language-autonym="Español" data-language-local-name="spansk" 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/Elektriv%C3%A4lja_potentsiaal" title="Elektrivälja potentsiaal – estisk" lang="et" hreflang="et" data-title="Elektrivälja potentsiaal" data-language-autonym="Eesti" data-language-local-name="estisk" 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/Potentzial_elektriko" title="Potentzial elektriko – baskisk" lang="eu" hreflang="eu" data-title="Potentzial elektriko" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%BE%D8%AA%D8%A7%D9%86%D8%B3%DB%8C%D9%84_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="پتانسیل الکتریکی – persisk" lang="fa" hreflang="fa" data-title="پتانسیل الکتریکی" data-language-autonym="فارسی" data-language-local-name="persisk" 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/S%C3%A4hk%C3%B6potentiaali" title="Sähköpotentiaali – finsk" lang="fi" hreflang="fi" data-title="Sähköpotentiaali" data-language-autonym="Suomi" data-language-local-name="finsk" 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/Potentiel_%C3%A9lectrique" title="Potentiel électrique – fransk" lang="fr" hreflang="fr" data-title="Potentiel électrique" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Poit%C3%A9inseal_leictreach" title="Poitéinseal leictreach – irsk" lang="ga" hreflang="ga" data-title="Poitéinseal leictreach" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Potencial_el%C3%A9ctrico" title="Potencial eléctrico – galicisk" lang="gl" hreflang="gl" data-title="Potencial eléctrico" data-language-autonym="Galego" data-language-local-name="galicisk" 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%A4%D7%95%D7%98%D7%A0%D7%A6%D7%99%D7%90%D7%9C_%D7%97%D7%A9%D7%9E%D7%9C%D7%99" title="פוטנציאל חשמלי – hebraisk" lang="he" hreflang="he" data-title="פוטנציאל חשמלי" data-language-autonym="עברית" data-language-local-name="hebraisk" 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%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%B5" title="विद्युत विभव – hindi" lang="hi" hreflang="hi" data-title="विद्युत विभव" 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/Elektri%C4%8Dni_potencijal" title="Električni potencijal – kroatisk" lang="hr" hreflang="hr" data-title="Električni potencijal" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Elektromos_potenci%C3%A1l" title="Elektromos potenciál – ungarsk" lang="hu" hreflang="hu" data-title="Elektromos potenciál" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Potensial_listrik" title="Potensial listrik – indonesisk" lang="id" hreflang="id" data-title="Potensial listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Potenziale_elettrico" title="Potenziale elettrico – italiensk" lang="it" hreflang="it" data-title="Potenziale elettrico" data-language-autonym="Italiano" data-language-local-name="italiensk" 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/%E9%9B%BB%E4%BD%8D" title="電位 – japansk" lang="ja" hreflang="ja" data-title="電位" data-language-autonym="日本語" data-language-local-name="japansk" 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%94%E1%83%9A%E1%83%94%E1%83%A5%E1%83%A2%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%9E%E1%83%9D%E1%83%A2%E1%83%94%E1%83%9C%E1%83%AA%E1%83%98%E1%83%90%E1%83%9A%E1%83%98" title="ელექტრული პოტენციალი – georgisk" lang="ka" hreflang="ka" data-title="ელექტრული პოტენციალი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%84%EC%9C%84" title="전위 – koreansk" lang="ko" hreflang="ko" data-title="전위" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D0%BD_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB" title="Електричен потенцијал – makedonsk" lang="mk" hreflang="mk" data-title="Електричен потенцијал" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A6%D0%B0%D1%85%D0%B8%D0%BB%D0%B3%D0%B0%D0%B0%D0%BD_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="Цахилгаан потенциал – mongolsk" lang="mn" hreflang="mn" data-title="Цахилгаан потенциал" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%B5" title="विद्युत विभव – marathisk" lang="mr" hreflang="mr" data-title="विद्युत विभव" data-language-autonym="मराठी" data-language-local-name="marathisk" 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/Keupayaan_elektrik" title="Keupayaan elektrik – malajisk" lang="ms" hreflang="ms" data-title="Keupayaan elektrik" data-language-autonym="Bahasa Melayu" data-language-local-name="malajisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elektrische_potentiaal" title="Elektrische potentiaal – nederlandsk" lang="nl" hreflang="nl" data-title="Elektrische potentiaal" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" 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/Elektrisk_potensial" title="Elektrisk potensial – nynorsk" lang="nn" hreflang="nn" data-title="Elektrisk potensial" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Elektrisk_potensial" title="Elektrisk potensial – bokmål" lang="nb" hreflang="nb" data-title="Elektrisk potensial" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AC%E0%AC%BF%E0%AC%A6%E0%AD%8D%E0%AD%9F%E0%AD%81%E0%AC%A4%E0%AD%8D_%E0%AC%AC%E0%AC%BF%E0%AC%AD%E0%AC%AC" title="ବିଦ୍ୟୁତ୍ ବିଭବ – oriya" lang="or" hreflang="or" data-title="ବିଦ୍ୟୁତ୍ ବିଭବ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="oriya" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Potencja%C5%82_elektryczny" title="Potencjał elektryczny – polsk" lang="pl" hreflang="pl" data-title="Potencjał elektryczny" data-language-autonym="Polski" data-language-local-name="polsk" 