Llei de Coulomb - Wikipedia

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</div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sitio"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Conteníu" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Conteníu</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover a la barra llateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">despintar</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">Entamu</div> </a> </li> <li id="toc-Desenvolvimientu_de_la_llei" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Desenvolvimientu_de_la_llei"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Desenvolvimientu de la llei</span> </div> </a> <button aria-controls="toc-Desenvolvimientu_de_la_llei-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>Alternar subsección Desenvolvimientu de la llei</span> </button> <ul id="toc-Desenvolvimientu_de_la_llei-sublist" class="vector-toc-list"> <li id="toc-Enunciáu_de_la_llei" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Enunciáu_de_la_llei"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Enunciáu de la llei</span> </div> </a> <ul id="toc-Enunciáu_de_la_llei-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Constante_de_Coulomb" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Constante_de_Coulomb"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Constante de Coulomb</span> </div> </a> <ul id="toc-Constante_de_Coulomb-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potencial_de_Coulomb" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Potencial_de_Coulomb"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Potencial de Coulomb</span> </div> </a> <ul id="toc-Potencial_de_Coulomb-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Llimitaciones_de_la_Llei_de_Coulomb" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Llimitaciones_de_la_Llei_de_Coulomb"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Llimitaciones de la Llei de Coulomb</span> </div> </a> <ul id="toc-Llimitaciones_de_la_Llei_de_Coulomb-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Verificación_esperimental_de_la_Llei_de_Coulomb" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Verificación_esperimental_de_la_Llei_de_Coulomb"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Verificación esperimental de la Llei de Coulomb</span> </div> </a> <ul id="toc-Verificación_esperimental_de_la_Llei_de_Coulomb-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Comparanza_ente_la_Llei_de_Coulomb_y_la_llei_de_gravitación_universal" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comparanza_ente_la_Llei_de_Coulomb_y_la_llei_de_gravitación_universal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Comparanza ente la Llei de Coulomb y la llei de gravitación universal</span> </div> </a> <ul id="toc-Comparanza_ente_la_Llei_de_Coulomb_y_la_llei_de_gravitación_universal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_tamién" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_tamién"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ver tamién</span> </div> </a> <ul id="toc-Ver_tamién-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencies"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Referencies</span> </div> </a> <button aria-controls="toc-Referencies-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>Alternar subsección Referencies</span> </button> <ul id="toc-Referencies-sublist" class="vector-toc-list"> <li id="toc-Bibliografía" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliografía"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Bibliografía</span> </div> </a> <ul id="toc-Bibliografía-sublist" class="vector-toc-list"> </ul> </li> </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="Conteníu" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Llei de Coulomb</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="Ir a un artículo en otro idioma. Disponible en 79 idiomas" > <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 llingües</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/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 – alemán de Suiza" lang="gsw" hreflang="gsw" data-title="Coulombsches Gesetz" data-language-autonym="Alemannisch" data-language-local-name="alemán de Suiza" 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 – amháricu" lang="am" hreflang="am" data-title="የኩሎምብ ህግ" data-language-autonym="አማርኛ" data-language-local-name="amháricu" 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 – árabe" lang="ar" hreflang="ar" data-title="قانون كولوم" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kulon_qanunu" title="Kulon qanunu – azerbaixanu" lang="az" hreflang="az" data-title="Kulon qanunu" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaixanu" class="interlanguage-link-target"><span>Azərbaycanca</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 – bielorrusu" lang="be" hreflang="be" data-title="Закон Кулона" data-language-autonym="Беларуская" data-language-local-name="bielorrusu" 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 – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Закон Кулёна" 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%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 – búlgaru" lang="bg" hreflang="bg" data-title="Закон на Кулон" data-language-autonym="Български" data-language-local-name="búlgaru" 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%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 – bengalín" lang="bn" hreflang="bn" data-title="কুলম্বের সূত্র" data-language-autonym="বাংলা" data-language-local-name="bengalín" 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/Coulombov_zakon" title="Coulombov zakon – bosniu" lang="bs" hreflang="bs" data-title="Coulombov zakon" data-language-autonym="Bosanski" data-language-local-name="bosniu" 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 – catalán" lang="ca" hreflang="ca" data-title="Llei de Coulomb" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Coulomb%C5%AFv_z%C3%A1kon" title="Coulombův zákon – checu" lang="cs" hreflang="cs" data-title="Coulombův zákon" data-language-autonym="Čeština" data-language-local-name="checu" 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%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 – chuvash" lang="cv" hreflang="cv" data-title="Кулон саккунĕ" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Coulombs_lov" title="Coulombs lov – danés" lang="da" hreflang="da" data-title="Coulombs lov" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Coulombsches_Gesetz" title="Coulombsches Gesetz – alemán" lang="de" hreflang="de" data-title="Coulombsches Gesetz" data-language-autonym="Deutsch" data-language-local-name="alemán" 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%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 – griegu" lang="el" hreflang="el" data-title="Νόμος του Κουλόμπ" data-language-autonym="Ελληνικά" data-language-local-name="griegu" 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 – inglés" lang="en" hreflang="en" data-title="Coulomb's law" data-language-autonym="English" data-language-local-name="inglés" 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/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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ley_de_Coulomb" title="Ley de Coulomb – español" lang="es" hreflang="es" data-title="Ley de Coulomb" data-language-autonym="Español" data-language-local-name="español" 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/Coulomb%27i_seadus" title="Coulomb'i seadus – estoniu" lang="et" hreflang="et" data-title="Coulomb'i seadus" data-language-autonym="Eesti" data-language-local-name="estoniu" 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/Coulomben_legea" title="Coulomben legea – vascu" lang="eu" hreflang="eu" data-title="Coulomben legea" data-language-autonym="Euskara" data-language-local-name="vascu" 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 – persa" lang="fa" hreflang="fa" data-title="قانون کولن" data-language-autonym="فارسی" data-language-local-name="persa" 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/Coulombin_laki" title="Coulombin laki – finlandés" lang="fi" hreflang="fi" data-title="Coulombin laki" data-language-autonym="Suomi" data-language-local-name="finlandés" 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/Loi_de_Coulomb_(%C3%A9lectrostatique)" title="Loi de Coulomb (électrostatique) – francés" lang="fr" hreflang="fr" data-title="Loi de Coulomb (électrostatique)" data-language-autonym="Français" data-language-local-name="francés" 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 – irlandés" lang="ga" hreflang="ga" data-title="Dlí Coulomb" data-language-autonym="Gaeilge" data-language-local-name="irlandés" 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 – gallegu" lang="gl" hreflang="gl" data-title="Lei de Coulomb" data-language-autonym="Galego" data-language-local-name="gallegu" 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%97%D7%95%D7%A7_%D7%A7%D7%95%D7%9C%D7%95%D7%9F" title="חוק קולון – hebréu" lang="he" hreflang="he" data-title="חוק קולון" data-language-autonym="עברית" data-language-local-name="hebréu" 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%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 – croata" lang="hr" hreflang="hr" data-title="Coulombov zakon" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Lwa_koulon" title="Lwa koulon – haitianu" lang="ht" hreflang="ht" data-title="Lwa koulon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitianu" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Coulomb-t%C3%B6rv%C3%A9ny" title="Coulomb-törvény – húngaru" lang="hu" hreflang="hu" data-title="Coulomb-törvény" data-language-autonym="Magyar" data-language-local-name="húngaru" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%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 – armeniu" lang="hy" hreflang="hy" data-title="Կուլոնի օրենք" data-language-autonym="Հայերեն" data-language-local-name="armeniu" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_Coulomb" title="Hukum Coulomb – indonesiu" lang="id" hreflang="id" data-title="Hukum Coulomb" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiu" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/K%C3%BAlombskraftur" title="Kúlombskraftur – islandés" lang="is" hreflang="is" data-title="Kúlombskraftur" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Forza_di_Coulomb" title="Forza di Coulomb – italianu" lang="it" hreflang="it" data-title="Forza di Coulomb" data-language-autonym="Italiano" data-language-local-name="italianu" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%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 – xaponés" lang="ja" hreflang="ja" data-title="クーロンの法則" data-language-autonym="日本語" data-language-local-name="xaponés" 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%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 – xeorxanu" lang="ka" hreflang="ka" data-title="კულონის კანონი" data-language-autonym="ქართული" data-language-local-name="xeorxanu" 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 – kazaquistanín" lang="kk" hreflang="kk" data-title="Кулон заңы" data-language-autonym="Қазақша" data-language-local-name="kazaquistanín" class="interlanguage-link-target"><span>Қазақша</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 – ḥemer" lang="km" hreflang="km" data-title="ច្បាប់គូឡុំ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="ḥemer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</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 – coreanu" lang="ko" hreflang="ko" data-title="쿨롱 법칙" data-language-autonym="한국어" data-language-local-name="coreanu" class="interlanguage-link-target"><span>한국어</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 – curdu" lang="ku" hreflang="ku" data-title="Hêza karebayî" data-language-autonym="Kurdî" data-language-local-name="curdu" 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 – kirguistanín" lang="ky" hreflang="ky" data-title="Кулон мыйзамы" data-language-autonym="Кыргызча" data-language-local-name="kirguistanín" class="interlanguage-link-target"><span>Кыргызча</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 – lituanu" lang="lt" hreflang="lt" data-title="Kulono dėsnis" data-language-autonym="Lietuvių" data-language-local-name="lituanu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kulona_likums" title="Kulona likums – letón" lang="lv" hreflang="lv" data-title="Kulona likums" data-language-autonym="Latviešu" data-language-local-name="letón" class="interlanguage-link-target"><span>Latviešu</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 – macedoniu" lang="mk" hreflang="mk" data-title="Кулонов закон" data-language-autonym="Македонски" data-language-local-name="macedoniu" 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-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 – mongol" lang="mn" hreflang="mn" data-title="Кулоны хууль" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hukum_Coulomb" title="Hukum Coulomb – malayu" lang="ms" hreflang="ms" data-title="Hukum Coulomb" data-language-autonym="Bahasa Melayu" data-language-local-name="malayu" class="interlanguage-link-target"><span>Bahasa Melayu</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 – birmanu" lang="my" hreflang="my" data-title="ကူးလောင်း၏ နိယာမ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmanu" class="interlanguage-link-target"><span>မြန်မာဘာသာ</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 – nepalés" lang="ne" hreflang="ne" data-title="कूलम्बको नियम" data-language-autonym="नेपाली" data-language-local-name="nepalés" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_van_Coulomb" title="Wet van Coulomb – neerlandés" lang="nl" hreflang="nl" data-title="Wet van Coulomb" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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/Coulomb-lova" title="Coulomb-lova – noruegu Nynorsk" lang="nn" hreflang="nn" data-title="Coulomb-lova" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegu 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/Coulombs_lov" title="Coulombs lov – noruegu Bokmål" lang="nb" hreflang="nb" data-title="Coulombs lov" data-language-autonym="Norsk bokmål" data-language-local-name="noruegu Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%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 – punyabí" lang="pa" hreflang="pa" data-title="ਕੂਲੌਂਬ ਦਾ ਨਿਯਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punyabí" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_Coulomba" title="Prawo Coulomba – polacu" lang="pl" hreflang="pl" data-title="Prawo Coulomba" data-language-autonym="Polski" data-language-local-name="polacu" class="interlanguage-link-target"><span>Polski</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 – piamontés" lang="pms" hreflang="pms" data-title="Lej ëd Coulomb" data-language-autonym="Piemontèis" data-language-local-name="piamontés" class="interlanguage-link-target"><span>Piemontèis</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 – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کولمب دا قنون" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</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 – portugués" lang="pt" hreflang="pt" data-title="Lei de Coulomb" data-language-autonym="Português" data-language-local-name="portugués" 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 – rumanu" lang="ro" hreflang="ro" data-title="Legea lui Coulomb" data-language-autonym="Română" data-language-local-name="rumanu" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="artículos destacaos"><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 – rusu" lang="ru" hreflang="ru" data-title="Закон Кулона" data-language-autonym="Русский" data-language-local-name="rusu" 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/Coulombov_zakon" title="Coulombov zakon – serbo-croata" lang="sh" hreflang="sh" data-title="Coulombov zakon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croata" 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/Coulomb%27s_law" title="Coulomb's law – Simple English" lang="en-simple" hreflang="en-simple" data-title="Coulomb's law" 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/Coulombov_z%C3%A1kon" title="Coulombov zákon – eslovacu" lang="sk" hreflang="sk" data-title="Coulombov zákon" data-language-autonym="Slovenčina" data-language-local-name="eslovacu" 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 – eslovenu" lang="sl" hreflang="sl" data-title="Coulombov zakon" data-language-autonym="Slovenščina" data-language-local-name="eslovenu" 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/Ligji_i_Kulombit" title="Ligji i Kulombit – albanu" lang="sq" hreflang="sq" data-title="Ligji i Kulombit" data-language-autonym="Shqip" data-language-local-name="albanu" 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%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 – serbiu" lang="sr" hreflang="sr" data-title="Кулонов закон" data-language-autonym="Српски / srpski" data-language-local-name="serbiu" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Coulombs_lag" title="Coulombs lag – suecu" lang="sv" hreflang="sv" data-title="Coulombs lag" data-language-autonym="Svenska" data-language-local-name="suecu" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%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-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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Coulomb_kanunu" title="Coulomb kanunu – turcu" lang="tr" hreflang="tr" data-title="Coulomb kanunu" data-language-autonym="Türkçe" data-language-local-name="turcu" 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%9A%D1%83%D0%BB%D0%BE%D0%BD_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD%D1%8B" title="Кулон законы – tártaru" lang="tt" hreflang="tt" data-title="Кулон законы" data-language-autonym="Татарча / tatarça" data-language-local-name="tártaru" 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%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%9A%D1%83%D0%BB%D0%BE%D0%BD%D0%B0" title="Закон Кулона – ucraín" lang="uk" hreflang="uk" data-title="Закон Кулона" data-language-autonym="Українська" data-language-local-name="ucraín" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kulon_qonuni" title="Kulon qonuni – uzbequistanín" lang="uz" hreflang="uz" data-title="Kulon qonuni" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbequistanín" 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/L%E1%BB%B1c_t%C4%A9nh_%C4%91i%E1%BB%87n" title="Lực tĩnh điện – vietnamín" lang="vi" hreflang="vi" data-title="Lực tĩnh điện" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamín" 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/%E5%BA%93%E4%BB%91%E5%AE%9A%E5%BE%8B" title="库仑定律 – chinu wu" lang="wuu" hreflang="wuu" data-title="库仑定律" data-language-autonym="吴语" data-language-local-name="chinu wu" 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/%E5%BA%93%E4%BB%91%E5%AE%9A%E5%BE%8B" title="库仑定律 – chinu" lang="zh" hreflang="zh" data-title="库仑定律" data-language-autonym="中文" data-language-local-name="chinu" class="interlanguage-link-target"><span>中文</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 – chinu lliterariu" lang="lzh" hreflang="lzh" data-title="庫侖定律" data-language-autonym="文言" data-language-local-name="chinu lliterariu" class="interlanguage-link-target"><span>文言</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 – cantonés" lang="yue" hreflang="yue" data-title="庫侖定律" data-language-autonym="粵語" data-language-local-name="cantonés" 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/Q83152#sitelinks-wikipedia" title="Editar los enllaces d'interllingua" class="wbc-editpage">Editar los enllaces</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="Espacios de nome"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div 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data-file-height="512" /></a></span></div></div> </div> <div id="siteSub" class="noprint">De Wikipedia</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="ast" dir="ltr"><table class="infobox plantia-xenerica" style="font-size:90%;width:25em"><tbody><tr><th colspan="2" style="text-align:center;font-size:125%;font-weight:bold;background-color: #acacac">Llei de Coulomb</th></tr><tr><td colspan="2" style="text-align:center;background-color: #cdcdcd"> llei física</td></tr><tr><td colspan="2" style="text-align:right"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q83152" title="Cambiar los datos en Wikidata"><img alt="Cambiar los datos en Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/12px-Arbcom_ru_editing.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/18px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/24px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:CoulombsLaw.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/CoulombsLaw.svg/280px-CoulombsLaw.svg.png" decoding="async" width="280" height="224" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/CoulombsLaw.svg/420px-CoulombsLaw.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/CoulombsLaw.svg/560px-CoulombsLaw.svg.png 2x" data-file-width="512" data-file-height="410" /></a><figcaption>Llei de Coulomb espresando los signos de cargues de distintu signu, y de cargues del mesmu signu.