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data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Til toppen)</div> </a> </li> <li id="toc-Historisk_bakgrunn" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historisk_bakgrunn"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historisk bakgrunn</span> </div> </a> <ul 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class="vector-toc-list"> </ul> </li> <li id="toc-Coulomb-potensialet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coulomb-potensialet"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Coulomb-potensialet</span> </div> </a> <ul id="toc-Coulomb-potensialet-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Korreksjoner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Korreksjoner"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Korreksjoner</span> </div> </a> <button aria-controls="toc-Korreksjoner-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Korreksjoner</span> </button> <ul id="toc-Korreksjoner-sublist" class="vector-toc-list"> <li id="toc-Kvanteelektrodynamikk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kvanteelektrodynamikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Kvanteelektrodynamikk</span> </div> </a> <ul id="toc-Kvanteelektrodynamikk-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksterne_lenker" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksterne_lenker"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Eksterne lenker</span> </div> </a> <ul id="toc-Eksterne_lenker-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="Innhold" 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="Vis/skjul innholdsfortegnelsen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vis/skjul innholdsfortegnelsen</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">Coulombs lov</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 artikkel på et annet språk. Tilgjengelig på 79 språk" > <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-79" 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">79 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Coulomb-lova" title="Coulomb-lova – norsk nynorsk" lang="nn" hreflang="nn" data-title="Coulomb-lova" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Coulombs_lov" title="Coulombs lov – dansk" lang="da" hreflang="da" data-title="Coulombs lov" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Coulombs_lag" title="Coulombs lag – svensk" lang="sv" hreflang="sv" data-title="Coulombs lag" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/K%C3%BAlombskraftur" title="Kúlombskraftur – islandsk" lang="is" hreflang="is" data-title="Kúlombskraftur" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Coulomb_se_wet" title="Coulomb se wet – afrikaans" lang="af" hreflang="af" data-title="Coulomb se wet" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Coulombsches_Gesetz" title="Coulombsches Gesetz – sveitsertysk" lang="gsw" hreflang="gsw" data-title="Coulombsches Gesetz" data-language-autonym="Alemannisch" data-language-local-name="sveitsertysk" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8A%A9%E1%88%8E%E1%88%9D%E1%89%A5_%E1%88%85%E1%8C%8D" title="የኩሎምብ ህግ – amharisk" lang="am" hreflang="am" data-title="የኩሎምብ ህግ" 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%82%D8%A7%D9%86%D9%88%D9%86_%D9%83%D9%88%D9%84%D9%88%D9%85" title="قانون كولوم – arabisk" lang="ar" hreflang="ar" data-title="قانون كولوم" 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/Llei_de_Coulomb" title="Llei de Coulomb – asturisk" lang="ast" hreflang="ast" data-title="Llei de Coulomb" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kulon_qanunu" title="Kulon qanunu – aserbajdsjansk" lang="az" hreflang="az" data-title="Kulon qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%81%E0%A6%B2%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="কুলম্বের সূত্র – bengali" lang="bn" hreflang="bn" data-title="কুলম্বের সূত্র" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%B0" title="Закон Кулона – belarusisk" lang="be" hreflang="be" data-title="Закон Кулона" 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%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%9A%D1%83%D0%BB%D1%91%D0%BD%D0%B0" title="Закон Кулёна – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Закон Кулёна" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" 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%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BD%D0%B0_%D0%9A%D1%83%D0%BB%D0%BE%D0%BD" title="Закон на Кулон – bulgarsk" lang="bg" hreflang="bg" data-title="Закон на Кулон" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Coulombov_zakon" title="Coulombov zakon – bosnisk" lang="bs" hreflang="bs" data-title="Coulombov zakon" 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/Llei_de_Coulomb" title="Llei de Coulomb – katalansk" lang="ca" hreflang="ca" data-title="Llei de Coulomb" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD_%D1%81%D0%B0%D0%BA%D0%BA%D1%83%D0%BD%C4%95" title="Кулон саккунĕ – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Кулон саккунĕ" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Coulomb%C5%AFv_z%C3%A1kon" title="Coulombův zákon – tsjekkisk" lang="cs" hreflang="cs" data-title="Coulombův zákon" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" 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/Coulombsches_Gesetz" title="Coulombsches Gesetz – tysk" lang="de" hreflang="de" data-title="Coulombsches Gesetz" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Coulomb%27i_seadus" title="Coulomb'i seadus – estisk" lang="et" hreflang="et" data-title="Coulomb'i seadus" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%9A%CE%BF%CF%85%CE%BB%CF%8C%CE%BC%CF%80" title="Νόμος του Κουλόμπ – gresk" lang="el" hreflang="el" data-title="Νόμος του Κουλόμπ" data-language-autonym="Ελληνικά" data-language-local-name="gresk" 