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siden." > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Utseende" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Utseende</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb" class=""><span>Doner</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Opprett_konto&returnto=Magnet&returntoquery=veaction%3Dedit%26redirect%3Dno" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Logg_inn&returnto=Magnet&returntoquery=veaction%3Dedit%26redirect%3Dno" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o" class=""><span>Logg inn</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out user-links-collapsible-item" title="Flere alternativer" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personlig" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personlig</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukermeny" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb"><span>Doner</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Magnet&returntoquery=veaction%3Dedit%26redirect%3Dno" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Magnet&returntoquery=veaction%3Dedit%26redirect%3Dno" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</span></a></li> </ul> </div> </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="Nettsted"> <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="Innhold" 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">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Til toppen)</div> </a> </li> <li id="toc-Historie_-_magnet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historie_-_magnet"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historie - magnet</span> </div> </a> <button aria-controls="toc-Historie_-_magnet-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Historie - magnet</span> </button> <ul id="toc-Historie_-_magnet-sublist" class="vector-toc-list"> <li id="toc-Gilbert" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gilbert"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Gilbert</span> </div> </a> <ul id="toc-Gilbert-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coulomb" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coulomb"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Coulomb</span> </div> </a> <ul id="toc-Coulomb-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Materiale" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Materiale"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Materiale</span> </div> </a> <ul id="toc-Materiale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetisering" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Magnetisering"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Magnetisering</span> </div> </a> <ul id="toc-Magnetisering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetiske_felt" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Magnetiske_felt"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Magnetiske felt</span> </div> </a> <button aria-controls="toc-Magnetiske_felt-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Magnetiske felt</span> </button> <ul id="toc-Magnetiske_felt-sublist" class="vector-toc-list"> <li id="toc-Magnetens_indre" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Magnetens_indre"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Magnetens indre</span> </div> </a> <ul id="toc-Magnetens_indre-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beregning_av_indre_felt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beregning_av_indre_felt"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Beregning av indre felt</span> </div> </a> <ul id="toc-Beregning_av_indre_felt-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetisk_hysterese" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Magnetisk_hysterese"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Magnetisk hysterese</span> </div> </a> <ul id="toc-Magnetisk_hysterese-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Permanent_magnetisering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Permanent_magnetisering"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Permanent magnetisering</span> </div> </a> <ul id="toc-Permanent_magnetisering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Magnetiske_krefter" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Magnetiske_krefter"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Magnetiske krefter</span> </div> </a> <button aria-controls="toc-Magnetiske_krefter-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Magnetiske krefter</span> </button> <ul id="toc-Magnetiske_krefter-sublist" class="vector-toc-list"> <li id="toc-Dipol-dipol_kraft" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dipol-dipol_kraft"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Dipol-dipol kraft</span> </div> </a> <ul id="toc-Dipol-dipol_kraft-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maxwell-spenning" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maxwell-spenning"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Maxwell-spenning</span> </div> </a> <ul id="toc-Maxwell-spenning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Regneeksempel" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Regneeksempel"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Regneeksempel</span> </div> </a> <ul id="toc-Regneeksempel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetisk_feltenergi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Magnetisk_feltenergi"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Magnetisk feltenergi</span> </div> </a> <ul id="toc-Magnetisk_feltenergi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kjøleskapsmagnet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kjøleskapsmagnet"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Kjøleskapsmagnet</span> </div> </a> <ul id="toc-Kjøleskapsmagnet-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Se_også" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_også"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Se også</span> </div> </a> <ul id="toc-Se_også-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksterne_lenker" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksterne_lenker"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Eksterne