</figcaption></figure> <p>La <b>llei de Coulomb</b> puede espresase como: <style data-mw-deduplicate="TemplateStyles:r4219309">.mw-parser-output .teorema-contenedor{min-width:50%;max-width:77%}.mw-parser-output .teorema{padding:.5em 2em .5em 1.5em;padding-right:2em;padding-left:1.5em;padding-bottom:0.5em;padding-top:0.5em;border:1px solid var(--border-color-base,#49768C);font-family:Georgia,serif}.mw-parser-output .teorema-pie{margin-top:-1em;text-align:right}</style> </p> <table class="teorema-contenedor"> <tbody><tr> <td><blockquote class="teorema"> <p>La magnitú de caúna de les fuercies llétriques con que interactúan dos cargues puntuales en reposu ye direutamente proporcional al productu de la magnitú de dambes cargues ya inversamente proporcional al cuadráu de la distancia que les dixebra y tien la direición de la llinia que les xune. La fuercia ye de repulsión si les cargues son d'igual signu, y d'atraición si son de signu contrariu. </p> </blockquote> </td></tr></tbody></table> <p>La constante de proporcionalidad depende de la constante dieléctrica del mediu nel que s'atopen les cargues. </p><p>Nomar en reconocencia del físicu francés <a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Charles-Augustin de Coulomb</a> (1736-1806), que la enunció en 1785 y forma la base de la <a href="/w/index.php?title=Electroest%C3%A1tica&action=edit&redlink=1" class="new" title="Electroestática (la páxina nun esiste)">electroestática</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Desenvolvimientu_de_la_llei">Desenvolvimientu de la llei</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=1" title="Editar seición: Desenvolvimientu de la llei" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=1" title="Editar el código fuente de la sección: Desenvolvimientu de la llei"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Charles-Augustin de Coulomb</a> desenvolvió la <a href="/w/index.php?title=Balanza_de_torsi%C3%B3n&action=edit&redlink=1" class="new" title="Balanza de torsión (la páxina nun esiste)">balanza de torsión</a> cola que determinó les propiedaes de la fuercia electrostática. Esti preséu consiste nuna barra que cuelga d'una fibra capaz de torcese. Si la barra xira, la fibra tiende a faela tornar a la so posición orixinal, colo que conociendo la fuercia de torsión que la fibra exerz sobre la barra, puede determinase la fuercia exercida nun puntu de la barra. La llei de <i>Coulomb </i> tamién conocida como llei de cargues tien que ver coles cargues llétriques d'un material, esto ye, depende de si les sos cargues son negatives o positives. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Inversa.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Inversa.png/250px-Inversa.png" decoding="async" width="250" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Inversa.png/375px-Inversa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/6/67/Inversa.png 2x" data-file-width="393" data-file-height="313" /></a><figcaption>Variación de la fuercia de Coulomb ente dos cargues puntuales en función de la distancia.</figcaption></figure> <p>Na barra de la balanza, Coulomb asitió una pequeña esfera cargada y de siguío, a distintes distancies, asitió otra esfera tamién cargada. Depués midió la fuercia ente elles reparando l'ángulu que xiraba la barra. </p><p>Diches midíes dexaron determinar que: </p> <ul><li>La fuercia d'interacción ente dos cargues <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_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368ce6ffac8ad638047b34fe40000193686f195e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{1}\,\!}"></span> y <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_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fabf55d8e51c20e94512c90d9e8e50c46bf73c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{2}\,\!}"></span> dobla la so magnitú si dalguna de les cargues dobla'l so valor, triplicar si dalguna de les cargues aumenta'l so valor nun factor de trés, y asina socesivamente. Concluyó entós que'l valor de la fuercia yera proporcional al productu de les cargues:</li></ul> <center><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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \propto \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∝</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \propto \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ae659030dd6edca6cae61c9f3672f590f80df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:1.676ex;" alt="{\displaystyle \propto \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368ce6ffac8ad638047b34fe40000193686f195e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{1}\,\!}"></span>     y     <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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \propto \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∝</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \propto \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ae659030dd6edca6cae61c9f3672f590f80df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:1.676ex;" alt="{\displaystyle \propto \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fabf55d8e51c20e94512c90d9e8e50c46bf73c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{2}\,\!}"></span></center> <p>en consecuencia: </p> <center><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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \propto \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∝</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \propto \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ae659030dd6edca6cae61c9f3672f590f80df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:1.676ex;" alt="{\displaystyle \propto \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{1}q_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}q_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d175307bfb41f0a8ae78f61c36c73709e670691b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:4.57ex; height:2.009ex;" alt="{\displaystyle q_{1}q_{2}\,\!}"></span></center> <ul><li>Si la distancia ente les cargues ye <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 r\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86937851b7cb70e8802197a7b5ddcf39c0b02445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,\!}"></span>, al doblala, la fuercia d'interacción mengua nun factor de 4 (2²); al triplicala, mengua nun factor de 9 (3²) y al cuadriplicar <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 r\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86937851b7cb70e8802197a7b5ddcf39c0b02445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,\!}"></span>, la fuercia ente cargues mengua nun factor de 16 (4²). Arriendes d'ello, la fuercia d'interacción ente dos cargues puntuales, ye inversamente proporcional al cuadráu de la distancia:</li></ul> <center><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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \propto \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∝</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \propto \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ae659030dd6edca6cae61c9f3672f590f80df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:1.676ex;" alt="{\displaystyle \propto \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1 \over r^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1 \over r^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39b8e5f77080c5c35212459dca400ab4941a7cdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:2.939ex; height:5.509ex;" alt="{\displaystyle 1 \over r^{2}\,\!}"></span></center> <p>Acomuñando dambes rellaciones: </p> <center><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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \propto \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∝</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \propto \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ae659030dd6edca6cae61c9f3672f590f80df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:1.676ex;" alt="{\displaystyle \propto \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{1}q_{2} \over r^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <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> </mstyle> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}q_{2} \over r^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1554a5df5e716b83390c148e4cdc4a19d967f271" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:5.019ex; height:5.176ex;" alt="{\displaystyle q_{1}q_{2} \over r^{2}\,\!}"></span></center> <p>Finalmente, introduzse una constante de proporcionalidad pa tresformar la rellación anterior nuna igualdá: </p> <center><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=\kappa {\frac {q_{1}q_{2}}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>κ</mi> <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> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\kappa {\frac {q_{1}q_{2}}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc31a2def41d7b2b7ace8dc30461c2e4325de2f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:11.584ex; height:5.176ex;" alt="{\displaystyle F=\kappa {\frac {q_{1}q_{2}}{r^{2}}}\,\!}"></span> </center> <p>onde pal sistema internacional d'unidaes: </p> <center><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 \kappa =9\times 10^{9}{\frac {N\cdot m^{2}}{C^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> <mo>=</mo> <mn>9</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mo>⋅</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa =9\times 10^{9}{\frac {N\cdot m^{2}}{C^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfdfe4334c07ba70a51b2e5d898c66156b8a032f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.493ex; height:6.009ex;" alt="{\displaystyle \kappa =9\times 10^{9}{\frac {N\cdot m^{2}}{C^{2}}}}"></span> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9daa41f6e8f78ea6bb5711d7ac97901ce564b94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{1}}"></span> y <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_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd2d05084feb02b8ba29b0673440fb673b102589" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{2}}"></span> son el valor de les cargues en Coulombs (<i>C</i>) </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> ye la distancia que dixebra a les cargues en metros (<i>m</i>) </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> ye la fuercia d'atraición o repulsión en Newtons (<i>N</i>) (cargues del mesmu signu se repelen, cargues de signu opuestu atráense) </p> </center> <div class="mw-heading mw-heading3"><h3 id="Enunciáu_de_la_llei"><span id="Enunci.C3.A1u_de_la_llei"></span>Enunciáu de la llei</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=2" title="Editar seición: Enunciáu de la llei" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=2" title="Editar el código fuente de la sección: Enunciáu de la llei"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La llei de Coulomb ye válida solo en condiciones estacionaries, esto ye, cuando nun hai movimientu de les cargues o, como aproximamientu cuando'l movimientu realizar a velocidaes baxes y en trayectories rectillinies uniformes. Ye por ello que ye llamada <i>fuercia electrostática</i>. </p><p>En términos matemáticos, la magnitú <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\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec86a832c57e76bd90bfa2600197fd4bb435ff02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.128ex; height:2.176ex;" alt="{\displaystyle F\,\!