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/Coulomb%27s_law" title="Coulomb's law – engelsk" lang="en" hreflang="en" data-title="Coulomb's law" data-language-autonym="English" data-language-local-name="engelsk" 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/Ley_de_Coulomb" title="Ley de Coulomb – spansk" lang="es" hreflang="es" data-title="Ley de Coulomb" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kulomba_le%C4%9Do" title="Kulomba leĝo – esperanto" lang="eo" hreflang="eo" data-title="Kulomba leĝo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Coulomben_legea" title="Coulomben legea – baskisk" lang="eu" hreflang="eu" data-title="Coulomben legea" 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%82%D8%A7%D9%86%D9%88%D9%86_%DA%A9%D9%88%D9%84%D9%86" title="قانون کولن – persisk" lang="fa" hreflang="fa" data-title="قانون کولن" data-language-autonym="فارسی" data-language-local-name="persisk" 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/Loi_de_Coulomb_(%C3%A9lectrostatique)" title="Loi de Coulomb (électrostatique) – fransk" lang="fr" hreflang="fr" data-title="Loi de Coulomb (électrostatique)" 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/Dl%C3%AD_Coulomb" title="Dlí Coulomb – irsk" lang="ga" hreflang="ga" data-title="Dlí Coulomb" 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/Lei_de_Coulomb" title="Lei de Coulomb – galisisk" lang="gl" hreflang="gl" data-title="Lei de Coulomb" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%BF%A8%EB%A1%B1_%EB%B2%95%EC%B9%99" title="쿨롱 법칙 – koreansk" lang="ko" hreflang="ko" data-title="쿨롱 법칙" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D6%82%D5%AC%D5%B8%D5%B6%D5%AB_%D6%85%D6%80%D5%A5%D5%B6%D6%84" title="Կուլոնի օրենք – armensk" lang="hy" hreflang="hy" data-title="Կուլոնի օրենք" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%82%E0%A4%B2%E0%A5%89%E0%A4%AE-%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="कूलॉम-नियम – hindi" lang="hi" hreflang="hi" data-title="कूलॉम-नियम" 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/Coulombov_zakon" title="Coulombov zakon – kroatisk" lang="hr" hreflang="hr" data-title="Coulombov zakon" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_Coulomb" title="Hukum Coulomb – indonesisk" lang="id" hreflang="id" data-title="Hukum Coulomb" 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/Forza_di_Coulomb" title="Forza di Coulomb – italiensk" lang="it" hreflang="it" data-title="Forza di Coulomb" data-language-autonym="Italiano" data-language-local-name="italiensk" 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%97%D7%95%D7%A7_%D7%A7%D7%95%D7%9C%D7%95%D7%9F" title="חוק קולון – hebraisk" lang="he" hreflang="he" data-title="חוק קולון" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%9A%E1%83%9D%E1%83%9C%E1%83%98%E1%83%A1_%E1%83%99%E1%83%90%E1%83%9C%E1%83%9D%E1%83%9C%E1%83%98" title="კულონის კანონი – georgisk" lang="ka" hreflang="ka" data-title="კულონის კანონი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD_%D0%B7%D0%B0%D2%A3%D1%8B" title="Кулон заңы – kasakhisk" lang="kk" hreflang="kk" data-title="Кулон заңы" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Lwa_koulon" title="Lwa koulon – haitisk" lang="ht" hreflang="ht" data-title="Lwa koulon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitisk" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/H%C3%AAza_karebay%C3%AE" title="Hêza karebayî – kurdisk" lang="ku" hreflang="ku" data-title="Hêza karebayî" data-language-autonym="Kurdî" data-language-local-name="kurdisk" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD_%D0%BC%D1%8B%D0%B9%D0%B7%D0%B0%D0%BC%D1%8B" title="Кулон мыйзамы – kirgisisk" lang="ky" hreflang="ky" data-title="Кулон мыйзамы" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kulona_likums" title="Kulona likums – latvisk" lang="lv" hreflang="lv" data-title="Kulona likums" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kulono_d%C4%97snis" title="Kulono dėsnis – litauisk" lang="lt" hreflang="lt" data-title="Kulono dėsnis" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Coulomb-t%C3%B6rv%C3%A9ny" title="Coulomb-törvény – ungarsk" lang="hu" hreflang="hu" data-title="Coulomb-törvény" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Кулонов закон – makedonsk" lang="mk" hreflang="mk" data-title="Кулонов закон" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%82%E0%B4%B3%E0%B5%8B%E0%B4%82_%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="കൂളോം നിയമം – malayalam" lang="ml" hreflang="ml" data-title="കൂളോം നിയമം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_Coulomb" title="Hukum Coulomb – malayisk" lang="ms" hreflang="ms" data-title="Hukum Coulomb" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D1%8B_%D1%85%D1%83%D1%83%D0%BB%D1%8C" title="Кулоны хууль – mongolsk" lang="mn" hreflang="mn" data-title="Кулоны хууль" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%B0%E1%80%B8%E1%80%9C%E1%80%B1%E1%80%AC%E1%80%84%E1%80%BA%E1%80%B8%E1%81%8F_%E1%80%94%E1%80%AD%E1%80%9A%E1%80%AC%E1%80%99" title="ကူးလောင်း၏ နိယာမ – burmesisk" lang="my" hreflang="my" data-title="ကူးလောင်း၏ နိယာမ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmesisk" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_van_Coulomb" title="Wet van Coulomb – nederlandsk" lang="nl" hreflang="nl" data-title="Wet van Coulomb" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%95%E0%A5%82%E0%A4%B2%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95%E0%A5%8B_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="कूलम्बको नियम – nepali" lang="ne" hreflang="ne" data-title="कूलम्बको नियम" data-language-autonym="नेपाली" data-language-local-name="nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%BC%E3%83%AD%E3%83%B3%E3%81%AE%E6%B3%95%E5%89%87" title="クーロンの法則 – japansk" lang="ja" hreflang="ja" data-title="クーロンの法則" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kulon_qonuni" title="Kulon