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/Potencial_el%C3%A9trico" title="Potencial elétrico – portugisisk" lang="pt" hreflang="pt" data-title="Potencial elétrico" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Poten%C8%9Bial_electric" title="Potențial electric – rumænsk" lang="ro" hreflang="ro" data-title="Potențial electric" data-language-autonym="Română" data-language-local-name="rumænsk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="Электростатический потенциал – russisk" lang="ru" hreflang="ru" data-title="Электростатический потенциал" data-language-autonym="Русский" data-language-local-name="russisk" 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/Elektri%C4%8Dni_potencijal" title="Električni potencijal – serbokroatisk" lang="sh" hreflang="sh" data-title="Električni potencijal" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" 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/Electric_potential" title="Electric potential – Simple English" lang="en-simple" hreflang="en-simple" data-title="Electric potential" 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/Elektrick%C3%BD_potenci%C3%A1l" title="Elektrický potenciál – slovakisk" lang="sk" hreflang="sk" data-title="Elektrický potenciál" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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/Elektri%C4%8Dni_potencial" title="Električni potencial – slovensk" lang="sl" hreflang="sl" data-title="Električni potencial" data-language-autonym="Slovenščina" data-language-local-name="slovensk" 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/Mundshm%C3%ABria_elektrike" title="Mundshmëria elektrike – albansk" lang="sq" hreflang="sq" data-title="Mundshmëria elektrike" data-language-autonym="Shqip" data-language-local-name="albansk" 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%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB" title="Електрични потенцијал – serbisk" lang="sr" hreflang="sr" data-title="Електрични потенцијал" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A8%E0%B8%B1%E0%B8%81%E0%B8%A2%E0%B9%8C%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="ศักย์ไฟฟ้า – thai" lang="th" hreflang="th" data-title="ศักย์ไฟฟ้า" data-language-autonym="ไทย" data-language-local-name="thai" 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/Elektrikong_potensiyal" title="Elektrikong potensiyal – tagalog" lang="tl" hreflang="tl" data-title="Elektrikong potensiyal" data-language-autonym="Tagalog" data-language-local-name="tagalog" 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/Elektrik_potansiyeli" title="Elektrik potansiyeli – tyrkisk" lang="tr" hreflang="tr" data-title="Elektrik potansiyeli" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="Электростатик потенциал – tatarisk" lang="tt" hreflang="tt" data-title="Электростатик потенциал" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" 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%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%BF%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D0%BB" title="Електростатичний потенціал – ukrainsk" lang="uk" hreflang="uk" data-title="Електростатичний потенціал" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur badge-Q70893996 mw-list-item" title=""><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%82%DB%8C_%D8%AC%D9%8F%DB%81%D8%AF" title="برقی جُہد – urdu" lang="ur" hreflang="ur" data-title="برقی جُہد" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Elektrostatik_potensial" title="Elektrostatik potensial – usbekisk" lang="uz" hreflang="uz" data-title="Elektrostatik potensial" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_th%E1%BA%BF" title="Điện thế – vietnamesisk" lang="vi" hreflang="vi" data-title="Điện thế" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" 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/%E7%94%B5%E5%8A%BF" title="电势 – wu-kinesisk" lang="wuu" hreflang="wuu" data-title="电势" data-language-autonym="吴语" data-language-local-name="wu-kinesisk" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9B%BB%E5%8B%A2" title="電勢 – kinesisk" lang="zh" hreflang="zh" data-title="電勢" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E5%8B%A2" title="電勢 – kantonesisk" lang="yue" hreflang="yue" data-title="電勢" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</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/Q55451#sitelinks-wikipedia" title="Redigér sproglinks" class="wbc-editpage">Redigér links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Navnerum"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet 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class="mw-content-ltr mw-parser-output" lang="da" dir="ltr"><p>Det <b>elektriske potential</b> er den <a href="/wiki/Potentiel_energi" title="Potentiel energi">potentielle energi</a> pr. <a href="/wiki/Elektrisk_ladning" title="Elektrisk ladning">ladning</a> i et <a href="/wiki/Elektrisk_felt" title="Elektrisk felt">elektrisk felt</a>. Forskellen i <a href="/wiki/Potential_(fysik)" title="Potential (fysik)">potential</a> mellem to punkter kaldes for <a href="/wiki/Sp%C3%A6nding" class="mw-redirect" title="Spænding">spændingen</a>, som spiller en central rolle i <a href="/wiki/Elektriske_kredsl%C3%B8b" class="mw-redirect" title="Elektriske kredsløb">elektriske kredsløb</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrisk_potential&veaction=edit&section=1" title="Redigér afsnit: Definition" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrisk_potential&action=edit&section=1" title="Edit