}"></span> de la fuercia que caúna de los dos cargues puntuales <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_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368ce6ffac8ad638047b34fe40000193686f195e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{1}\,\!}"></span> y <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_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fabf55d8e51c20e94512c90d9e8e50c46bf73c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{2}\,\!}"></span> exerz sobre la otra separaes por una distancia <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 d\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e22c8b8823a4a874b8ca5bbe1a6ce658a7822853" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.603ex; height:2.176ex;" alt="{\displaystyle d\,\!}"></span> esprésase como: </p> <style data-mw-deduplicate="TemplateStyles:r4219090">.mw-parser-output .ecuacion{padding:5px 10px;background-color:var(--background-color-base);color:var(--color-base);margin-left:30px;margin-bottom:0.8em;margin-top:0.5em;min-width:50%}.mw-parser-output .ecuacion .referencia{float:right;width:10%;text-align:end}.mw-parser-output .ecuacion cite{font-style:normal}</style><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\kappa {\frac {\left|q_{1}q_{2}\right|}{d^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>|</mo> <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> <mo>|</mo> </mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\kappa {\frac {\left|q_{1}q_{2}\right|}{d^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08e25b2dfd06cf1f16efc7d1c3f5b95165116b40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:12.878ex; height:6.009ex;" alt="{\displaystyle F=\kappa {\frac {\left|q_{1}q_{2}\right|}{d^{2}}}\,}"></span> </p> </blockquote> <p><i>Daes dos <a href="/wiki/Carga_ll%C3%A9trica" title="Carga llétrica">cargues</a> puntuales <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_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368ce6ffac8ad638047b34fe40000193686f195e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{1}\,\!}"></span> y <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_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fabf55d8e51c20e94512c90d9e8e50c46bf73c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{2}\,\!}"></span> dixebraes una distancia <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 d\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e22c8b8823a4a874b8ca5bbe1a6ce658a7822853" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.603ex; height:2.176ex;" alt="{\displaystyle d\,\!}"></span> nel <a href="/w/index.php?title=Vac%C3%ADu_(f%C3%ADsica)&action=edit&redlink=1" class="new" title="Vacíu (física) (la páxina nun esiste)">vacíu</a>, atráense o repelen ente sigo con una <a href="/wiki/Fuercia" title="Fuercia">fuercia</a> que la so magnitú ta dada por:</i> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\kappa {\frac {q_{1}q_{2}}{d^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>κ</mi> <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>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\kappa {\frac {q_{1}q_{2}}{d^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc533c6f4eddc87a97ca0da6b42897efbf94be12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.584ex; height:5.176ex;" alt="{\displaystyle F=\kappa {\frac {q_{1}q_{2}}{d^{2}}}\,}"></span> </p> </blockquote> <p>La Llei de Coulomb esprésase meyor con magnitúes <a href="/w/index.php?title=Vector_(f%C3%ADsica)&action=edit&redlink=1" class="new" title="Vector (física) (la páxina nun esiste)">vectoriales</a>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{12}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}}{d^{2}}}\mathbf {o} _{d}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}\mathbf {r} _{12}}{\|\mathbf {r} _{12}\|^{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>12</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <mi>ε</mi> </mrow> </mfrac> </mrow> <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>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">o</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <mi>ε</mi> </mrow> </mfrac> </mrow> <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> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mrow> <mrow> <mo fence="false" stretchy="false">‖</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <msup> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} _{12}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}}{d^{2}}}\mathbf {o} _{d}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}\mathbf {r} _{12}}{\|\mathbf {r} _{12}\|^{3}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6700450aaacdbc6cf3250dcf2c37206b110d1164" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:34.415ex; height:6.009ex;" alt="{\displaystyle \mathbf {F} _{12}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}}{d^{2}}}\mathbf {o} _{d}={\frac {1}{4\pi \varepsilon }}{\frac {q_{1}q_{2}\mathbf {r} _{12}}{\|\mathbf {r} _{12}\|^{3}}}\,}"></span> </p> </blockquote> <p>onde <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 {o} _{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">o</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {o} _{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d172c1e0f55286aee8001115997d6e5f5e573f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.429ex; height:2.009ex;" alt="{\displaystyle \mathbf {o} _{d}}"></span> ye un <a href="/wiki/Vector" title="Vector">vector</a> unitariu (que va de la carga 1 a la carga 2), siendo la so direición dende la <a href="/wiki/Carga_ll%C3%A9trica" title="Carga llétrica">cargues</a> que produz la fuercia escontra la carga que la esperimenta; <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 {r} _{12}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{12}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad95a00663a4c1e30d4def04a67ace874a3448c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.978ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{12}}"></span> ye'l vector de separación ente les cargues. Al aplicar esta fórmula nun exerciciu, tien d'asitiase'l signu de les cargues <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9daa41f6e8f78ea6bb5711d7ac97901ce564b94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{1}}"></span> o <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_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd2d05084feb02b8ba29b0673440fb673b102589" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.091ex; height:2.009ex;" alt="{\displaystyle q_{2}}"></span>, según sían estes positives o negatives. </p><p>L'esponente de la distancia, de la llei de Coulomb ye, hasta onde se sabe anguaño, esautamente 2. Esperimentalmente sábese que, si l'esponente fora de la forma <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 (2+\delta )\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2+\delta )\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff75cbcc49c82dffbf53b2d5c68ac1781b68ee99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:7.248ex; height:2.843ex;" alt="{\displaystyle (2+\delta )\,\!}"></span>, entós <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 \left|\delta \right|<10^{-16}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>δ</mi> <mo>|</mo> </mrow> <mo><</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>16</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\delta \right|<10^{-16}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae1a4658c3bbb3258eb1e4c9126d9f5dcef043c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:11.308ex; height:3.176ex;" alt="{\displaystyle \left|\delta \right|<10^{-16}\,\!}"></span>. </p> <figure class="mw-halign-center" typeof="mw:File/Frame"><a href="/wiki/Ficheru:Ley_de_Coulomb.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7c/Ley_de_Coulomb.PNG" decoding="async" width="499" height="89" class="mw-file-element" data-file-width="499" data-file-height="89" /></a><figcaption><center>Representación gráfica de la Llei de Coulomb pa dos cargues del mesmu signu.</center></figcaption></figure> <p>Reparar qu'esto satisfai la tercera de la llei de Newton por cuenta de qu'implica que fuercies d'igual magnitú actúen sobre <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 \scriptstyle q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa1434a0cfcdd5dd1d8a289e9294706500275166" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.565ex; height:1.676ex;" alt="{\displaystyle \scriptstyle q_{1}}"></span> y <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 \scriptstyle q_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57a5f018a63cbc615d4d614ce1f57944fcf7e331" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.565ex; height:1.676ex;" alt="{\displaystyle \scriptstyle q_{2}}"></span>. La llei de Coulomb ye una ecuación vectorial ya inclúi el fechu de que la fuercia actúa a lo llargo de la llinia d'unión ente les cargues. </p> <div class="mw-heading mw-heading3"><h3 id="Constante_de_Coulomb">Constante de Coulomb</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=3" title="Editar seición: Constante de Coulomb" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=3" title="Editar el código fuente de la sección: Constante de Coulomb"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r4219085">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Artículu principal: <a href="/w/index.php?title=Constante_de_Coulomb&action=edit&redlink=1" class="new" title="Constante de Coulomb (la páxina nun esiste)">Constante de Coulomb</a></div> <p>La constante <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 \kappa \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9af498836ebe4be809ac299c65143d79ed1545c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.726ex; height:1.676ex;" alt="{\displaystyle \kappa \,\!}"></span> ye la <a href="/w/index.php?title=Llista_de_constantes_f%C3%ADsiques&action=edit&redlink=1" class="new" title="Llista de constantes físiques (la páxina nun esiste)">Constante de Coulomb</a> y el so valor pa unidaes <a href="/wiki/Sistema_Internacional_d%27Unidaes" class="mw-redirect" title="Sistema Internacional d'Unidaes">SI</a> ye <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 \scriptstyle 1/(4\pi \varepsilon )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>π</mi> <mi>ε</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle 1/(4\pi \varepsilon )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/129692bd2a6ddc8e9a9d7032ccc11df7fdff2c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.84ex; height:2.176ex;" alt="{\displaystyle \scriptstyle 1/(4\pi \varepsilon )\,}"></span> <a href="/wiki/Newton_(unid%C3%A1)" title="Newton (unidá)">N</a><a href="/wiki/Metru_cuadr%C3%A1u" title="Metru cuadráu">m²</a>/<a href="/wiki/Culombiu" title="Culombiu">C²</a>. </p><p>De la mesma la constante <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 =\varepsilon _{r}\varepsilon _{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon =\varepsilon _{r}\varepsilon _{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3a835acd7da019b292ea8b0c58d85f758d93b29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:8.764ex; height:2.009ex;" alt="{\displaystyle \varepsilon =\varepsilon _{r}\varepsilon _{0}\,\!