lenker</span> </div> </a> <ul id="toc-Eksterne_lenker-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Innhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vis/skjul innholdsfortegnelsen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vis/skjul innholdsfortegnelsen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Magnet</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå til en artikkel på et annet språk. Tilgjengelig på 129 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-129" 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">129 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Magnet" title="Magnet – norsk nynorsk" lang="nn" hreflang="nn" data-title="Magnet" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Magnet" title="Magnet – dansk" lang="da" hreflang="da" data-title="Magnet" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Magnet" title="Magnet – svensk" lang="sv" hreflang="sv" data-title="Magnet" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Segull" title="Segull – islandsk" lang="is" hreflang="is" data-title="Segull" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Magneet" title="Magneet – afrikaans" lang="af" hreflang="af" data-title="Magneet" 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/Magnet" title="Magnet – sveitsertysk" lang="gsw" hreflang="gsw" data-title="Magnet" data-language-autonym="Alemannisch" data-language-local-name="sveitsertysk" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%98%E1%8C%8D%E1%8A%90%E1%8C%A2%E1%88%B5" title="መግነጢስ – amharisk" lang="am" hreflang="am" data-title="መግነጢስ" data-language-autonym="አማርኛ" data-language-local-name="amharisk" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%BA%D9%86%D8%A7%D8%B7%D9%8A%D8%B3" title="مغناطيس – arabisk" lang="ar" hreflang="ar" data-title="مغناطيس" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Im%C3%A1n" title="Imán – aragonsk" lang="an" hreflang="an" data-title="Imán" data-language-autonym="Aragonés" data-language-local-name="aragonsk" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%9A%E0%A7%81%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%95" title="চুম্বক – assamesisk" lang="as" hreflang="as" data-title="চুম্বক" data-language-autonym="অসমীয়া" data-language-local-name="assamesisk" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Im%C3%A1n" title="Imán – asturisk" lang="ast" hreflang="ast" data-title="Imán" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Achkatasiri" title="Achkatasiri – aymara" lang="ay" hreflang="ay" data-title="Achkatasiri" data-language-autonym="Aymar aru" data-language-local-name="aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Maqnit" title="Maqnit – aserbajdsjansk" lang="az" hreflang="az" data-title="Maqnit" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AF%D9%85%DB%8C%D8%B1%D9%82%D8%A7%D9%BE%D8%A7%D9%86" title="دمیرقاپان – søraserbajdsjansk" lang="azb" hreflang="azb" data-title="دمیرقاپان" data-language-autonym="تۆرکجه" data-language-local-name="søraserbajdsjansk" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A7%81%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%95" title="চুম্বক – bengali" lang="bn" hreflang="bn" data-title="চুম্বক" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Khip-chio%CC%8Dh" title="Khip-chio̍h – minnan" lang="nan" hreflang="nan" data-title="Khip-chio̍h" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – basjkirsk" lang="ba" hreflang="ba" data-title="Магнит" data-language-autonym="Башҡортса" data-language-local-name="basjkirsk" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D1%96%D1%82" title="Магніт – belarusisk" lang="be" hreflang="be" data-title="Магніт" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D1%96%D1%82" title="Магніт – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Магніт" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – bulgarsk" lang="bg" hreflang="bg" data-title="Магнит" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Magnet" title="Magnet – bairisk" lang="bar" hreflang="bar" data-title="Magnet" data-language-autonym="Boarisch" data-language-local-name="bairisk" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Magnet" title="Magnet – bosnisk" lang="bs" hreflang="bs" data-title="Magnet" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A1%D1%83%D1%80%D0%B0%D0%BD%D0%B7%D0%B0%D0%BD" title="Суранзан – burjatisk" lang="bxr" hreflang="bxr" data-title="Суранзан" data-language-autonym="Буряад" data-language-local-name="burjatisk" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Imant" title="Imant – katalansk" lang="ca" hreflang="ca" data-title="Imant" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Магнит" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Magnet" title="Magnet – tsjekkisk" lang="cs" hreflang="cs" data-title="Magnet" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Magnet" title="Magnet – walisisk" lang="cy" hreflang="cy" data-title="Magnet" data-language-autonym="Cymraeg" data-language-local-name="walisisk" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%A9" title="هندة – marokkansk-arabisk" lang="ary" hreflang="ary" data-title="هندة" data-language-autonym="الدارجة" data-language-local-name="marokkansk-arabisk" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Magnet" title="Magnet – tysk" lang="de" hreflang="de" data-title="Magnet" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Magnet" title="Magnet – estisk" lang="et" hreflang="et" data-title="Magnet" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B3%CE%BD%CE%AE%CF%84%CE%B7%CF%82" title="Μαγνήτης – gresk" lang="el" hreflang="el" data-title="Μαγνήτης" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Magnet" title="Magnet – engelsk" lang="en" hreflang="en" data-title="Magnet" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Im%C3%A1n" title="Imán – spansk" lang="es" hreflang="es" data-title="Imán" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Magneto" title="Magneto – esperanto" lang="eo" hreflang="eo" data-title="Magneto" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Iman" title="Iman – baskisk" lang="eu" hreflang="eu" data-title="Iman" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%87%D9%86%D8%B1%D8%A8%D8%A7" title="آهنربا – persisk" lang="fa" hreflang="fa" data-title="آهنربا" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Chumbak_loha" title="Chumbak loha – fijiansk hindi" lang="hif" hreflang="hif" data-title="Chumbak loha" data-language-autonym="Fiji Hindi" data-language-local-name="fijiansk hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Aimant" title="Aimant – fransk" lang="fr" hreflang="fr" data-title="Aimant" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Maighn%C3%A9ad" title="Maighnéad – irsk" lang="ga" hreflang="ga" data-title="Maighnéad" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Im%C3%A1n" title="Imán – galisisk" lang="gl" hreflang="gl" data-title="Imán" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9E%90%EC%84%9D" title="자석 – koreansk" lang="ko" hreflang="ko" data-title="자석" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A3%D5%B6%D5%AB%D5%BD" title="Մագնիս – armensk" lang="hy" hreflang="hy" data-title="Մագնիս" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95" title="चुम्बक – hindi" lang="hi" hreflang="hi" data-title="चुम्बक" 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/Magnet" title="Magnet – kroatisk" lang="hr" hreflang="hr" data-title="Magnet" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Magneto" title="Magneto – ido" lang="io" hreflang="io" data-title="Magneto" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Magnet" title="Magnet – indonesisk" lang="id" hreflang="id" data-title="Magnet" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Magnete" title="Magnete – interlingua" lang="ia" hreflang="ia" data-title="Magnete" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Magnete" title="Magnete – interlingue" lang="ie" hreflang="ie" data-title="Magnete" data-language-autonym="Interlingue" data-language-local-name="interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-ik mw-list-item"><a href="https://ik.wikipedia.org/wiki/Nipitchak" title="Nipitchak – inupiak" lang="ik" hreflang="ik" data-title="Nipitchak" data-language-autonym="Iñupiatun" data-language-local-name="inupiak" class="interlanguage-link-target"><span>Iñupiatun</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Magnete" title="Magnete – italiensk" lang="it" hreflang="it" data-title="Magnete" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%92%D7%A0%D7%98" title="מגנט – hebraisk" lang="he" hreflang="he" data-title="מגנט" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Magn%C3%A8t" title="Magnèt – javanesisk" lang="jv" hreflang="jv" data-title="Magnèt" data-language-autonym="Jawa" data-language-local-name="javanesisk" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%AF%E0%B2%B8%E0%B3%8D%E0%B2%95%E0%B2%BE%E0%B2%82%E0%B2%A4" title="ಅಯಸ್ಕಾಂತ – kannada" lang="kn" hreflang="kn" data-title="ಅಯಸ್ಕಾಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%92%E1%83%9C%E1%83%98%E1%83%A2%E1%83%98" title="მაგნიტი – georgisk" lang="ka" hreflang="ka" data-title="მაგნიტი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D9%85%D8%A0%D9%82%D9%86%D8%A7%D8%B7%DB%8C%D9%96%D8%B3" title="مؠقناطیٖس – kasjmiri" lang="ks" hreflang="ks" data-title="مؠقناطیٖس" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="kasjmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – kasakhisk" lang="kk" hreflang="kk" data-title="Магнит" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Sumaku" title="Sumaku – swahili" lang="sw" hreflang="sw" data-title="Sumaku" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Ki%C5%9Fanek" title="Kişanek – kurdisk" lang="ku" hreflang="ku" data-title="Kişanek" data-language-autonym="Kurdî" data-language-local-name="kurdisk" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – kirgisisk" lang="ky" hreflang="ky" data-title="Магнит" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Magnes" title="Magnes – latin" lang="la" hreflang="la" data-title="Magnes" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Magn%C4%93ts" title="Magnēts – latvisk" lang="lv" hreflang="lv" data-title="Magnēts" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Magnetas" title="Magnetas – litauisk" lang="lt" hreflang="lt" data-title="Magnetas" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Magneet" title="Magneet – limburgsk" lang="li" hreflang="li" data-title="Magneet" data-language-autonym="Limburgs" data-language-local-name="limburgsk" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Magnet" title="Magnet – lombardisk" lang="lmo" hreflang="lmo" data-title="Magnet" data-language-autonym="Lombard" data-language-local-name="lombardisk" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%81lland%C3%B3_m%C3%A1gnes" title="Állandó mágnes – ungarsk" lang="hu" hreflang="hu" data-title="Állandó mágnes" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82" title="Магнет – makedonsk" lang="mk" hreflang="mk" data-title="Магнет" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="കാന്തം – malayalam" lang="ml" hreflang="ml" data-title="കാന്തം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%82%E0%A4%AC%E0%A4%95" title="चुंबक – marathi" lang="mr" hreflang="mr" data-title="चुंबक" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%AD%E1%83%90%E1%83%AD%E1%83%9B%E1%83%94%E1%83%9C%E1%83%A2%E1%83%98" title="ჭაჭმენტი – mingrelsk" lang="xmf" hreflang="xmf" data-title="ჭაჭმენტი" data-language-autonym="მარგალური" data-language-local-name="mingrelsk" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Besi_berani" title="Besi berani – malayisk" lang="ms" hreflang="ms" data-title="Besi berani" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Basi_barani" title="Basi barani – minangkabau" lang="min" hreflang="min" data-title="Basi barani" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/C%E1%B9%B3%CC%80-ti%C3%A9k" title="Cṳ̀-tiék – mindong" lang="cdo" hreflang="cdo" data-title="Cṳ̀-tiék" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A1%D0%BE%D1%80%D0%BE%D0%BD%D0%B7" title="Соронз – mongolsk" lang="mn" hreflang="mn" data-title="Соронз" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%B6%E1%80%9C%E1%80%AD%E1%80%AF%E1%80%80%E1%80%BA" title="သံလိုက် – burmesisk" lang="my" hreflang="my" data-title="သံလိုက်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmesisk" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Magneet" title="Magneet – nederlandsk" lang="nl" hreflang="nl" data-title="Magneet" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95" title="चुम्बक – nepali" lang="ne" hreflang="ne" data-title="चुम्बक" data-language-autonym="नेपाली" data-language-local-name="nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95" title="चुम्बक – newari" lang="new" hreflang="new" data-title="चुम्बक" data-language-autonym="नेपाल भाषा" data-language-local-name="newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%A3%81%E7%9F%B3" title="磁石 – japansk" lang="ja" hreflang="ja" data-title="磁石" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Magneet" title="Magneet – nordfrisisk" lang="frr" hreflang="frr" data-title="Magneet" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisisk" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Asimant" title="Asimant – oksitansk" lang="oc" hreflang="oc" data-title="Asimant" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Maagneetii(loobilaa)" title="Maagneetii(loobilaa) – oromo" lang="om" hreflang="om" data-title="Maagneetii(loobilaa)" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Magnit" title="Magnit – usbekisk" lang="uz" hreflang="uz" data-title="Magnit" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9A%E0%A9%81%E0%A9%B0%E0%A8%AC%E0%A8%95" title="ਚੁੰਬਕ – panjabi" lang="pa" hreflang="pa" data-title="ਚੁੰਬਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%85%D9%82%DD%A8%D8%A7%D8%B7%DB%8C%D8%B3" title="مقݨاطیس – vestpunjabi" lang="pnb" hreflang="pnb" data-title="مقݨاطیس" data-language-autonym="پنجابی" data-language-local-name="vestpunjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D9%82%D9%86%D8%A7%D8%B7%D9%8A%D8%B3" title="مقناطيس – pashto" lang="ps" hreflang="ps" data-title="مقناطيس" data-language-autonym="پښتو" data-language-local-name="pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Magnete" title="Magnete – piemontesisk" lang="pms" hreflang="pms" data-title="Magnete" data-language-autonym="Piemontèis" data-language-local-name="piemontesisk" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Magneet" title="Magneet – nedertysk" lang="nds" hreflang="nds" data-title="Magneet" data-language-autonym="Plattdüütsch" data-language-local-name="nedertysk" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Magnes" title="Magnes – polsk" lang="pl" hreflang="pl" data-title="Magnes" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%8Dman" title="Íman – portugisisk" lang="pt" hreflang="pt" data-title="Íman" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ksh mw-list-item"><a href="https://ksh.wikipedia.org/wiki/Mangneet" title="Mangneet – kølnsk" lang="ksh" hreflang="ksh" data-title="Mangneet" data-language-autonym="Ripoarisch" data-language-local-name="kølnsk" class="interlanguage-link-target"><span>Ripoarisch</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Magnet" title="Magnet – rumensk" lang="ro" hreflang="ro" data-title="Magnet" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/K%27askachimuq" title="K'askachimuq – quechua" lang="qu" hreflang="qu" data-title="K'askachimuq" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9C%D0%B0%D2%91%D0%BD%D0%B5%D1%82" title="Маґнет – rusinsk" lang="rue" hreflang="rue" data-title="Маґнет" data-language-autonym="Русиньскый" data-language-local-name="rusinsk" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B8%D1%82" title="Магнит – russisk" lang="ru" hreflang="ru" data-title="Магнит" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Magnet" title="Magnet – skotsk" lang="sco" hreflang="sco" data-title="Magnet" data-language-autonym="Scots" data-language-local-name="skotsk" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Magneti" title="Magneti – albansk" lang="sq" hreflang="sq" data-title="Magneti" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Calamita" title="Calamita – siciliansk" lang="scn" hreflang="scn" data-title="Calamita" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Magnet" title="Magnet – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Magnet" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%DA%86%D9%82%D9%85%D9%82" title="چقمق – sindhi" lang="sd" hreflang="sd" data-title="چقمق" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Magnet" title="Magnet – slovakisk" lang="sk" hreflang="sk" data-title="Magnet" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Magnet" title="Magnet – slovensk" lang="sl" hreflang="sl" data-title="Magnet" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%D9%88%DA%AF%D9%86%D8%A7%D8%AA%DB%8C%D8%B3" title="موگناتیس – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="موگناتیس" data-language-autonym="کوردی" data-language-local-name="sentralkurdisk" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D0%B5%D1%82" title="Магнет – serbisk" lang="sr" hreflang="sr" data-title="Магнет" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Magnet" title="Magnet – serbokroatisk" lang="sh" hreflang="sh" data-title="Magnet" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Magn%C3%A9t" title="Magnét – sundanesisk" lang="su" hreflang="su" data-title="Magnét" data-language-autonym="Sunda" data-language-local-name="sundanesisk" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Magneetti" title="Magneetti – finsk" lang="fi" hreflang="fi" data-title="Magneetti" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Batubalani" title="Batubalani – tagalog" lang="tl" hreflang="tl" data-title="Batubalani" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%BE%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="காந்தம் – tamil" lang="ta" hreflang="ta" data-title="காந்தம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%85%E0%B0%AF%E0%B0%B8%E0%B1%8D%E0%B0%95%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B0%82" title="అయస్కాంతం – telugu" lang="te" hreflang="te" data-title="అయస్కాంతం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B9%87%E0%B8%81" title="แม่เหล็ก – thai" lang="th" hreflang="th" data-title="แม่เหล็ก" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9E%D2%B3%D0%B0%D0%BD%D1%80%D0%B0%D0%B1%D0%BE" title="Оҳанрабо – tadsjikisk" lang="tg" hreflang="tg" data-title="Оҳанрабо" data-language-autonym="Тоҷикӣ" data-language-local-name="tadsjikisk" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%85%E0%B2%AF%E0%B2%B8%E0%B3%8D%E0%B2%95%E0%B2%BE%E0%B2%82%E0%B2%A4" title="ಅಯಸ್ಕಾಂತ – tulu" lang="tcy" hreflang="tcy" data-title="ಅಯಸ್ಕಾಂತ" data-language-autonym="ತುಳು" data-language-local-name="tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/M%C4%B1knat%C4%B1s" title="Mıknatıs – tyrkisk" lang="tr" hreflang="tr" data-title="Mıknatıs" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%A1%D0%BE%D1%80%D1%83%D0%BD%D0%B7%D0%B0" title="Сорунза – tuvinsk" lang="tyv" hreflang="tyv" data-title="Сорунза" data-language-autonym="Тыва дыл" data-language-local-name="tuvinsk" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B3%D0%BD%D1%96%D1%82" title="Магніт – ukrainsk" lang="uk" hreflang="uk" data-title="Магніт" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%82%D9%86%D8%A7%D8%B7%DB%8C%D8%B3" title="مقناطیس – urdu" lang="ur" hreflang="ur" data-title="مقناطیس" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Magnit" title="Magnit – vepsisk" lang="vep" hreflang="vep" data-title="Magnit" data-language-autonym="Vepsän kel’" data-language-local-name="vepsisk" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nam_ch%C3%A2m" title="Nam châm – vietnamesisk" lang="vi" hreflang="vi" data-title="Nam châm" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Inmant" title="Inmant – vallonsk" lang="wa" hreflang="wa" data-title="Inmant" data-language-autonym="Walon" data-language-local-name="vallonsk" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Batubarani" title="Batubarani – waray-waray" lang="war" hreflang="war" data-title="Batubarani" data-language-autonym="Winaray" data-language-local-name="waray-waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Bijjaan" title="Bijjaan – wolof" lang="wo" hreflang="wo" data-title="Bijjaan" data-language-autonym="Wolof" data-language-local-name="wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%90%B8%E9%93%81%E7%9F%B3" title="吸铁石 – wu" lang="wuu" hreflang="wuu" data-title="吸铁石" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9E%D7%90%D7%92%D7%A0%D7%A2%D7%98" title="מאגנעט – jiddisk" lang="yi" hreflang="yi" data-title="מאגנעט" data-language-autonym="ייִדיש" data-language-local-name="jiddisk" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Gb%C3%A9ringb%C3%A9rin" title="Gbéringbérin – joruba" lang="yo" hreflang="yo" data-title="Gbéringbérin" data-language-autonym="Yorùbá" data-language-local-name="joruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%94%9D%E7%9F%B3" title="攝石 – kantonesisk" lang="yue" hreflang="yue" data-title="攝石" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Magnets" title="Magnets – samogitisk" lang="sgs" hreflang="sgs" data-title="Magnets" data-language-autonym="Žemaitėška" data-language-local-name="samogitisk" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A3%81%E9%90%B5" title="磁鐵 – kinesisk" lang="zh" hreflang="zh" data-title="磁鐵" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-bbc mw-list-item"><a href="https://bbc.wikipedia.org/wiki/Bosi_Barani" title="Bosi Barani – batak toba" lang="bbc" hreflang="bbc" data-title="Bosi Barani" data-language-autonym="Batak Toba" data-language-local-name="batak toba" class="interlanguage-link-target"><span>Batak Toba</span></a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/Bosi_Barani" title="Bosi Barani – Komering" lang="kge" hreflang="kge" data-title="Bosi Barani" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target"><span>Kumoring</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/Q11421#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</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="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Magnet" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskusjon:Magnet" rel="discussion" title="Diskusjon om innholdssiden [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Bytt språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">norsk bokmål</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visninger"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Magnet"><span>Les</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Magnet&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Magnet&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Magnet&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Verktøy" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Verktøy</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Magnet"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Magnet&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Magnet&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Magnet&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Magnet" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Magnet" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopedi</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nb" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:MagnetEZ.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/MagnetEZ.jpg/250px-MagnetEZ.jpg" decoding="async" width="250" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/MagnetEZ.jpg/375px-MagnetEZ.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/0/08/MagnetEZ.jpg 2x" data-file-width="470" data-file-height="480" /></a><figcaption>En «hesteskomagnet» laget av en spesiell jernlegering kalt <a href="/w/index.php?title=Alnico&action=edit&redlink=1" class="new" title="Alnico (ikke skrevet ennå)">Alnico</a>. Magneten har form som en hestesko slik at de to magnetiske polene er nær hverandre og skaper et sterkt <a href="/wiki/Magnetfelt" title="Magnetfelt">magnetfelt</a> som kan løfte et tungt jernstykke.