qonuni – usbekisk" lang="uz" hreflang="uz" data-title="Kulon qonuni" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%82%E0%A8%B2%E0%A9%8C%E0%A8%82%E0%A8%AC_%E0%A8%A6%E0%A8%BE_%E0%A8%A8%E0%A8%BF%E0%A8%AF%E0%A8%AE" title="ਕੂਲੌਂਬ ਦਾ ਨਿਯਮ – panjabi" lang="pa" hreflang="pa" data-title="ਕੂਲੌਂਬ ਦਾ ਨਿਯਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%D9%88%D9%84%D9%85%D8%A8_%D8%AF%D8%A7_%D9%82%D9%86%D9%88%D9%86" title="کولمب دا قنون – vestpunjabi" lang="pnb" hreflang="pnb" data-title="کولمب دا قنون" data-language-autonym="پنجابی" data-language-local-name="vestpunjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%85%E1%9F%92%E1%9E%94%E1%9E%B6%E1%9E%94%E1%9F%8B%E1%9E%82%E1%9E%BC%E1%9E%A1%E1%9E%BB%E1%9F%86" title="ច្បាប់គូឡុំ – khmer" lang="km" hreflang="km" data-title="ច្បាប់គូឡុំ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Lej_%C3%ABd_Coulomb" title="Lej ëd Coulomb – piemontesisk" lang="pms" hreflang="pms" data-title="Lej ëd Coulomb" data-language-autonym="Piemontèis" data-language-local-name="piemontesisk" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_Coulomba" title="Prawo Coulomba – polsk" lang="pl" hreflang="pl" data-title="Prawo Coulomba" 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/Lei_de_Coulomb" title="Lei de Coulomb – portugisisk" lang="pt" hreflang="pt" data-title="Lei de Coulomb" 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/Legea_lui_Coulomb" title="Legea lui Coulomb – rumensk" lang="ro" hreflang="ro" data-title="Legea lui Coulomb" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="utmerket artikkel-merke"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%B0" title="Закон Кулона – russisk" lang="ru" hreflang="ru" data-title="Закон Кулона" data-language-autonym="Русский" data-language-local-name="russisk" 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/Ligji_i_Kulombit" title="Ligji i Kulombit – albansk" lang="sq" hreflang="sq" data-title="Ligji i Kulombit" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Coulomb%27s_law" title="Coulomb's law – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Coulomb's law" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" 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/Coulombov_z%C3%A1kon" title="Coulombov zákon – slovakisk" lang="sk" hreflang="sk" data-title="Coulombov zákon" 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/Coulombov_zakon" title="Coulombov zakon – slovensk" lang="sl" hreflang="sl" data-title="Coulombov zakon" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" title="Кулонов закон – serbisk" lang="sr" hreflang="sr" data-title="Кулонов закон" 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-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Coulombov_zakon" title="Coulombov zakon – serbokroatisk" lang="sh" hreflang="sh" data-title="Coulombov zakon" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Coulombin_laki" title="Coulombin laki – finsk" lang="fi" hreflang="fi" data-title="Coulombin laki" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Batas_ni_Coulomb" title="Batas ni Coulomb – tagalog" lang="tl" hreflang="tl" data-title="Batas ni Coulomb" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%82%E0%AE%B2%E0%AF%81%E0%AE%AE%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A4%E0%AE%BF" title="கூலும் விதி – tamil" lang="ta" hreflang="ta" data-title="கூலும் விதி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D1%83%D0%BB%D0%BE%D0%BD_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD%D1%8B" title="Кулон законы – tatarisk" lang="tt" hreflang="tt" data-title="Кулон законы" 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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Coulomb_kanunu" title="Coulomb kanunu – tyrkisk" lang="tr" hreflang="tr" data-title="Coulomb kanunu" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%B0" title="Закон Кулона – ukrainsk" lang="uk" hreflang="uk" data-title="Закон Кулона" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%DA%A9%D9%88%D9%84%D9%85%D8%A8" title="قانون کولمب – urdu" lang="ur" hreflang="ur" data-title="قانون کولمب" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%E1%BB%B1c_t%C4%A9nh_%C4%91i%E1%BB%87n" title="Lực tĩnh điện – vietnamesisk" lang="vi" hreflang="vi" data-title="Lực tĩnh điện" 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-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%BA%AB%E4%BE%96%E5%AE%9A%E5%BE%8B" title="庫侖定律 – klassisk kinesisk" lang="lzh" hreflang="lzh" data-title="庫侖定律" data-language-autonym="文言" data-language-local-name="klassisk kinesisk" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BA%93%E4%BB%91%E5%AE%9A%E5%BE%8B" title="库仑定律 – wu" lang="wuu" hreflang="wuu" data-title="库仑定律" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%BA%AB%E4%BE%96%E5%AE%9A%E5%BE%8B" title="庫侖定律 – kantonesisk" lang="yue" hreflang="yue" data-title="庫侖定律" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BA%93%E4%BB%91%E5%AE%9A%E5%BE%8B" title="库仑定律 – kinesisk" lang="zh" hreflang="zh" data-title="库仑定律" data-language-autonym="中文" data-language-local-name="kinesisk" 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/Q83152#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</a></span></div> </div> </div> </div> </header> <div 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<div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopedi</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nb" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Bcoulomb.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Bcoulomb.png/200px-Bcoulomb.png" decoding="async" width="200" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Bcoulomb.png/300px-Bcoulomb.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Bcoulomb.png/400px-Bcoulomb.png 2x" data-file-width="1664" data-file-height="2085" /></a><figcaption>Illustrasjon av torsjonsvekten som Coulomb benyttet.