section's source code: Definition"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hvis en ladning <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> </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/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> har den elektriske potentielle energi <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 W_{\text{pot}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{\text{pot}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dff1adfda917410d56c914cadb43a015a349ddf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.802ex; height:2.843ex;" alt="{\displaystyle W_{\text{pot}}}"></span> i punktet <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 {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6aec3c9ce13b53e9e24c98e7cce4212627884c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.223ex; height:2.343ex;" alt="{\displaystyle {\vec {r}}}"></span>, er potentialet <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>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> altså givet ved: </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 \phi ({\vec {r}})={\frac {W_{\text{pot}}({\vec {r}})}{q}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mrow> <mi>q</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ({\vec {r}})={\frac {W_{\text{pot}}({\vec {r}})}{q}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eef7fe42061e3f1ec2c7ce0276fe7c9bcef81109" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.186ex; height:6.176ex;" alt="{\displaystyle \phi ({\vec {r}})={\frac {W_{\text{pot}}({\vec {r}})}{q}}}"></span></dd></dl> <p>For et <a href="/wiki/Konservativt_kraftfelt" title="Konservativt kraftfelt">konservativt kraftfelt</a> generelt er <a href="/wiki/Kraft" title="Kraft">kraften</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 {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> givet ved gradienten til den potentielle energi <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 W_{\text{pot}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{\text{pot}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dff1adfda917410d56c914cadb43a015a349ddf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.802ex; height:2.843ex;" alt="{\displaystyle W_{\text{pot}}}"></span>: </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 {\vec {F}}=-{\vec {\nabla }}W_{\text{pot}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=-{\vec {\nabla }}W_{\text{pot}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ed24042dcfe1f4da84aac2294bcc7c2828f0f50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.415ex; height:3.509ex;" alt="{\displaystyle {\vec {F}}=-{\vec {\nabla }}W_{\text{pot}}}"></span></dd></dl> <p>På samme måde er det elektriske felt <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> </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/2bc18ae485a72f148e85ccbeff2b3dcdd4f5f3f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}}"></span> den negative gradient til potentialet: </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 {\vec {E}}=-{\vec {\nabla }}\phi }"> <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> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}=-{\vec {\nabla }}\phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc41a75a4a599047a5aea2cf51af49bee89347c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.004ex; height:3.176ex;" alt="{\displaystyle {\vec {E}}=-{\vec {\nabla }}\phi }"></span></dd></dl> <p>Omvendt kan det elektriske potential skrives som integralet af det elektriske felt. <sup id="cite_ref-Demtröder_potential_1-0" class="reference"><a href="#cite_note-Demtröder_potential-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Spænding"><span id="Sp.C3.A6nding"></span>Spænding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrisk_potential&veaction=edit&section=2" title="Redigér afsnit: Spænding" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrisk_potential&action=edit&section=2" title="Edit section's source code: Spænding"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="detail"><span><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/15px-Nuvola_apps_download_manager2-70%25.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/23px-Nuvola_apps_download_manager2-70%25.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/30px-Nuvola_apps_download_manager2-70%25.svg.png 2x" data-file-width="60" data-file-height="60" /></span></span> <span>Hovedartikel: <a href="/wiki/Sp%C3%A6nding" class="mw-redirect" title="Spænding">Spænding</a>.</span></span></div> <p>I et <a href="/wiki/Elektrisk_kredsl%C3%B8b" class="mw-redirect" title="Elektrisk kredsløb">elektrisk kredsløb</a> bevæger ladninger sig fra et højt potential - genereret af en <a href="/w/index.php?title=Sp%C3%A6ndingskilde&action=edit&redlink=1" class="new" title="Spændingskilde (ikke skrevet endnu)">spændingskilde</a> - til et lavere potential. Forskellen i potential mellem to punkter i kredsløbet kaldes for spændingen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span>: <sup id="cite_ref-Demtröder_potential_1-1" class="reference"><a href="#cite_note-Demtröder_potential-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=\Delta \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=\Delta \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c30655f62ac5cb25b03dc3653c3ac46f508cd29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.202ex; height:2.509ex;" alt="{\displaystyle U=\Delta \phi }"></span></dd></dl> <p>I såkaldte ohmske modstande kan spændingen relateres til <a href="/wiki/Str%C3%B8mstyrke" class="mw-redirect" title="Strømstyrke">strømstyrken</a> vha. <a href="/wiki/Ohms_lov" title="Ohms lov">Ohms lov</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Eksempel:_Punktladning">Eksempel: Punktladning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrisk_potential&veaction=edit&section=3" title="Redigér afsnit: Eksempel: Punktladning" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrisk_potential&action=edit&section=3" title="Edit section's source code: Eksempel: Punktladning"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="detail"><span><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/15px-Nuvola_apps_download_manager2-70%25.