</figcaption></figure> <p>En <b>magnet</b> er et objekt som omgir seg med et <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetisk felt</a>. Den kan være laget av et <a href="/wiki/Ferromagnetisme" title="Ferromagnetisme">ferromagnetisk</a> (eller <a href="/w/index.php?title=Ferrimagnetisk&action=edit&redlink=1" class="new" title="Ferrimagnetisk (ikke skrevet ennå)">ferrimagnetisk</a>) materiale slik at den har en permanent <a href="/wiki/Magnetisme" title="Magnetisme">magnetisering</a> eller den kan være en <a href="/wiki/Elektromagnet" title="Elektromagnet">elektromagnet</a> som er avhengig av en <a href="/wiki/Elektrisk_str%C3%B8m" title="Elektrisk strøm">elektrisk strømforsyning</a>. Fysiske fenomen forbundet med magneter omtales som <a href="/wiki/Magnetisme" title="Magnetisme">magnetisme</a> som igjen er forklart ved <a href="/wiki/Elektromagnetisme" title="Elektromagnetisme">elektromagnetisk teori</a>. </p><p>Magneter utnyttes i <a href="/wiki/Elektrisk_motor" title="Elektrisk motor">elektriske motorer</a>, <a href="/wiki/H%C3%B8yttaler" title="Høyttaler">høyttalere</a>, <a href="/wiki/Metalldetektor" title="Metalldetektor">metalldetektorer</a>, <a href="/wiki/Harddisk" title="Harddisk">harddisker</a>, <a href="/wiki/Lydb%C3%A5nd" class="mw-redirect" title="Lydbånd">lydbånd</a>/databånd, følere i <a href="/wiki/Tyverialarm" class="mw-redirect" title="Tyverialarm">tyverialarmer</a>, dørlukkere, <a href="/wiki/Teleslynge" title="Teleslynge">teleslynger</a> for <a href="/wiki/H%C3%B8reapparat" title="Høreapparat">høreapparater</a>, <a href="/wiki/Katodestr%C3%A5ler%C3%B8r" class="mw-redirect" title="Katodestrålerør">katodestrålerør</a>/TV-rør og <a href="/wiki/MRI" class="mw-redirect" title="MRI">MR</a>-maskiner (bildedannelse ved magnetisk resonans). I mange hjem kan magneter sees sittende fast på kjøleskapsdører. </p><p>Noen <a href="/wiki/Bergart" title="Bergart">steiner</a> har naturlige magnetfelt og var de første, permanente magneter. I dag kan magneter produseres industrielt. Navnet <i>magnet</i> kommer fra byen <a href="/wiki/Magnis%C3%ADa" class="mw-redirect" title="Magnisía">Magnisía</a> i <a href="/wiki/Hellas" title="Hellas">Hellas</a> hvor det i <a href="/wiki/Oldtid" class="mw-disambig" title="Oldtid">oldtiden</a> ble funnet det magnetiske <a href="/wiki/Mineral" title="Mineral">mineralet</a> <a href="/wiki/Magnetitt" title="Magnetitt">magnetitt</a> med den <a href="/wiki/Kjemisk_formel" title="Kjemisk formel">kjemiske formelen</a> Fe<sub>3</sub>O<sub>4</sub>. </p><p>Av slike materialer ble det tidlig lagt <a href="/wiki/Kompass" title="Kompass">kompass</a> hvor den bevegelig delen er en permanent magnet. Den retter seg inn langs <a href="/wiki/Jordens_magnetfelt" title="Jordens magnetfelt">Jordens magnetfelt</a>. På den måten sies den enden av magneten som peker mot Den magnetiske nordpolen å være en «nordpol» N for magneten, mens den andre enden kalles magnetens «sydpol» S. Man kan ikke isolere en enkelt N- eller S-pol. Slike magnetiske ladninger eller <a href="/wiki/Magnetisk_monopol" title="Magnetisk monopol">monopoler</a> finnes ikke. Derimot fremkommer magnetiske effekter fra <a href="/wiki/Elektrisk_str%C3%B8m" title="Elektrisk strøm">elektriske strømmer</a> som ble vist av <a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a>, <a href="/wiki/Amp%C3%A8re" class="mw-redirect" title="Ampère">Ampère</a> og formulert i <a href="/wiki/Biot-Savarts_lov" title="Biot-Savarts lov">Biot-Savarts lov</a>. </p><p>De detaljerte egenskapene til magnetiske materialer ble først forstått ved etableringen av moderne <a href="/wiki/Kvantemekanikk" title="Kvantemekanikk">kvantemekanikk</a>. Deres magnetiske felt skyldes bevegelsen til <a href="/wiki/Elektron" title="Elektron">elektronene</a> i materialets <a href="/wiki/Atom" title="Atom">atomer</a> i samspill med deres <a href="/wiki/Spinn" title="Spinn">spinn</a>. Slik forklares også at egenskapene til permanente magneter forsvinner ved tilstrekkelig høy oppvarming. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historie_-_magnet">Historie - magnet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=1" title="Rediger avsnitt: Historie - magnet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=1" title="Rediger kildekoden til seksjonen Historie - magnet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Rupes_Nigra.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Rupes_Nigra.jpg/240px-Rupes_Nigra.jpg" decoding="async" width="240" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Rupes_Nigra.jpg/360px-Rupes_Nigra.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Rupes_Nigra.jpg/480px-Rupes_Nigra.jpg 2x" data-file-width="564" data-file-height="477" /></a><figcaption>På et kart over området rundt Nordpolen tegnet <a href="/wiki/Mercator" class="mw-redirect" title="Mercator">Mercator</a> i 1595 inn et stort fjell som skulle forklare magnetisk tiltrekning.</figcaption></figure> <p>Lenge før magnetiske kompassnåler ble først brukt i Europa, var deres nytte kjent i <a href="/wiki/Kina" title="Kina">Kina</a>. Der var det kjent at en magnet som svinger i et vannrett plan, alltid peker i retningene nord og sør. De oppfant med andre ord kompasset. De gamle grekerne hadde mange filosofiske tanker om emnet uten at de nødvendigvis var basert på så mye praktisk erfaring. <a href="/wiki/Lucretius" title="Lucretius">Lucretius</a> i sitt store verk <i>De Rerum Natura</i> omtalte hvordan en magnet kunne holde fast på en jernring. Dermed ble ringen <a href="/wiki/Magnetisering" title="Magnetisering">magnetisert</a> slik at den igjen kunne holde fast i andre ringer. På samme måte kunne en nål av jern bringes i nærheten av en permanent magnet og selv bli magnetisk.<sup id="cite_ref-EB_1-0" class="reference"><a href="#cite_note-EB-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Kompasset kom til Europa på 1200-tallet. Dets virkning var i mange år omgitt av myter og overtro. For eksempel mente noen at dets virkning skyldes <a href="/wiki/Nordstjernen" title="Nordstjernen">Nordstjernen</a> eller var forårsaket av spesielle forhold ved den geografiske <a href="/wiki/Nordpolen" title="Nordpolen">Nordpolen</a>.