</figcaption></figure> <p><b>Coulombs lov</b> sier at <a href="/wiki/Kraft" title="Kraft">kraften</a> mellom to <a href="/wiki/Elektrisk_ladning" title="Elektrisk ladning">elektrisk ladde</a> partikler er <a href="/wiki/Proporsjonalitet" title="Proporsjonalitet">proporsjonal</a> med produktet av ladningene og omvendt proporsjonal med kvadratet av avstanden mellom dem. Den har derfor samme form som <a href="/wiki/Newtons_gravitasjonslov" title="Newtons gravitasjonslov">Newtons gravitasjonslov</a> hvor masser erstattes med elektriske ladninger. Loven ble påvist av <a href="/wiki/Charles_Augustin_Coulomb" title="Charles Augustin Coulomb">Charles Augustin Coulomb</a> og dannet grunnlaget for utvikling av den moderne teori for <a href="/wiki/Elektromagnetisme" title="Elektromagnetisme">elektromagnetisme</a>. Siden den tid er den eksperimentelt verifisert på mange forskjellige måter. Den er en <a href="/wiki/Naturlov" title="Naturlov">naturlov</a> og ekvivalent med <a href="/wiki/Maxwells_ligninger" class="mw-redirect" title="Maxwells ligninger">Maxwells første lov</a>, også kalt <a href="/wiki/Gauss%27_lov" class="mw-redirect" title="Gauss' lov">Gauss' lov</a>. </p><p>Kalles de to ladningene for <i>q</i><sub>1</sub> og <i>q</i><sub>2</sub>, skrives loven for den elektriske Coulomb-kraften <i>F </i> på formen </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25e791fb1cd6c2665dcfe63b7813009a800a6b66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:12.068ex; height:5.176ex;" alt="{\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}"></span></dd></dl> <p>når <i>r</i> er avstanden mellom ladningene. Proporsjonalitetskonstanten <i>k<sub>e</sub></i> kalles ofte for <a href="/wiki/Coulombs_konstant" title="Coulombs konstant">Coulombs konstant</a> og har en størrelse som er avhengig av hva slags <a href="/wiki/M%C3%A5leenhet" title="Måleenhet">målenheter</a> benyttes. I det vanlige <a href="/wiki/SI-systemet" title="SI-systemet">SI-systemet</a> har den verdien </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 k_{e}={\frac {1}{4\pi \varepsilon _{0}}}=8.987742438\times 10^{9}\;\mathrm {Nm^{2}C^{-2}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <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> <mo>=</mo> <mn>8.987742438</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <msup> <mi mathvariant="normal">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{e}={\frac {1}{4\pi \varepsilon _{0}}}=8.987742438\times 10^{9}\;\mathrm {Nm^{2}C^{-2}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3baeec2cac83925de804cbbff4c829ee584e8359" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.755ex; height:5.676ex;" alt="{\displaystyle k_{e}={\frac {1}{4\pi \varepsilon _{0}}}=8.987742438\times 10^{9}\;\mathrm {Nm^{2}C^{-2}} }"></span></dd></dl> <p>der <i>ε</i><sub>0</sub>  er den <a href="/wiki/Elektrisk_konstant" title="Elektrisk konstant">elektriske konstanten</a>. Når de to ladningene har samme fortegn, er kraften frastøtende. Hvis ikke, får den motsatt fortegn som betyr at kraften er tiltrekkende. </p><p>Kraften mellom to ladninger i bevegelse får, i tillegg til Coulomb-kraften, et bidrag fra <a href="/wiki/Magnetfelt" title="Magnetfelt">magnetiske krefter</a>. For store hastigheter må disse kreftene beskrives ved <a href="/wiki/Spesiell_relativitetsteori" class="mw-redirect" title="Spesiell relativitetsteori">spesiell relativitetsteori</a>. Coulombs lov alene gir derfor ikke en fullgod beskrivelse. For veldig små avstander mellom partiklene blir Coulombs lov modifisert med bidrag fra <a href="/wiki/Kvanteelektrodynamikk" title="Kvanteelektrodynamikk">kvanteelektrodynamikken</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historisk_bakgrunn">Historisk bakgrunn</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=1" title="Rediger avsnitt: Historisk bakgrunn" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=1" title="Rediger kildekoden til seksjonen Historisk bakgrunn"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fra de første observasjoner av krefter mellom elektrisk ladete objekter på 1700-tallet var det klart at disse avtok med avstanden mellom dem. På den tiden var <a href="/wiki/Newtons_gravitasjonslov" title="Newtons gravitasjonslov">Newtons gravitasjonslov</a> den eneste kjente matematiske lovmessighet for en <a href="/wiki/Kraft" title="Kraft">kraft</a>, så mange trodde at elektriske krefter ville oppføre seg på tilsvarende vis. Kvantitative målinger ble gjort på mange hold.<sup id="cite_ref-Heilbron_1-0" class="reference"><a href="#cite_note-Heilbron-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Ved konstruksjon av meget nøyaktige <a href="/wiki/Cavendish-eksperimentet#Torsjonsvekten" title="Cavendish-eksperimentet">torsjonsvekter</a> lyktes det den franske fysikeren <a href="/wiki/Charles_Augustin_Coulomb" title="Charles Augustin Coulomb">Charles Augustin Coulomb</a> i 1784 å påvise at den elektriske kraften mellom punktladninger varierer med avstanden på samme måte som i Newtons tyngdelov. Tilsvarende målinger hadde tidligere blitt gjort av den engelske naturviter <a href="/wiki/Henry_Cavendish" title="Henry Cavendish">Henry Cavendish</a>, men ble først kjent etter hans død. </p><p>Det er ennå ikke helt forstått hvorfor både Newtons gravitasjonslov og Coulombs elektriske lov gir krefter som avtar med avstanden. Ved bruk av <a href="/wiki/Kvantefeltteori" title="Kvantefeltteori">kvantefeltteori</a> kan man si at begge deler skyldes utveksling av masseløse partikler, henholdsvis <a href="/wiki/Graviton" title="Graviton">graviton</a> og <a href="/wiki/Foton" title="Foton">foton</a>. Alternativt kan man tenke seg, som i <a href="/w/index.php?title=Kaluza-Klein-teori&action=edit&redlink=1" class="new" title="Kaluza-Klein-teori (ikke skrevet ennå)">Kaluza-Klein-teori</a>, at <a href="/wiki/Universet" title="Universet">Universet</a> har flere enn fire <a href="/wiki/Dimensjon" title="Dimensjon">dimensjoner</a>. En ren gravitasjonskraft i en slik verden vil da se ut som både gravitasjon og <a href="/wiki/Elektromagnetisme" title="Elektromagnetisme">elektromagnetisme</a> i vår verden med fire dimensjoner og med samme kraftlov. </p> <div class="mw-heading mw-heading2"><h2 id="Matematisk_formulering">Matematisk formulering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=2" title="Rediger avsnitt: Matematisk formulering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=2" title="Rediger kildekoden til seksjonen Matematisk formulering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ved sine målinger fant Coulomb ikke bare ut at kraften mellom to ladete partikler avtar med kvadratet av avstanden mellom dem, men han viste også at kraften var rettet langs forbindelseslinjen mellom dem. I tillegg var den proporsjonal med produktet av de to ladningene. Kalles disse <i>q</i><sub>1</sub> og <i>q</i><sub>2</sub>, kan Coulombs lov derfor skrives på <a href="/wiki/Vektor_(matematikk)" title="Vektor (matematikk)">vektoriell form</a> som<sup id="cite_ref-HLL_2-0" class="reference"><a href="#cite_note-HLL-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 \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}\mathbf {e} _{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}\mathbf {e} _{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/271c99a9f6bb84a811b39a638e1728ad5d1f43a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.551ex; height:5.509ex;" alt="{\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}\mathbf {e} _{r}}"></span></dd></dl> <p>hvor <b>e</b><sub><i>r</i></sub>  er enhetsvektor i samme retningen som vektoren <b>r</b><sub>12</sub> = <b>r</b><sub>1</sub> - <b>r</b><sub>2</sub> som forbinder de to ladningene og med lengde <i>r</i> = |<b>r</b><sub>12</sub>|. På denne formen uttrykker den kraften <b>F</b>  mellom ladningene. Mer presist består denne av en kraft <b>F</b><sub>1</sub>  på </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File"><a href="/wiki/Fil:Coulombslawgraph.svg" class="mw-file-description" title="Représentation graphique de la loi de Coulomb"><img alt="Représentation graphique de la loi de Coulomb" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Coulombslawgraph.svg/392px-Coulombslawgraph.svg.png" decoding="async" width="392" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Coulombslawgraph.svg/588px-Coulombslawgraph.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Coulombslawgraph.svg/784px-Coulombslawgraph.svg.png 2x" data-file-width="392" data-file-height="67" /></a><figcaption>Représentation graphique de la loi de Coulomb</figcaption></figure> <p>ladning <i>q</i><sub>1</sub>  som skyldes tilstedeværelsen av ladning <i>q</i><sub>2</sub>. Fullt ut kan da denne kraften skrives som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{1}-\mathbf {r} _{2} \over |\mathbf {r} _{1}-\mathbf {r} _{2}|^{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <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> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{1}-\mathbf {r} _{2} \over |\mathbf {r} _{1}-\mathbf {r} _{2}|^{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549934a18034c3a7a5274ea942e3f8bc46d475df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.641ex; height:6.176ex;" alt="{\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{1}-\mathbf {r} _{2} \over |\mathbf {r} _{1}-\mathbf {r} _{2}|^{3}}}"></span></dd></dl> <p>Etter <a href="/wiki/Newtons_tredje_lov" class="mw-redirect" title="Newtons tredje lov">Newtons tredje lov</a> om kraft og motkraft, virker det en tilsvarende kraft <b>F</b><sub>2</sub>  på ladning <i>q</i><sub>2</sub>  med <b>F</b><sub>1</sub> = - <b>F</b><sub>2</sub>. </p><p>På denne formen er loven ikke bare gyldig for punktladninger. Hvis den ene eller begge ladningene består av sfærisk symmetriske ladningsfordelinger, kan man benytte <a href="/wiki/Newtons_skallteorem" title="Newtons skallteorem">Newtons skallteorem</a> til å vise at Coulombs lov fremdeles er gyldig. Det er på samme måte som at Newtons gravitasjonslov er gyldig for kraften mellom to store <a href="/wiki/Planet" title="Planet">planeter</a> så lenge disse er runde. For den elektriske kraften mellom to vilkårlig elektrisk ladete objekter som ikke har denne symmetrien, er ikke loven lenger gyldig. </p> <div class="mw-heading mw-heading3"><h3 id="Coulomb-feltet">Coulomb-feltet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=3" title="Rediger avsnitt: Coulomb-feltet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=3" title="Rediger kildekoden til seksjonen Coulomb-feltet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kraften som virker på den første ladningen, kan skrives som <b>F</b><sub>1</sub> = <i>q</i><sub>1</sub><b>E</b><sub>1</sub>  hvor <b>E</b><sub>1</sub> = <b>E</b>(<b>r</b><sub>1</sub>)  er det <a href="/wiki/Elektrisk_felt" title="Elektrisk felt">elektriske feltet</a> skapt av ladning <i>q</i><sub>2</sub>  i posisjonen til <i>q</i><sub>1</sub>, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (\mathbf {r} )={\frac {q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} -\mathbf {r} _{2} \over |\mathbf {r} -\mathbf {r} _{2}|^{3}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <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> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (\mathbf {r} )={\frac {q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} -\mathbf {r} _{2} \over |\mathbf {r} -\mathbf {r} _{2}|^{3}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f5f2feb44a771aefd7ef750c7482853162304d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.165ex; height:6.176ex;" alt="{\displaystyle \mathbf {E} (\mathbf {r} )={\frac {q_{2}}{4\pi \varepsilon _{0}}}{\mathbf {r} -\mathbf {r} _{2} \over |\mathbf {r} -\mathbf {r} _{2}|^{3}}.