}"></span> onde <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 _{r}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{r}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00360861b8449e78c645980d62ca348275c64bf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.444ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{r}\,\!}"></span> ye la <a href="/w/index.php?title=Permitividad&action=edit&redlink=1" class="new" title="Permitividad (la páxina nun esiste)">permitividad relativa</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 \varepsilon _{r}\geq 1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>≥</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{r}\geq 1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34cda8c82c8577da05302f03c38842c0273423ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:6.705ex; height:2.509ex;" alt="{\displaystyle \varepsilon _{r}\geq 1\,\!}"></span>, y <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}=8,85\times 10^{-12}\,\!}"> <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</mn> <mo>,</mo> <mn>85</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{0}=8,85\times 10^{-12}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba8004e4f788ac14957e843cbe6c28f0ce331747" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:18.465ex; height:3.009ex;" alt="{\displaystyle \varepsilon _{0}=8,85\times 10^{-12}\,\!}"></span> <a href="/wiki/Faradiu" title="Faradiu">F</a>/<a href="/wiki/Metru" title="Metru">m</a> ye la <a href="/w/index.php?title=Permitividad&action=edit&redlink=1" class="new" title="Permitividad (la páxina nun esiste)">permitividad del vacíu</a>. Cuando'l mediu qu'arrodia a les cargues nun ye'l vacíu hai que tener en cuenta la <a href="/w/index.php?title=Constante_diel%C3%A9ctrica&action=edit&redlink=1" class="new" title="Constante dieléctrica (la páxina nun esiste)">constante dieléctrica</a> y la <a href="/w/index.php?title=Permitividad&action=edit&redlink=1" class="new" title="Permitividad (la páxina nun esiste)">permitividad</a> del material. La ecuación de la llei de Coulomb queda finalmente espresada de la siguiente manera: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\kappa {\frac {\left|q_{1}\right|\left|q_{2}\right|}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow> <mo>|</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>|</mo> </mrow> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\kappa {\frac {\left|q_{1}\right|\left|q_{2}\right|}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4018dfa36168b9af66c7d9760c0b17e3a71c3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:14.558ex; height:6.009ex;" alt="{\displaystyle F=\kappa {\frac {\left|q_{1}\right|\left|q_{2}\right|}{r^{2}}}\,\!}"></span> </p> </blockquote> <p>La constante, si les unidaes de les cargues atópase en Coulomb ye la siguiente <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 \scriptstyle K=9\cdot 10^{9}\mathrm {N\cdot m^{2}/C^{2}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>K</mi> <mo>=</mo> <mn>9</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mo>⋅</mo> <msup> <mi mathvariant="normal">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle K=9\cdot 10^{9}\mathrm {N\cdot m^{2}/C^{2}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebee3d0f0ab8b95ac643af113e261bdb5e9d9224" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.225ex; height:2.509ex;" alt="{\displaystyle \scriptstyle K=9\cdot 10^{9}\mathrm {N\cdot m^{2}/C^{2}} }"></span> y la so resultancia va ser en sistema MKS (<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 \scriptstyle N/C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>C</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle N/C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43e0696575496ffdd3d2691e64602b2e04ab6d94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.53ex; height:2.176ex;" alt="{\displaystyle \scriptstyle N/C}"></span>). Sicasí, si la unidá de les cargues tán en UES (q), la constante espresar de la siguiente forma <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 \scriptstyle K=\mathrm {dyn\cdot cm^{2}/ues} ^{2}(q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>K</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">y</mi> <mi mathvariant="normal">n</mi> <mo>⋅</mo> <mi mathvariant="normal">c</mi> <msup> <mi mathvariant="normal">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle K=\mathrm {dyn\cdot cm^{2}/ues} ^{2}(q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e691fee2f7b0268d19f172aeaac725a9a33b0790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.804ex; height:2.843ex;" alt="{\displaystyle \scriptstyle K=\mathrm {dyn\cdot cm^{2}/ues} ^{2}(q)}"></span> y la so resultancia va tar nes unidaes CGS (<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 \scriptstyle D/UES(q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>U</mi> <mi>E</mi> <mi>S</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle D/UES(q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0acdb8f038557d1cc6112accb6cf1f4ebbd3324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.794ex; height:2.176ex;" alt="{\displaystyle \scriptstyle D/UES(q)}"></span>). </p> <div class="mw-heading mw-heading3"><h3 id="Potencial_de_Coulomb">Potencial de Coulomb</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=4" title="Editar seición: Potencial de Coulomb" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=4" title="Editar el código fuente de la sección: Potencial de Coulomb"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La llei de Coulomb establez que la presencia d'una carga puntual xeneral induz en tol espaciu l'apaición d'un <a href="/w/index.php?title=Campu_de_fuercies_(f%C3%ADsica)&action=edit&redlink=1" class="new" title="Campu de fuercies (física) (la páxina nun esiste)">campu de fuercias</a> qu'aparra según la <a href="/w/index.php?title=Llei_de_la_inversa_del_cuadr%C3%A1u&action=edit&redlink=1" class="new" title="Llei de la inversa del cuadráu (la páxina nun esiste)">llei de la inversa del cuadráu</a>. Pa modelizar el campu por cuenta de delles cargues llétriques puntuales estátiques puede usase'l <a href="/w/index.php?title=Principiu_de_superposici%C3%B3n&action=edit&redlink=1" class="new" title="Principiu de superposición (la páxina nun esiste)">principiu de superposición</a> dada la aditividad de les fuercies sobre una partícula. Sicasí, matemáticamente el manexu d'espresiones vectoriales d'esi tipu puede aportar a complicáu, polo que frecuentemente resulta más senciellu definir un <a href="/wiki/Potencial_ll%C3%A9tricu" title="Potencial llétricu">potencial llétricu</a>. Pa ello a una carga puntual <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 \scriptstyle q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa1434a0cfcdd5dd1d8a289e9294706500275166" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.565ex; height:1.676ex;" alt="{\displaystyle \scriptstyle q_{1}}"></span> asígnase-y una función esguilar o <b>potencial de Coulomb</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \phi _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \phi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e62013385c90825acd4f56c916ce00943259fb52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.811ex; height:2.009ex;" alt="{\displaystyle \scriptstyle \phi _{1}}"></span> tal que la fuercia dao pola llei de Coulomb sía expresable como: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{12}=q_{2}{\boldsymbol {\nabla }}\phi _{1}}"> <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>12</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">∇</mi> </mrow> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} _{12}=q_{2}{\boldsymbol {\nabla }}\phi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f66f4b3c3628f41395349d6586d189e8adf363d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.415ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{12}=q_{2}{\boldsymbol {\nabla }}\phi _{1}}"></span> </p> </blockquote> <p>De la llei de Coulomb deduzse que la función esguilar que satisfai l'anterior ecuación ye: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{1}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}}{\|\mathbf {r} -\mathbf {r} _{q_{1}}\|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <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> <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> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mo fence="false" 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"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">‖</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{1}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}}{\|\mathbf {r} -\mathbf {r} _{q_{1}}\|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/518d17e75c21c434068b815fa37c20c38bedcbf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:23.921ex; height:6.176ex;" alt="{\displaystyle \phi _{1}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}}{\|\mathbf {r} -\mathbf {r} _{q_{1}}\|}}}"></span> </p> </blockquote> <p>Onde: </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 {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.102ex; height:1.676ex;" alt="{\displaystyle \mathbf {r} }"></span>, ye'l vector posición xenéricu d'un puntu onde pretende definise el potencial de Coulomb y <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 {r} _{q_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{q_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/972fa6aa7980003b6679a6fbb39da59036b41155" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.899ex; height:2.343ex;" alt="{\displaystyle \mathbf {r} _{q_{1}}}"></span>, ye'l</dd></dl> <p>vector de posición de la carga llétrica <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_{1}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a35103ae786ef644681698e6992483762b16fb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.478ex; height:2.009ex;" alt="{\displaystyle q_{1}\,}"></span> que'l so campu pretende caracterizase por mediu del potencial. </p> <div class="mw-heading mw-heading3"><h3 id="Llimitaciones_de_la_Llei_de_Coulomb">Llimitaciones de la Llei de Coulomb</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=5" title="Editar seición: Llimitaciones de la Llei de Coulomb" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=5" title="Editar el código fuente de la sección: Llimitaciones de la Llei de Coulomb"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>La espresión matemática solo ye aplicable a cargues puntuales estacionaries, y pa casos estáticos más complicaos de carga precisa ser xeneralizada por aciu el <a href="/wiki/Potencial_ll%C3%A9tricu" title="Potencial