<sup id="cite_ref-Blundell_2-0" class="reference"><a href="#cite_note-Blundell-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>På begynnelsen av 1900-tallet var de vanligste permanentmagnetene laget av jernlegeringer med wolfram, krom eller kobolt <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>. Den sterke permanentmagneten av materialet <a href="/w/index.php?title=Alnico&action=edit&redlink=1" class="new" title="Alnico (ikke skrevet ennå)">alnico</a> ble oppfunnet i 1932 <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>. Den var minst 9 ganger sterkere enn alle eksisterende wolfram-baserte magneter og 1.5 ganger sterkere enn kobolt-baserte magneter. <a href="/wiki/Ferritt" title="Ferritt">Ferritt</a>-baserte magneter ble vanlige i løpet av 1950-tallet. I 1966 ble <a href="/wiki/Samarium" title="Samarium">samarium</a>-magneten oppfunnet og i 1983 ble <a href="/wiki/Neodym" title="Neodym">neodym</a>-magneten oppfunnet. </p> <div class="mw-heading mw-heading3"><h3 id="Gilbert">Gilbert</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=2" title="Rediger avsnitt: Gilbert" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=2" title="Rediger kildekoden til seksjonen Gilbert"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den første, vitenskapelige undersøkelse av magnetiske fenomen ble foretatt av <a href="/wiki/William_Gilbert" title="William Gilbert">William Gilbert</a> som presenterte sine resultat i det kjente verket <i>De Magnete</i> i 1600. Han viste at Jorden selv er en magnet som retter inn kompassnålene. Videre bekreftet han mer presist at mens to ulike poler tiltrekker hverandre, vil to like poler som NN eller SS frastøte hverandre. Ved å dele en magnet i to mellom N-polen og S-polen, fikk man ikke isolert disse, men derimot to nye magneter med hver sine N- og S-poler. Ved å gjenta denne oppdelingen, ville man fortsatt ikke kunne isolere en enkelt pol. Vanlige stavmagneter har to poler. Men magnetiseres en jernring, får man en ringmagnet uten poler. </p><p>Med Gilberts forklaring er grunnen til at kompassnålens N-pol peker mot nord, at det finnes en magnetisk S-pol i området rundt den geografiske Nordpolen. Det betyr at <a href="/wiki/Den_magnetiske_nordpol" class="mw-redirect" title="Den magnetiske nordpol">Den magnetiske nordpolen</a> i virkeligheten er en magnetisk sydpol, og tilsvarende er <a href="/wiki/Den_magnetiske_sydpol" class="mw-redirect" title="Den magnetiske sydpol">Den magnetiske sydpolen</a> en N-pol. </p><p>Ved bruk av kompassnåler som kan bevege seg både i det horisontale og vertikale planet, kan man kartlegge retningen til det <a href="/wiki/Jordens_magnetfelt" title="Jordens magnetfelt">jordmagnetiske feltet</a> i hvert punkt. Denne retningen blir angitt ved to vinkler som angir den horisontale, magnetiske <a href="/wiki/Misvisning" title="Misvisning">deklinasjon</a> og den vertikale, magnetiske <a href="/wiki/Inklinasjon" title="Inklinasjon">inklinasjon</a>. Det ble tidlig klart at disse verdiene varierte langsomt med tiden. Allerede i 1692 foreslo <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> at dette skyldes at de magnetiske polene er festet til en bevegelig sfære inni <a href="/wiki/Jorden" title="Jorden">Jorden</a>. Denne forklaringen er ikke så forskjellig fra hva man vet idag der Jordens <a href="/wiki/Magnetfelt" title="Magnetfelt">magnetfelt</a> skyldes <a href="/wiki/Elektrisk_str%C3%B8m" title="Elektrisk strøm">elektriske strømmer</a> i dens indre.<sup id="cite_ref-EB_1-1" class="reference"><a href="#cite_note-EB-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Coulomb">Coulomb</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=3" title="Rediger avsnitt: Coulomb" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=3" title="Rediger kildekoden til seksjonen Coulomb"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Magnetic_field_near_pole.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Magnetic_field_near_pole.svg/150px-Magnetic_field_near_pole.svg.png" decoding="async" width="150" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Magnetic_field_near_pole.svg/225px-Magnetic_field_near_pole.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Magnetic_field_near_pole.svg/300px-Magnetic_field_near_pole.svg.png 2x" data-file-width="300" data-file-height="500" /></a><figcaption>Coulomb undersøkte loven for kraften av en magnet på en kompassnål.</figcaption></figure> <p>På samme måte som <a href="/wiki/Elektrisitet" title="Elektrisitet">elektriske fenomen</a> i tiden etter Gilbert ble forsøkt forklart ved strømninger av to væsker, prøvde man også å beskrive magnetiske fenomen ved en lignende modell. Overskudd eller underskudd av disse væskene skulle da gi opphav til to typer magnetiske ladninger som manifester seg som tilsvarende magnetiske poler. N-polen skyldes positiv ladning og S-polen består av negativ ladning. Som konvensjon ble valgt at de magnetiske kraftlinjene skal gå fra N-pol til S-pol analogt med elektriske <a href="/wiki/Feltlinje" title="Feltlinje">feltlinjer</a>. </p><p>Magnetiske krefter var forventet å opptre på samme måte som <a href="/wiki/Coulombs_lov" title="Coulombs lov">elektriske krefter</a>, det vil si variere med kvadratet av avstanden som i <a href="/wiki/Newtons_gravitasjonslov" title="Newtons gravitasjonslov">Newtons gravitasjonslov</a>. Kalles de to magnetiske ladningene for <i>q<sub>m</sub></i> og <i>q'<sub>m</sub></i>, skulle den forventete kraftloven da ha formen </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=k_{m}{q_{m}q_{m}' \over r^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> <mo>′</mo> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=k_{m}{q_{m}q_{m}' \over r^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf7b4466c53d91818069442d41a4c50ab34255bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.986ex; height:5.676ex;" alt="{\displaystyle F=k_{m}{q_{m}q_{m}' \over r^{2}}}"></span></dd></dl> <p>hvor <i>r</i>  er den relative avstanden og <i>k<sub>m</sub></i>  er en konstant avhengig av hvilke målenheter som benyttes analogt med <a href="/wiki/Coulombs_konstant" title="Coulombs konstant">Coulombs konstant</a> <i>k<sub>e</sub></i>  for den elektriske kraften. I <a href="/wiki/SI-systemet" title="SI-systemet">SI-systemet</a> har den verdien <span class="nowrap"><i>k<sub>m</sub></i> = <i>μ</i><sub>0</sub>/4<i>π</i></span> = 10<sup>-7</sup> N/A<sup>2</sup> hvor <i>μ</i><sub>0</sub>  ofte omtales som <a href="/wiki/Permeabilitet_(fysikk)" title="Permeabilitet (fysikk)">den magnetiske konstanten</a>. Enheten for magnetisk ladning <i>q<sub>m</sub> </i> er derfor <a href="/wiki/Ampere" title="Ampere">A</a>⋅<a href="/wiki/Meter" title="Meter">m</a> i dette mest brukte målesystemet. Denne loven for magnetiske krefter ble først tatt systematisk i bruk av <a href="/wiki/John_Michell" title="John Michell">John Michell</a>. </p><p>På slutten av 1700-tallet gjorde <a href="/wiki/Charles_Augustin_Coulomb" title="Charles Augustin Coulomb">Coulomb</a> nøyaktige målinger av kreftene som virket på polene til magnetnåler. Hans resultat så ut til å være i overensstemmelse med denne loven, men den viste seg snart å ikke være generelt gyldig. Allerede da ble det klart at magnetiske krefter er mer kompliserte enn de tilsvarende elektriske kreftene. Med oppdagelsene til <a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a> og <a href="/wiki/Amp%C3%A8re" class="mw-redirect" title="Ampère">Ampère</a> ble det klart at det er <a href="/wiki/Elektrisk_str%C3%B8m" title="Elektrisk strøm">elektriske strømmer</a> som gir opphav til <a href="/wiki/Magnetisme" title="Magnetisme">magnetisme</a>. Denne teoretiske forståelsen gjorde det mulig til å finne mer presise lovmessigheter for magnetiske krefter samtidig som den ga en bedre, mikroskopisk forklaring av egenskapene til magnetiske materialer.