}"></span></dd></dl> <p>Feltet er radielt rettet ut fra punktet <b>r</b><sub>2</sub> og avtar i styrke med kvadratet av avstanden fra dette punktet. Matematisk sett divergerer det i origo fordi det er skapt av en punktladning. En slik ladning har formelt ingen utstrekning, men forekommer ikke i virkeligheten. For eksempel har et <a href="/wiki/Proton" title="Proton">proton</a> en utstrekning på omtrent 10<sup>-15</sup> m. Et <a href="/wiki/Elektron" title="Elektron">elektron</a> er enda mindre, med en utstrekning som ikke er veldefinert på grunn av <a href="/wiki/Kvantefeltteori" title="Kvantefeltteori">kvanteeffekter</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Elektrisches-feld-positive-punktladung.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Elektrisches-feld-positive-punktladung.svg/250px-Elektrisches-feld-positive-punktladung.svg.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Elektrisches-feld-positive-punktladung.svg/375px-Elektrisches-feld-positive-punktladung.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Elektrisches-feld-positive-punktladung.svg/500px-Elektrisches-feld-positive-punktladung.svg.png 2x" data-file-width="600" data-file-height="600" /></a><figcaption>Elektriske feltlinjer fra en rund, positiv ladet partikkel er radielle.</figcaption></figure> <p>Det elektriske feltet utenfor mange slike ladninger er gitt ved summen av feltene fra hver av dem, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (\mathbf {r} )=\sum _{i}{q_{i}(\mathbf {r} -\mathbf {r} _{i}) \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} _{i}|^{3}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (\mathbf {r} )=\sum _{i}{q_{i}(\mathbf {r} -\mathbf {r} _{i}) \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} _{i}|^{3}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7780588962479a480a600ae1c1212d793baa77ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.816ex; height:6.843ex;" alt="{\displaystyle \mathbf {E} (\mathbf {r} )=\sum _{i}{q_{i}(\mathbf {r} -\mathbf {r} _{i}) \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} _{i}|^{3}}.}"></span></dd></dl> <p>Dette er et eksempel på <a href="/wiki/Superposisjonsprinsippet" title="Superposisjonsprinsippet">superposisjonsprinsippet</a>. Hvis disse ladningene er kontinuerlig fordelt med en <a href="/wiki/Elektrisk_ladning" title="Elektrisk ladning">ladningstetthet</a> <i>ρ</i>(<b>r</b>), vil det resulterende feltet være gitt ved integralet<sup id="cite_ref-Griffiths_3-0" class="reference"><a href="#cite_note-Griffiths-3"><span class="cite-bracket">[</span>3<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 \mathbf {E} (\mathbf {r} )=\int d^{3}x'{\rho (\mathbf {r} ')(\mathbf {r} -\mathbf {r} ') \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} '|^{3}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∫</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mi>x</mi> <mo>′</mo> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>′</mo> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (\mathbf {r} )=\int d^{3}x'{\rho (\mathbf {r} ')(\mathbf {r} -\mathbf {r} ') \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} '|^{3}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29cc6b539ce1eba84d257f546e0f6f2d3baffb65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:28.827ex; height:6.843ex;" alt="{\displaystyle \mathbf {E} (\mathbf {r} )=\int d^{3}x'{\rho (\mathbf {r} ')(\mathbf {r} -\mathbf {r} ') \over 4\pi \varepsilon _{0}|\mathbf {r} -\mathbf {r} '|^{3}}.}"></span></dd></dl> <p>I alminnelighet vil ikke disse beregningene gi et resulterende felt som har samme form som et Coulomb-felt. Men i det spesielle tilfellet at alle ladningene under betraktning har en sfærisk symmetrisk fordeling sentrert om origo, sier <a href="/wiki/Newtons_skallteorem" title="Newtons skallteorem">Newtons skallteorem</a> at feltet utenfor disse ladningene er nøyaktig det samme som om alle var plassert i origo. Det vil derfor ha formen </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (\mathbf {r} )={Q\mathbf {r} \over 4\pi \varepsilon _{0}r^{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (\mathbf {r} )={Q\mathbf {r} \over 4\pi \varepsilon _{0}r^{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c938914bc7d4be5c60c58883aa4ada9b1e1d0cf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.338ex; height:6.009ex;" alt="{\displaystyle \mathbf {E} (\mathbf {r} )={Q\mathbf {r} \over 4\pi \varepsilon _{0}r^{3}}}"></span></dd></dl> <p>hvor <i>Q </i> er summen av alle ladninger som ligger innenfor et skall med radius <i>r</i>. Alternativt kan man i dette tilfellet finne det samme resultatet ved bruk av <a href="/wiki/Gauss%27_lov" class="mw-redirect" title="Gauss' lov">Gauss' lov</a> på integralform. Det har stor betydning i mange viktige sammenhenger i fysikken. </p> <div class="mw-heading mw-heading3"><h3 id="Coulomb-potensialet">Coulomb-potensialet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=4" title="Rediger avsnitt: Coulomb-potensialet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=4" title="Rediger kildekoden til seksjonen Coulomb-potensialet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Coulomb-kraften er <a href="/wiki/Potensiell_energi#Konservative_krefter" title="Potensiell energi">konservativ</a> som betyr at den kan uttrykkes ved <a href="/wiki/Gradient" title="Gradient">gradienten</a> til en <a href="/wiki/Potensiell_energi" title="Potensiell energi">potensiell energi</a>. Derfor kan man kan skrive det elektriske feltet som <span class="nowrap"><b>E</b> = -<b>∇</b><i>V</i> </span> hvor <i>V</i>  er det <a href="/wiki/Elektrisk_potensial" title="Elektrisk potensial">elektriske potensialet</a>. Ved å benytte at </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 {\boldsymbol {\nabla }}{1 \over