llétricu">potencial llétricu</a>. El campu llétrico creáu por una distribución de carga dada por <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span></li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi (\mathbf {r} )={\frac {1}{4\pi \epsilon }}\int _{V}{\frac {\rho (\mathbf {r} ')}{\|\mathbf {r} -\mathbf {r} '\|}}d^{3}\mathbf {r} '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</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> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <mi>ϵ</mi> </mrow> </mfrac> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <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> </mrow> <mrow> <mo fence="false" 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 fence="false" stretchy="false">‖</mo> </mrow> </mfrac> </mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi (\mathbf {r} )={\frac {1}{4\pi \epsilon }}\int _{V}{\frac {\rho (\mathbf {r} ')}{\|\mathbf {r} -\mathbf {r} '\|}}d^{3}\mathbf {r} '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d80f1fb645e22d72aa474a697e6991286508592e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.182ex; height:6.509ex;" alt="{\displaystyle \phi (\mathbf {r} )={\frac {1}{4\pi \epsilon }}\int _{V}{\frac {\rho (\mathbf {r} ')}{\|\mathbf {r} -\mathbf {r} '\|}}d^{3}\mathbf {r} '}"></span> </p> </blockquote> <ul><li>Cuando les cargues llétriques tán en movimientu ye necesariu reemplazar inclusive'l potencial de Coulomb pol <a href="/w/index.php?title=Potenciales_de_Li%C3%A9nard-Wiechert&action=edit&redlink=1" class="new" title="Potenciales de Liénard-Wiechert (la páxina nun esiste)">potencial vector de Liénard-Wiechert</a>, especialmente si les velocidaes de les partícules son cercanes a la <a href="/wiki/Velocid%C3%A1_de_la_lluz" title="Velocidá de la lluz">velocidá de la lluz</a>.</li> <li>Pa cargues a distancies pequeñes (del orde del tamañu de los <a href="/wiki/%C3%81tomos" class="mw-redirect" title="Átomos">átomos</a>), la fuercia electrostática efectiva ten de ser correxida por factores cuánticos. Pa campos bien intensos puede asoceder el fenómenu de la creación bonal de pares de partícula-antipartícula que riquen correxir el campu pa distancies bien curties.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Verificación_esperimental_de_la_Llei_de_Coulomb"><span id="Verificaci.C3.B3n_esperimental_de_la_Llei_de_Coulomb"></span>Verificación esperimental de la Llei de Coulomb</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=6" title="Editar seición: Verificación esperimental de la Llei de Coulomb" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=6" title="Editar el código fuente de la sección: Verificación esperimental de la Llei de Coulomb"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Frame"><a href="/wiki/Ficheru:Verificacion_ley_coulomb.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Verificacion_ley_coulomb.png" decoding="async" width="400" height="300" class="mw-file-element" data-file-width="400" data-file-height="300" /></a><figcaption>Montaxe esperimental pa verificar la llei de Coulomb.</figcaption></figure> <p>Ye posible verificar la llei de Coulomb por aciu un esperimentu senciellu. Considérense dos pequeñes esferes de masa "m" cargaes con cargues iguales, del mesmu signu, y que cuelguen de dos filos de llargor l, tal como s'indica na figura axunta. Sobre cada esfera actúen trés fuercies: el pesu <i>mg</i>, la tensión de la cuerda <i>T</i> y la fuercia de repulsión llétrica ente les bolines <i><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_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e5c87f7528c540268ceddba9924ad0252d0280" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{1}\,\!}"></span></i>. Nel equilibriu: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="referencia">(<cite id="Equation_1"><a href="#Eqnref_1">1</a></cite>)</span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\ \sin \theta _{1}=F_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mtext> </mtext> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\ \sin \theta _{1}=F_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11480cbf9fee088e0c668332378c0072dd07a421" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:14.026ex; height:2.509ex;" alt="{\displaystyle T\ \sin \theta _{1}=F_{1}\,\!}"></span> </p> </blockquote> <p>y tamién: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="referencia">(<cite id="Equation_2"><a href="#Eqnref_2">2</a></cite>)</span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\ \cos \theta _{1}=mg\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mtext> </mtext> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\ \cos \theta _{1}=mg\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f73e09a58b19f85dfdbf93f668eacfd29ed17b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:14.889ex; height:2.509ex;" alt="{\displaystyle T\ \cos \theta _{1}=mg\,\!}"></span> </p> </blockquote> <p>Estremando (<span id="Eqnref_1" class="plainlinks neverexpand"><a class="external text" href="https://ast.wikipedia.org/wiki/Llei_de_Coulomb#Equation_1">1</a></span>) ente (<span id="Eqnref_2" class="plainlinks neverexpand"><a class="external text" href="https://ast.wikipedia.org/wiki/Llei_de_Coulomb#Equation_2">2</a></span>) miembru a miembru, llógrase: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sin \theta _{1}}{\cos \theta _{1}}}={\frac {F_{1}}{mg}}\Rightarrow F_{1}=mg\tan \theta _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mi>m</mi> <mi>g</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">⇒</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin \theta _{1}}{\cos \theta _{1}}}={\frac {F_{1}}{mg}}\Rightarrow F_{1}=mg\tan \theta _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06847ced1b162ba3402e932517b5318c68e8363a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.266ex; height:5.843ex;" alt="{\displaystyle {\frac {\sin \theta _{1}}{\cos \theta _{1}}}={\frac {F_{1}}{mg}}\Rightarrow F_{1}=mg\tan \theta _{1}}"></span> </p> </blockquote> <p>Siendo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e16ae345a1cf1fbc516df2ed79e09d7efea58cac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.024ex; height:2.509ex;" alt="{\displaystyle L_{1}\,\!}"></span> la separación d'equilibriu ente les esferes cargaes, la fuercia <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_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e5c87f7528c540268ceddba9924ad0252d0280" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{1}\,\!}"></span> de repulsión ente elles, vale, acordies cola llei de Coulomb <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 \scriptstyle F_{1}=q^{2}/(4\pi \varepsilon _{0}L_{1}^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle F_{1}=q^{2}/(4\pi \varepsilon _{0}L_{1}^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2882dd6b1e65ae9f94764ebc353ac920a6fd2ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.176ex; height:2.509ex;" alt="{\displaystyle \scriptstyle F_{1}=q^{2}/(4\pi \varepsilon _{0}L_{1}^{2})}"></span> y, poro, cumplir la siguiente igualdá: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="referencia">(<cite id="Equation_3"><a href="#Eqnref_3">3</a></cite>)</span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}=mg\tan \theta _{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}=mg\tan \theta _{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17263cae336dc49a7cba6038bd1b4b7a3cdf9cdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-right: -0.387ex; width:21.026ex; height:6.676ex;" alt="{\displaystyle {\frac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}=mg\tan \theta _{1}\,\!}"></span> </p> </blockquote> <p>Al descargar una de les esferes y ponela, de siguío, en contautu cola esfera cargada, caúna d'elles adquier una carga <i>q</i>/2, nel equilibriu la so separación va ser <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{2}<L_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{2}<L_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2998bb980a6e6b5e247b5fd77b790bda7c6ae1f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:8.76ex; height:2.509ex;" alt="{\displaystyle L_{2}<L_{1}\,\!}"></span> y la fuercia de repulsíón ente les mesmes va tar dada por: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{2}={\frac {{(q/2)}^{2}}{4\pi \varepsilon _{0}L_{2}^{2}}}={\frac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{2}={\frac {{(q/2)}^{2}}{4\pi \varepsilon _{0}L_{2}^{2}}}={\frac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/757e12609c047d481503a491ae752fec450c9c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-right: -0.387ex; width:25.344ex; height:7.009ex;" alt="{\displaystyle F_{2}={\frac {{(q/2)}^{2}}{4\pi \varepsilon _{0}L_{2}^{2}}}={\frac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\,\!}"></span> </p> </blockquote> <p>Por tar n'equilibriu, tal como se dedució más arriba: <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_{2}=mg.\tan \theta _{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mo>.</mo> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{2}=mg.\tan \theta _{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9996b6721e26ed2b55381591c6685e40c0ff6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:16.116ex; height:2.509ex;" alt="{\displaystyle F_{2}=mg.\tan \theta _{2}\,\!}"></span>. Y de manera similar llógrase: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="referencia">(<cite id="Equation_4"><a href="#Eqnref_4">4</a></cite>)</span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\frac {q^{2}}{4}}{4\pi \varepsilon _{0}L_{2}^{2}}}=mg.\tan \theta _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>4</mn> </mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mo>.</mo> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\frac {q^{2}}{4}}{4\pi \varepsilon _{0}L_{2}^{2}}}=mg.\tan \theta _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/356c980f962be38cefb1c465fdddf7ad4cc64548" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:21.286ex; height:8.176ex;" alt="{\displaystyle {\frac {\frac {q^{2}}{4}}{4\pi \varepsilon _{0}L_{2}^{2}}}=mg.