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/23px-Nuvola_apps_download_manager2-70%25.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Nuvola_apps_download_manager2-70%25.svg/30px-Nuvola_apps_download_manager2-70%25.svg.png 2x" data-file-width="60" data-file-height="60" /></span></span> <span>Hovedartikel: <a href="/wiki/Coulombs_lov" title="Coulombs lov">Coulombs lov</a>.</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fil:Electric_potential_varying_charge.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Electric_potential_varying_charge.gif/220px-Electric_potential_varying_charge.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/f/f8/Electric_potential_varying_charge.gif 1.5x" data-file-width="300" data-file-height="300" /></a><figcaption>Potentialet omkring en ladning, når ladningen bliver mindre og mindre. Først er ladningen positiv (rød), men bliver derefter negativ (blå).</figcaption></figure> <p>I følge Coulombs lov er kraften mellem en ladning <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> </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/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> og en ladning <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> </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/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> givet ved: </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 {\vec {F}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}{\hat {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mi>q</mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}{\hat {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ded8a9145a4dadb9cb490116e2e53fd21c71e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.373ex; height:5.843ex;" alt="{\displaystyle {\vec {F}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}{\hat {r}}}"></span></dd></dl> <p>hvor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acb0a8377db20e42274444cb181d51b5532b5844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.138ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{0}}"></span> <a href="/wiki/Vakuumpermittiviteten" title="Vakuumpermittiviteten">vakuumpermittiviteten</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 \varepsilon _{0}=8.854187817...\times 10^{-12}{\text{F}}{\text{m}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>8.854187817...</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>F</mtext> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{0}=8.854187817...\times 10^{-12}{\text{F}}{\text{m}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d40ff0a265dd285e8c0070a395db4a96b740e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.555ex; height:3.009ex;" alt="{\displaystyle \varepsilon _{0}=8.854187817...\times 10^{-12}{\text{F}}{\text{m}}^{-1}}"></span> (<a href="/wiki/Farad" title="Farad">Farad</a> pr. <a href="/wiki/Meter" title="Meter">meter</a>)</dd></dl> <p>mens <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 {\hat {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1009619964ce33a4a02aaa7cf82adc0fb0a50f23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.292ex; height:2.176ex;" alt="{\displaystyle {\hat {r}}}"></span> er <a href="/wiki/Enhedsvektor" title="Enhedsvektor">enhedsvektoren</a>, der går fra ladning <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> </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/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> til <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> </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/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span>. Det elektriske felt omkring <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> </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/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> er derfor <sup id="cite_ref-Demtröder_Coulomb_2-0" class="reference"><a href="#cite_note-Demtröder_Coulomb-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {E}}={\frac {\vec {F}}{q}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r^{2}}}{\hat {r}}}"> <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> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> <mi>q</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}={\frac {\vec {F}}{q}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r^{2}}}{\hat {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd4be519b079db52af70d3877a05cc16d4335490" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.279ex; height:6.509ex;" alt="{\displaystyle {\vec {E}}={\frac {\vec {F}}{q}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r^{2}}}{\hat {r}}}"></span></dd></dl> <p>Følgelig er potentialet altså givet ved integralet: </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 \phi ({\vec {r}})=\int _{r}^{\infty }{\vec {E}}({\vec {r}}')\cdot {\text{d}}{\vec {r}}'=\int _{r}^{\infty }{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r'^{2}}}{\hat {r}}\cdot {\text{d}}{\vec {r}}'={\frac {Q}{4\pi \varepsilon _{0}}}\int _{r}^{\infty }{\frac {1}{r'^{2}}}{\text{d}}r'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>′</mo> </msup> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <msup> <mi>r</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <msup> <mi>r</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ({\vec {r}})=\int _{r}^{\infty }{\vec {E}}({\vec {r}}')\cdot {\text{d}}{\vec {r}}'=\int _{r}^{\infty }{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r'^{2}}}{\hat {r}}\cdot {\text{d}}{\vec {r}}'={\frac {Q}{4\pi \varepsilon _{0}}}\int _{r}^{\infty }{\frac {1}{r'^{2}}}{\text{d}}r'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cf7e360c6cfb643ad999fdffa034e2721f46352" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:65.569ex; height:5.843ex;" alt="{\displaystyle \phi ({\vec {r}})=\int _{r}^{\infty }{\vec {E}}({\vec {r}}')\cdot {\text{d}}{\vec {r}}'=\int _{r}^{\infty }{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r'^{2}}}{\hat {r}}\cdot {\text{d}}{\vec {r}}'={\frac {Q}{4\pi \varepsilon _{0}}}\int _{r}^{\infty }{\frac {1}{r'^{2}}}{\text{d}}r'}"></span></dd></dl> <p>Grænsen <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 \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> kan vælges frit uden fysisk betydning, men den er her valgt for at potentialet er nul uendeligt langt væk fra <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> </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/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span>. Integralet af én over afstanden i anden er minus én over afstanden: </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 \phi ({\vec {r}})={\frac {Q}{4\pi \varepsilon _{0}}}\left[-{\frac {1}{r'}}\right]_{r}^{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msubsup> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mo>′</mo> </msup> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ({\vec {r}})={\frac {Q}{4\pi \varepsilon _{0}}}\left[-{\frac {1}{r'}}\right]_{r}^{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/442eac333beb6331183a7e9327ea53e3f1b3f4ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.693ex; height:6.176ex;" alt="{\displaystyle \phi ({\vec {r}})={\frac {Q}{4\pi \varepsilon _{0}}}\left[-{\frac {1}{r'}}\right]_{r}^{\infty }}"></span></dd></dl> <p>Én over uendelig er blot nul, så potentialet er derfor givet ved: </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 \phi ({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/990fb6a4621cdc3cf8357c4fa87111dd0635a8ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.659ex; height:5.843ex;" alt="{\displaystyle \phi ({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r}}}"></span></dd></dl> <p>Det ses, at potentialet som forventet er nul, når afstanden er uendelig stor. Potentialet blevet derimod større og større, jo mindre afstanden bliver. Hvis ladningerne <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> </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/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> og <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> </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/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> har samme fortegn, vil de altså frastøde hinanden, mens ladninger med forskelligt fortegn tiltrækker hinanden. </p> <div class="mw-heading mw-heading2"><h2 id="Litteraturhenvisninger">Litteraturhenvisninger</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektrisk_potential&veaction=edit&section=4" title="Redigér afsnit: Litteraturhenvisninger" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektrisk_potential&action=edit&section=4" title="Edit section's source code: Litteraturhenvisninger"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r11780210">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Demtröder_potential-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Demtröder_potential_1-0"><sup>a</sup></a> <a href="#cite_ref-Demtröder_potential_1-1"><sup>b</sup></a></span> <span class="reference-text">Demtröder, Wolfgang. "Elektrostatik", <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-642-29944-5"><i>Experimentalphysik 2 - Elektrizität und Optik</i></a> (6. udgave), Springer Spektrum. 2002, s. 9-11. <a href="/wiki/Internationalt_Standardbognummer" title="Internationalt Standardbognummer">ISBN</a> <a href="/wiki/Speciel:ISBN-s%C3%B8gning/978-3-642-29943-8" title="Speciel:ISBN-søgning/978-3-642-29943-8">978-3-642-29943-8</a>.</span> </li> <li id="cite_note-Demtröder_Coulomb-2"><span class="mw-cite-backlink"><a href="#cite_ref-Demtröder_Coulomb_2-0">^</a></span> <span class="reference-text">Demtröder, Wolfgang. "Elektrostatik", <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-642-29944-5"><i>Experimentalphysik 2 - Elektrizität und Optik</i></a> (6. udgave), Springer Spektrum. 2002, s. 3-5. <a href="/wiki/Internationalt_Standardbognummer" title="Internationalt Standardbognummer">ISBN</a> <a href="/wiki/Speciel:ISBN-s%C3%B8gning/978-3-642-29943-8" title="Speciel:ISBN-søgning/978-3-642-29943-8">978-3-642-29943-8</a>.</span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r11759279">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist 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