r}=-{\mathbf {r} \over r^{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">∇</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\nabla }}{1 \over r}=-{\mathbf {r} \over r^{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/498e5a48ae1983fb8df15fe23ff26104cbaa75c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:12.07ex; height:5.509ex;" alt="{\displaystyle {\boldsymbol {\nabla }}{1 \over r}=-{\mathbf {r} \over r^{3}}}"></span></dd></dl> <p>er potensialet utenfor en sfærisk ladning <i>Q</i> sentrert om origo </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 V(\mathbf {r} )={Q \over 4\pi \varepsilon _{0}r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </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> <mi>r</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\mathbf {r} )={Q \over 4\pi \varepsilon _{0}r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04ff5b6b4ba5b16d6a1208c61db781c0d196baf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.314ex; height:5.843ex;" alt="{\displaystyle V(\mathbf {r} )={Q \over 4\pi \varepsilon _{0}r}}"></span></dd></dl> <p>Dette er Coulomb-potensialet. I <a href="/wiki/Atomfysikk" title="Atomfysikk">atomfysikken</a> inngår det i <a href="/wiki/Schr%C3%B6dinger-ligning" title="Schrödinger-ligning">Schrödinger-ligningen</a> for elektronene i et atom som holdes på plass av Coulomb-kraften fra atomkjernen. </p> <div class="mw-heading mw-heading2"><h2 id="Korreksjoner">Korreksjoner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=5" title="Rediger avsnitt: Korreksjoner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=5" title="Rediger kildekoden til seksjonen Korreksjoner"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Coulombs lov er strengt tatt kun gyldig for partikler som er helt i ro. Dette er den <a href="/wiki/Elektrostatikk" title="Elektrostatikk">elektrostatiske</a> grensen av mer generell <a href="/wiki/Elektrodynamikk" title="Elektrodynamikk">elektrodynamikk</a> som beskriver elektrisk ladde partikler i bevegelse. Men beveger den ene partikkelen seg, vil den skape et <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetisk felt</a> som kan påvirke den andre. Så lenge hastigheten <b>v</b>  til partikkelen med ladning <i>q</i>  er liten, er dette magnetfeltet gitt ved <a href="/wiki/Biot-Savarts_lov" title="Biot-Savarts lov">Biot-Savarts lov</a> som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} ={\mu _{0}q \over 4\pi r^{3}}\mathbf {v} \times \mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>q</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} ={\mu _{0}q \over 4\pi r^{3}}\mathbf {v} \times \mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2d5fa9664ca5bae377b60d664644c44729af906" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.786ex; height:5.176ex;" alt="{\displaystyle \mathbf {B} ={\mu _{0}q \over 4\pi r^{3}}\mathbf {v} \times \mathbf {r} }"></span></dd></dl> <p>hvor vektoren <b>r</b>  forbinder denne partikkelen med den andre partikkelen med ladning <i>q</i> ' og hastighet <b>v</b> '. Den blir derfor utsatt for en <a href="/wiki/Lorentz-kraft" title="Lorentz-kraft">magnetisk kraft</a> <span class="nowrap"><i>q' </i><b>v</b> '× <b>B</b> </span> som virker i tillegg til den vanlig Coulomb-kraften mellom partiklene. Denne effekten kan oppfattes som en korreksjon til Coulombs lov. Men den er ikke den eneste da avstanden mellom partiklene og deres hastigheter i alminnelighet også vil variere med tiden. Det vil derfor også magnetfeltet gjøre. På grunn av <a href="/wiki/Faradays_induksjonslov" title="Faradays induksjonslov">Faradays induksjonslov</a> vil det dermed oppstå et <a href="/wiki/Elektrisk_felt" title="Elektrisk felt">elektrisk felt</a> i tillegg til det som gir den vanlige Coulomb-kraften. Alt i alt vil mange slike korreksjoner inngå i en utvidet formel som tar hensyn til alle disse effektene. </p><p>Fra uttrykket for den magnetiske kraften ser man at det er av størrelsesorden <i>v</i><sup> 2</sup>/<i>c</i><sup> 2</sup> der den kvadrerte <a href="/wiki/Lyshastigheten" class="mw-redirect" title="Lyshastigheten">lyshastigheten</a> <span class="nowrap"><i>c</i><sup> 2</sup> = 1/<i>ε</i><sub>0</sub><i>μ</i><sub>0</sub></span> og <i>v</i> er den omtrentlige hastigheten til partiklene. Disse magnetiske korreksjonene er derfor veldig små for vanlige hastigheter og sies å være «relativistiske» da de kan betraktes som en konsekvens av den <a href="/wiki/Spesiell_relativitet" class="mw-redirect" title="Spesiell relativitet">spesielle relativitetsteorien</a>. Selve begrepet <a href="/wiki/Kraft" title="Kraft">kraft</a> er da mer komplisert å benytte. </p><p>I stedet er det enklere å fokusere på den <a href="/wiki/Potensiell_energi" title="Potensiell energi">potensielle energien</a> for to ladete partikler som beveger seg. Denne korreksjonen til Coulomb-potensialet kalles <a href="/wiki/Darwin-vekselvirkning" title="Darwin-vekselvirkning">Darwin-vekselvirkningen</a> og kan gis en mer kompakt form. Da den vil avhenge av hastighetene til partiklene, vil den resulterende kraften mellom partiklene også avhenge av deres <a href="/wiki/Akselerasjon" title="Akselerasjon">akselerasjon</a>.<sup id="cite_ref-Jackson_4-0" class="reference"><a href="#cite_note-Jackson-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Denne utvidete kraften er ikke lenger rettet fra den ene ladningen til den andre. Kraften som den ene partikkelen utøver på den andre, ikke er like stor og motsatt rettet til kraften som den andre partikkelen utøver på den første. Den oppfyller derfor ikke <a href="/wiki/Newtons_lover" class="mw-redirect" title="Newtons lover">Newtons tredje lov</a>. Det er kanskje ikke så overraskende når spesiell relativitet gjelder. I dette tilfellet er årsaken at det magnetiske feltet som opptrer sammen med det elektriske, har en <a href="/wiki/Elektromagnetisk_felt#Elektromagnetisk_impulstetthet" title="Elektromagnetisk felt">elektromagnetiske impuls</a> som varierer med tiden. Den tidsderiverte av denne gir en ekstra kraft som balanserer det hele ut.