\tan \theta _{2}}"></span> </p> </blockquote> <p>Estremando (<span id="Eqnref_3" class="plainlinks neverexpand"><a class="external text" href="https://ast.wikipedia.org/wiki/Llei_de_Coulomb#Equation_3">3</a></span>) ente (<span id="Eqnref_4" class="plainlinks neverexpand"><a class="external text" href="https://ast.wikipedia.org/wiki/Llei_de_Coulomb#Equation_4">4</a></span>), miembru a miembru, llegar a la siguiente igualdá: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="referencia">(<cite id="Equation_5"><a href="#Eqnref_5">5</a></cite>)</span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\left({\cfrac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}\right)}{\left({\cfrac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\right)}}={\frac {mg\tan \theta _{1}}{mg\tan \theta _{2}}}\Longrightarrow 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}={\frac {\tan \theta _{1}}{\tan \theta _{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mi>g</mi> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>m</mi> <mi>g</mi> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo stretchy="false">⟹</mo> <mn>4</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\left({\cfrac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}\right)}{\left({\cfrac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\right)}}={\frac {mg\tan \theta _{1}}{mg\tan \theta _{2}}}\Longrightarrow 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}={\frac {\tan \theta _{1}}{\tan \theta _{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/242848b152be0a1364751f39f79a492da608da79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:50.025ex; height:15.843ex;" alt="{\displaystyle {\frac {\left({\cfrac {q^{2}}{4\pi \varepsilon _{0}L_{1}^{2}}}\right)}{\left({\cfrac {q^{2}/4}{4\pi \varepsilon _{0}L_{2}^{2}}}\right)}}={\frac {mg\tan \theta _{1}}{mg\tan \theta _{2}}}\Longrightarrow 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}={\frac {\tan \theta _{1}}{\tan \theta _{2}}}}"></span> </p> </blockquote> <p>Midiendo los ángulos <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 \theta _{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta _{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7df43ebc350e759712600b3a099792c4e58a77f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.532ex; height:2.509ex;" alt="{\displaystyle \theta _{1}\,\!}"></span> y <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 \theta _{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta _{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/992d9999222a99e674ae7de7f4d4b5180d8b66d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.532ex; height:2.509ex;" alt="{\displaystyle \theta _{2}\,\!}"></span> y les separaciones ente les cargues <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{1}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{1}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e16ae345a1cf1fbc516df2ed79e09d7efea58cac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.024ex; height:2.509ex;" alt="{\displaystyle L_{1}\,\!}"></span> y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9059b4ea2f2d14c8f3ae63ca977ece69115ef3be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.024ex; height:2.509ex;" alt="{\displaystyle L_{2}\,\!}"></span> ye posible verificar que la igualdá cumplir dientro del error esperimental. Na práutica, los ángulos pueden resultar difíciles de midir, asina que si'l llargor de los filos que sostienen les esferes son lo suficientemente llargos, los ángulos van resultar lo bastante pequeños como pa faer el siguiente aproximamientu: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \theta \approx \sin \theta ={\frac {\frac {L}{2}}{l}}={\frac {L}{2l}}\Longrightarrow {\frac {\tan \theta _{1}}{\tan \theta _{2}}}\approx {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>θ</mi> <mo>≈</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <mi>L</mi> <mn>2</mn> </mfrac> <mi>l</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <mrow> <mn>2</mn> <mi>l</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">⟹</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> </mfrac> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> </mfrac> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \theta \approx \sin \theta ={\frac {\frac {L}{2}}{l}}={\frac {L}{2l}}\Longrightarrow {\frac {\tan \theta _{1}}{\tan \theta _{2}}}\approx {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81800268185d4633825566776a69433a8b176d3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:42.494ex; height:8.843ex;" alt="{\displaystyle \tan \theta \approx \sin \theta ={\frac {\frac {L}{2}}{l}}={\frac {L}{2l}}\Longrightarrow {\frac {\tan \theta _{1}}{\tan \theta _{2}}}\approx {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}}"></span> </p> </blockquote> <p>Con esti aproximamientu, la rellación (<span id="Eqnref_5" class="plainlinks neverexpand"><a class="external text" href="https://ast.wikipedia.org/wiki/Llei_de_Coulomb#Equation_5">5</a></span>) tresformar n'otra muncho más simple: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> </mfrac> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> </mfrac> </mfrac> </mrow> <mo>≈</mo> <mn>4</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">⟹</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/637e299b640f36d72e67ec8d5d8460e849e4fd7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; margin-right: -0.387ex; width:20.67ex; height:8.843ex;" alt="{\displaystyle {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow \,\!}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {L_{1}}{L_{2}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow {\frac {L_{1}}{L_{2}}}\approx {\sqrt[{3}]{4}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mn>4</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">⟹</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {L_{1}}{L_{2}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow {\frac {L_{1}}{L_{2}}}\approx {\sqrt[{3}]{4}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c9166e7d5f120fd7a63a5c035838dbe36df9dcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-right: -0.387ex; width:30.836ex; height:6.509ex;" alt="{\displaystyle {\frac {L_{1}}{L_{2}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Longrightarrow {\frac {L_{1}}{L_{2}}}\approx {\sqrt[{3}]{4}}\,\!}"></span> </p> </blockquote> <p>D'esta forma, la verificación amenorgar a midir la separación ente cargues y comprobar que'l so cociente averar al valor indicáu. </p> <div class="mw-heading mw-heading2"><h2 id="Comparanza_ente_la_Llei_de_Coulomb_y_la_llei_de_gravitación_universal"><span id="Comparanza_ente_la_Llei_de_Coulomb_y_la_llei_de_gravitaci.C3.B3n_universal"></span>Comparanza ente la Llei de Coulomb y la llei de gravitación universal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=7" title="Editar seición: Comparanza ente la Llei de Coulomb y la llei de gravitación universal" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=7" title="Editar el código fuente de la sección: Comparanza ente la Llei de Coulomb y la llei de gravitación universal"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Esta comparanza ye relevante una y bones dambes lleis dicten el comportamientu de dos de les fuercies fundamentales de la naturaleza por aciu espresiones matemátiques que la so semeyanza ye bultable. </p><p>La <a href="/w/index.php?title=Llei_de_la_gravitaci%C3%B3n_universal&action=edit&redlink=1" class="new" title="Llei de la gravitación universal (la páxina nun esiste)">llei de la gravitación universal</a> establez que la fuercia d'atraición ente dos mases ye direutamente proporcional al productu de les mesmes ya inversamente proporcional al cuadráu de la distancia que les dixebra. Espresándolo matemáticamente: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</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> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd1fa02ed85cbd9a6ae8291651c3c55e859aa52d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.078ex; height:5.009ex;" alt="{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\,}"></span> </p> </blockquote> <p>Siendo: </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 G=6,67\cdot 10^{-11}\ {\text{N}}\cdot {\text{m}}^{2}\cdot {\text{kg}}^{-2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <mn>6</mn> <mo>,</mo> <mn>67</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>N</mtext> </mrow> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>kg</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G=6,67\cdot 10^{-11}\ {\text{N}}\cdot {\text{m}}^{2}\cdot {\text{kg}}^{-2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af24d03a8899e941dfb24d7bc035babf6f9b2fb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:30.387ex; height:3.009ex;" alt="{\displaystyle G=6,67\cdot 10^{-11}\ {\text{N}}\cdot {\text{m}}^{2}\cdot {\text{kg}}^{-2}\,}"></span> la <a href="/wiki/Constante_de_gravitaci%C3%B3n_universal" title="Constante de gravitación universal">constante de gravitación universal</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 m_{1},\ m_{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mtext> </mtext> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{1},\ m_{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449b418cb4c2b619125ccc22864f0fd19f980f55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.191ex; height:2.009ex;" alt="{\displaystyle m_{1},\ m_{2}\,}"></span> les mases de los cuerpos en cuestión y :<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 r\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f08ce4d4c86c5b43f36c8435fb598da6471047c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,}"></span></dd></dl> <p>la distancia ente los centros de les mases. A pesar del chocante paecíu nes espresiones de dambes lleis atopen dos estremes importantes. La primera ye que nel casu de la gravedá nun se pudieron reparar mases de distintu signu como asocede nel casu de les cargues llétriques, y la fuercia ente mases siempres ye curiosa. La segunda tien que ver colos órdenes de magnitú de la fuercia de gravedá y de la fuercia llétrico. Pa esclarialo vamos analizar como actúen dambes ente un protón y un electrón nel átomu d'hidróxenu. La separación permediu ente l'electrón y el protón ye de 5,3·10<sup>-11</sup> <a href="/wiki/Metru" title="Metru">m</a>. La carga del electrón y la del protón valen <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 y^{-}=-1,6\times 10^{-19}C\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mi>C</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y^{-}=-1,6\times 10^{-19}C\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5374e441467235abc61f2c8a8ec53de92c992f1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:21.41ex; height:3.009ex;" alt="{\displaystyle y^{-}=-1,6\times 10^{-19}C\,\!}"></span> y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p^{+}=1,6\times 10^{-19}C\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mi>C</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{+}=1,6\times 10^{-19}C\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a12b56953f41c55aa365c36bc9ef98b332a74bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; margin-right: -0.387ex; width:19.7ex; height:3.009ex;" alt="{\displaystyle p^{+}=1,6\times 10^{-19}C\,\!}"></span> respeutivamente y les sos mases son <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 m_{y^{-}}=9,11\times 10^{-31}kg\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> </msub> <mo>=</mo> <mn>9</mn> <mo>,</mo> <mn>11</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>31</mn> </mrow> </msup> <mi>k</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{y^{-}}=9,11\times 10^{-31}kg\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eef6b7d0cef66cc78c4d96f322c4232c66573ff3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:22.95ex; height:3.343ex;" alt="{\displaystyle m_{y^{-}}=9,11\times 10^{-31}kg\,\!}"></span> y <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 m_{p^{+}}=1,67\times 10^{-27}kg\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>27</mn> </mrow> </msup> <mi>k</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{p^{+}}=1,67\times 10^{-27}kg\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77960e9949c73aeb6468245d0c5db67a6dca771e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:22.956ex; height:3.343ex;" alt="{\displaystyle m_{p^{+}}=1,67\times 10^{-27}kg\,\!}"></span>. Sustituyendo los datos: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <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_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {Nm^{2}}{C^{2}}}{\frac {|-1,6\times 10^{-19}C|\times |1,6\times 10^{-19}C|}{5,3\times 10^{-11}m^{2}}}=8,2\times 10^{-8}N\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mi>κ</mi> <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> <mo>=</mo> <mn>8</mn> <mo>,</mo> <mn>99</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>1</mn> <mo>,</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mn>5</mn> <mo>,</mo> <mn>3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>8</mn> <mo>,</mo> <mn>2</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>8</mn> </mrow> </msup> <mi>N</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {Nm^{2}}{C^{2}}}{\frac {|-1,6\times 10^{-19}C|\times |1,6\times 10^{-19}C|}{5,3\times 10^{-11}m^{2}}}=8,2\times 10^{-8}N\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e8a5a494e014f90dc50c6b73bf6fcb59eabd4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-right: -0.387ex; width:84.672ex; height:6.843ex;" alt="{\displaystyle F_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {Nm^{2}}{C^{2}}}{\frac {|-1,6\times 10^{-19}C|\times |1,6\times 10^{-19}C|}{5,3\times 10^{-11}m^{2}}}=8,2\times 10^{-8}N\,\!}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{G}=G{\frac {m_{1}m_{2}}{r^{2}}}=6,67\times 10^{-11}{\frac {Nm^{2}}{kg^{2}}}{\frac {9,11\times 10^{-31}kg\times 1,67\times 10^{-27}kg}{5,3\times 10^{-11}m^{2}}}=3,6\times 10^{-47}N\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</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> <mo>=</mo> <mn>6</mn> <mo>,</mo> <mn>67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>k</mi> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>9</mn> <mo>,</mo> <mn>11</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>31</mn> </mrow> </msup> <mi>k</mi> <mi>g</mi> <mo>×</mo> <mn>1</mn> <mo>,</mo> <mn>67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>27</mn> </mrow> </msup> <mi>k</mi> <mi>g</mi> </mrow> <mrow> <mn>5</mn> <mo>,</mo> <mn>3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>47</mn> </mrow> </msup> <mi>N</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{G}=G{\frac {m_{1}m_{2}}{r^{2}}}=6,67\times 10^{-11}{\frac {Nm^{2}}{kg^{2}}}{\frac {9,11\times 10^{-31}kg\times 1,67\times 10^{-27}kg}{5,3\times 10^{-11}m^{2}}}=3,6\times 10^{-47}N\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/783cfb22eedd8d0548b0753029153c2031f08803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-right: -0.387ex; width:88.145ex; height:6.843ex;" alt="{\displaystyle F_{G}=G{\frac {m_{1}m_{2}}{r^{2}}}=6,67\times 10^{-11}{\frac {Nm^{2}}{kg^{2}}}{\frac {9,11\times 10^{-31}kg\times 1,67\times 10^{-27}kg}{5,3\times 10^{-11}m^{2}}}=3,6\times 10^{-47}N\,\!}"></span>.</dd></dl> </blockquote> <p>Al comparar resultancies reparar que la fuercia llétrico ye d'unos 39 órdenes de magnitú cimera a encomalo gravitacional. Lo qu'esto representa pue ser ilustráu por aciu un exemplu bien llamativu. 1 <a href="/wiki/Coulomb" class="mw-redirect" title="Coulomb">C</a> equival a la carga que pasa en 1 <a href="/wiki/Segundu" title="Segundu">s</a> por cualesquier puntu d'un conductor pol que circula una corriente d'intensidá 1 <a href="/wiki/Amperiu" title="Amperiu">A</a> constante. En viviendes con tensiones de 220 <a href="/wiki/Voltiu" title="Voltiu">V</a><sub>rms</sub>, esto equival a un segundu d'una bombilla de 220 <a href="/wiki/Vatiu" title="Vatiu">W</a> (120 W pa les instalaciones doméstiques de 120 V<sub>rms</sub>). </p><p>Si fuera posible concentrar la mentada carga en dos puntos con una separación de 1 metru, la fuercia d'interacción sería: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090"><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {{\text{Nm}}^{2}}{{\text{C}}^{2}}}{\frac {1\ {\text{C}}\times 1\ {\text{C}}}{{1\ {\text{m}}}^{2}}}=8,99\times 10^{9}\ {\text{N}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mi>κ</mi> <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> <mo>=</mo> <mn>8</mn> <mo>,</mo> <mn>99</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>Nm</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> <mo>×</mo> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>8</mn> <mo>,</mo> <mn>99</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>N</mtext> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {{\text{Nm}}^{2}}{{\text{C}}^{2}}}{\frac {1\ {\text{C}}\times 1\ {\text{C}}}{{1\ {\text{m}}}^{2}}}=8,99\times 10^{9}\ {\text{N}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0d63966467346a62fe0610556b94aa5bfe4fbef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-right: -0.387ex; width:58.915ex; height:6.343ex;" alt="{\displaystyle F_{Y}=\kappa {\frac {q_{1}q_{2}}{r^{2}}}=8,99\times 10^{9}{\frac {{\text{Nm}}^{2}}{{\text{C}}^{2}}}{\frac {1\ {\text{C}}\times 1\ {\text{C}}}{{1\ {\text{m}}}^{2}}}=8,99\times 10^{9}\ {\text{N}}\,\!}"></span> </p> </blockquote> <p>esto ye, 916 millones de <a href="/wiki/Quilopondiu" title="Quilopondiu">quilopondios</a>, o'l pesu d'una masa de casi un millón de <a href="/wiki/Tonelada" title="Tonelada">tonelaes</a> (un teragramu). Si tales cargues pudieren concentrase de la forma indicada más arriba, alloñar so la influencia d'esta enorme fuercia. Si d'esta hipotética disposición de cargues resulten fuercies tan enormes, ¿por qué nun se reparen esplegues dramáticos debíos a les fuercies llétriques? La respuesta xeneral ye que nun puntu dau de cualquier conductor nunca hai demasiáu alloñamientu de la neutralidá llétrica. La naturaleza nunca atropa un Coulomb de carga nun puntu. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_tamién"><span id="Ver_tami.C3.A9n"></span>Ver tamién</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=8" title="Editar seición: Ver tamién" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=8" title="Editar el código fuente de la sección: Ver tamién"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Carga_ll%C3%A9trica" title="Carga llétrica">Carga llétrica</a></li> <li><a href="/w/index.php?title=Campu_ll%C3%A9trico&action=edit&redlink=1" class="new" title="Campu llétrico (la páxina nun esiste)">Campu llétrico</a></li> <li><a href="/wiki/Lletricid%C3%A1" title="Lletricidá">Lletricidá</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencies">Referencies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=9" title="Editar seición: Referencies" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=9" title="Editar el código fuente de la sección: Referencies"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3503771">@media only screen and (max-width:600px){.mw-parser-output .llistaref{column-count:1!important}}</style><div class="llistaref" style="list-style-type: decimal;"></div> <div class="mw-heading mw-heading3"><h3 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Llei_de_Coulomb&veaction=edit&section=10" title="Editar seición: Bibliografía" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Llei_de_Coulomb&action=edit&section=10" title="Editar el código fuente de la sección: Bibliografía"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite style="font-style:normal" id="Referencia-Coulomb-1788">Coulomb, Charles Augustin (1788).  Imprimerie Royale: <i>Histoire de l'Académie Royale des Sciences</i>.</cite></li> <li><cite style="font-style:normal">Griffiths, David J. (1998).  Prentice Hall: <i>Introduction to Electrodynamics</i>. <a href="/wiki/Especial:FuentesDeLibros/0-13-805326-X" title="Especial:FuentesDeLibros/0-13-805326-X">ISBN 0-13-805326-X</a>.</cite></li> <li><cite style="font-style:normal">Tipler, Paul A.;  Mosca, Gene (2008)  W. H. Freeman and Company: <i>Physics for Scientists and Engineers</i>. <a href="/wiki/Especial:FuentesDeLibros/0-7167-8964-7" title="Especial:FuentesDeLibros/0-7167-8964-7">ISBN 0-7167-8964-7</a>.</cite></li> <li><cite style="font-style:normal">Young, Hugh D.;  Freedman, Roger A. (2010)  Addison-Wesley (Pearson): <i>Sears and Zemansky's University Physics : With Modern Physics</i>. <a href="/wiki/Especial:FuentesDeLibros/978-0-321-69686-1" title="Especial:FuentesDeLibros/978-0-321-69686-1">ISBN 978-0-321-69686-1</a>.</cite></li></ul> <p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Sacáu de «<a dir="ltr" href="https://ast.wikipedia.org/w/index.php?title=Llei_de_Coulomb&oldid=4219308">https://ast.wikipedia.org/w/index.php?title=Llei_de_Coulomb&oldid=4219308</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categor%C3%ADas" title="Especial:Categorías">Categoríes</a>: <ul><li><a href="/wiki/Categor%C3%ADa:Wikipedia:Art%C3%ADculos_con_plant%C3%ADes_de_notes_d%27encabezamientu_enllaciando_a_p%C3%A1xines_que_nun_esisten" title="Categoría:Wikipedia:Artículos con plantíes de notes d'encabezamientu enllaciando a páxines que nun esisten">Wikipedia:Artículos con plantíes de notes d'encabezamientu enllaciando a páxines que nun esisten</a></li><li><a href="/wiki/Categor%C3%ADa:Wikipedia:Revisar_traducci%C3%B3n" title="Categoría:Wikipedia:Revisar traducción">Wikipedia:Revisar traducción</a></li><li><a href="/wiki/Categor%C3%ADa:Lleis_electromagn%C3%A9tiques" title="Categoría:Lleis electromagnétiques">Lleis electromagnétiques</a></li><li><a href="/w/index.php?title=Categor%C3%ADa:Electrost%C3%A1tica&action=edit&redlink=1" class="new" title="Categoría:Electrostática (la páxina nun esiste)">Electrostática</a></li><li><a href="/wiki/Categor%C3%ADa:Ciencia_y_teunolox%C3%ADa_de_Francia" title="Categoría:Ciencia y teunoloxía de Francia">Ciencia y teunoloxía de Francia</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categoríes anubríes: <ul><li><a href="/wiki/Categor%C3%ADa:Wikipedia:Art%C3%ADculos_qu%27usen_ficha_ensin_datos_en_fileres" title="Categoría:Wikipedia:Artículos qu'usen ficha ensin datos en fileres">Wikipedia:Artículos qu'usen ficha ensin datos en fileres</a></li><li><a href="/wiki/Categor%C3%ADa:Wikipedia:Tradubot" title="Categoría:Wikipedia:Tradubot">Wikipedia:Tradubot</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> La última edición d'esta páxina foi'l 25 xnt 2024 a les 13:18.</li> <li id="footer-info-copyright">El testu ta disponible baxo la <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.es">Llicencia Creative Commons Reconocimientu/CompartirIgual 4.0</a>; puen aplicase términos adicionales. 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