<sup id="cite_ref-Griffiths_3-1" class="reference"><a href="#cite_note-Griffiths-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Kvanteelektrodynamikk">Kvanteelektrodynamikk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=6" title="Rediger avsnitt: Kvanteelektrodynamikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=6" title="Rediger kildekoden til seksjonen Kvanteelektrodynamikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Andre korreksjoner kommer fra <a href="/wiki/Kvantemekanikk" title="Kvantemekanikk">kvantemekanikken</a>. Da det elektriske feltet blir veldig sterkt i nærheten av en punktladning, tillater <a href="/wiki/Heisenbergs_usikkerhetsrelasjon" class="mw-redirect" title="Heisenbergs usikkerhetsrelasjon">Heisenbergs usikkerhetsrelasjon</a> at <a href="/wiki/Elektron" title="Elektron">elektroner</a> og <a href="/wiki/Positron" title="Positron">positroner</a> skapes i korte øyeblikk og vil avskjerme ladningen. Denne effekten kan beregnes fra <a href="/wiki/Kvanteelektrodynamikk" title="Kvanteelektrodynamikk">kvanteelektrodynamikk</a> og gir det modifiserte Coulomb-potensialet </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 V(r)={Q \over 4\pi \varepsilon _{0}r}{\Big [}1+{2\alpha \over 3\pi }{\Big (}\ln {\hbar \over rm_{e}c}-\gamma -{5 \over 6}+\cdots {\Big )}{\Big ]}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>r</mi> <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> <mi>r</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">[</mo> </mrow> </mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>α</mi> </mrow> <mrow> <mn>3</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mrow> <mi>r</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>γ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(r)={Q \over 4\pi \varepsilon _{0}r}{\Big [}1+{2\alpha \over 3\pi }{\Big (}\ln {\hbar \over rm_{e}c}-\gamma -{5 \over 6}+\cdots {\Big )}{\Big ]}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51d6463ab0e8855e33f43d3873df5237763b57d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.256ex; height:5.843ex;" alt="{\displaystyle V(r)={Q \over 4\pi \varepsilon _{0}r}{\Big [}1+{2\alpha \over 3\pi }{\Big (}\ln {\hbar \over rm_{e}c}-\gamma -{5 \over 6}+\cdots {\Big )}{\Big ]}}"></span></dd></dl> <p>ved de minste avstander. Her er <i>ħ</i> den reduserte <a href="/wiki/Plancks_konstant" title="Plancks konstant">Planck-konstanten</a> og <i>m<sub>e</sub></i>  er elektronets <a href="/wiki/Masse" title="Masse">masse</a>. Videre er <span class="nowrap"><i>α</i> = 1/137.036... </span> <a href="/wiki/Finstrukturkonstant" title="Finstrukturkonstant">finstrukturkonstanten</a>, mens <span class="nowrap"><i>γ</i> = 0.5772...</span> er <a href="/wiki/Euler-Mascheronis_konstant" title="Euler-Mascheronis konstant">Euler-Mascheronis konstant</a>. Med denne kvantekorreksjonen er Coulomb-potensialet gått over til å bli «Uehling»-potensialet».<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Effekten av det kan observeres i <a href="/wiki/Finstruktur" title="Finstruktur">finstrukturen</a> i <a href="/wiki/Emisjonsspekter" title="Emisjonsspekter">atomers spektra</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=7" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=7" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Heilbron-1"><b><a href="#cite_ref-Heilbron_1-0">^</a></b> <span class="reference-text"> J.L. Heilbron, <i>Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics</i>, University California Press, Berkeley (1979).<a href="/wiki/Spesial:Bokkilder/0520034783" class="internal mw-magiclink-isbn">ISBN 0-520-03478-3</a>.</span> </li> <li id="cite_note-HLL-2"><b><a href="#cite_ref-HLL_2-0">^</a></b> <span class="reference-text">O. Hunderi, J.R. Lien og G. Løvhøiden, <i>Generell fysikk for universiteter og høgskoler, Bind 2</i>, Universitetsforlaget, Oslo (2001). <a href="/wiki/Spesial:Bokkilder/9788215000060" class="internal mw-magiclink-isbn">ISBN 978-82-1500-006-0</a>.</span> </li> <li id="cite_note-Griffiths-3"><b>^</b> <a href="#cite_ref-Griffiths_3-0"><sup>a</sup></a> <a href="#cite_ref-Griffiths_3-1"><sup>b</sup></a> <span class="reference-text"> D.J. Griffiths, <i>Introduction to Electrodynamics</i>, Prentice Hall, New Jersey (1999). <a href="/wiki/Spesial:Bokkilder/013805326X" class="internal mw-magiclink-isbn">ISBN 0-13-805326-X</a>.</span> </li> <li id="cite_note-Jackson-4"><b><a href="#cite_ref-Jackson_4-0">^</a></b> <span class="reference-text"> J. D. Jackson, <i>Classical Electrodynamics</i>, John Wiley & Sons, New York (1998). <a href="/wiki/Spesial:Bokkilder/047130932X" class="internal mw-magiclink-isbn">ISBN 0-4713-0932-X</a>.</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"> C. Itzykson and J-B. Zuber, <i>Quantum Field Theory</i>, McGraw-Hill, New York (1980). <a href="/wiki/Spesial:Bokkilder/0070320713" class="internal mw-magiclink-isbn">ISBN 0-07-032071-3</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Eksterne_lenker">Eksterne lenker</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coulombs_lov&veaction=edit&section=8" title="Rediger avsnitt: Eksterne lenker" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Coulombs_lov&action=edit&section=8" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>R. Williams, <a rel="nofollow" class="external text" href="https://www.aps.org/publications/apsnews/201606/physicshistory.cfm"><i>June 1785: Coulomb Measures the Electric Force</i></a>, APS News <b>25</b> (6), 2016.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23230704">.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 dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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