<sup id="cite_ref-Whittaker_5-0" class="reference"><a href="#cite_note-Whittaker-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Materiale">Materiale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=4" title="Rediger avsnitt: Materiale" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=4" title="Rediger kildekoden til seksjonen Materiale"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Magnetitt er et naturlig forekommende magnetisk materiale, men i seg selv er det ingen god permanentmagnet. Det er blitt utviklet en rekke andre materialer som i dag brukes for permanentmagneter. De vanligste er <a href="/wiki/Ferritt" title="Ferritt">ferritt</a>-baserte magneter, <a href="/w/index.php?title=Alnico&action=edit&redlink=1" class="new" title="Alnico (ikke skrevet ennå)">alnico</a>-baserte og magneter som inneholder <a href="/wiki/Sjeldne_jordarter" title="Sjeldne jordarter">sjeldne jordarter</a> (neodym eller samarium). De sistnevnte er de sterkeste. </p><p><a href="/wiki/Ferritt" title="Ferritt">Ferritt</a> er et keramisk materiale bestående av i hovedsak jernoksid. Magnetene som lages av ferritt er billige, men sprø, og må behandles mer eller mindre som annen keramikk. De brukes ofte til kjøleskapmagneter og lignende. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Neodymium_magnet_-_19-11-2010.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Neodymium_magnet_-_19-11-2010.JPG/250px-Neodymium_magnet_-_19-11-2010.JPG" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Neodymium_magnet_-_19-11-2010.JPG/375px-Neodymium_magnet_-_19-11-2010.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Neodymium_magnet_-_19-11-2010.JPG/500px-Neodymium_magnet_-_19-11-2010.JPG 2x" data-file-width="3072" data-file-height="2048" /></a><figcaption>Neodym-magnet</figcaption></figure> <p>Alnico-magneter er laget av en legering mellom <a href="/wiki/Aluminium" title="Aluminium">aluminium</a>, <a href="/wiki/Nikkel" title="Nikkel">nikkel</a>, <a href="/wiki/Kobolt" title="Kobolt">kobolt</a> og <a href="/wiki/Jern" title="Jern">jern</a>. Inntil de sjeldne jordart-magnetene ble oppfunnet, var alnico-magneter de definitivt sterkeste. De ble oppfunnet i 1932. </p><p>Magneter som lages av sjeldne jordarter er de sterkeste permanentmagnetene vi i dag kjenner til. De ble først utviklet på 1970 og 1980-tallet. De vanligste består av <a href="/wiki/Neodym" title="Neodym">neodym</a> eller <a href="/wiki/Samarium" title="Samarium">samarium</a>. Disse magnetene er sprø og utsatte for <a href="/wiki/Korrosjon" title="Korrosjon">korrosjon</a> og blir derfor vanligvis platterte med et beskyttende materiale. Neodym-magneten er en legering av jern, neodym og <a href="/wiki/Bor_(grunnstoff)" title="Bor (grunnstoff)">bor</a>. Samarium-magneten er en legering av samarium og kobolt. Selv om neodym-magneten er sterkere ved romtemperatur og mye billigere enn samarium-magneten, tåler samarium-magneten høyere temperatur <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Magnetisering">Magnetisering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=5" title="Rediger avsnitt: Magnetisering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=5" title="Rediger kildekoden til seksjonen Magnetisering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ved sine eksperimenter og analyse av disse ble Ampère overbevist om at alle magnetiske fenomen skyldes elektriske strømmer som går i lukkete sløyfer. Dette skulle gjelde også for det <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetiske feltet</a> fra permanente magneter. I disse skulle det finnes mikroskopiske strømsløyfer som ga opphav til magnetiske effekter på nøyaktig samme måte som de han hadde observert fra strømførende ledninger. Hver slik strømsløyfe kan beskrives som en <a href="/wiki/Magnetisk_dipol" title="Magnetisk dipol">magnetisk dipol</a>. Med fremveksten av moderne <a href="/wiki/Atomfysikk" title="Atomfysikk">atomfysikk</a> har dette bildet vist seg å være en meget profetisk antagelse da hans mikroskopiske strømsløyfer tilsvarer elektronenes gang i lukkete baner omkring atomene. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:VFPt_Solenoid_correct3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/VFPt_Solenoid_correct3.svg/200px-VFPt_Solenoid_correct3.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/VFPt_Solenoid_correct3.svg/300px-VFPt_Solenoid_correct3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/VFPt_Solenoid_correct3.svg/400px-VFPt_Solenoid_correct3.svg.png 2x" data-file-width="490" data-file-height="490" /></a><figcaption>Magnetiske <b>B</b>-feltlinjer i en magnet forårsaket av Ampère-strømmer i overflaten.</figcaption></figure> <p>I denne modellen til Ampère gir alle de mikroskopiske strømsløyfene opphav til en kontinuerlig fordeling av <a href="/wiki/Magnetisk_moment" title="Magnetisk moment">magnetiske dipolmoment</a>. Det er vanlig å betegne deres midlere tetthet med <a href="/wiki/Vektorfelt" title="Vektorfelt">vektorfeltet</a> <b>M</b> som kalles materialets <a href="/wiki/Magnetisering" title="Magnetisering">magnetisering</a>. I prinsippet kan denne variere i rommet, men i mange praktiske situasjoner er den konstant både i størrelse og retning. Det magnetiske momentet til et lite volum <i>V</i> er da <span class="nowrap"><b>m</b> = <b>M</b><i>V</i></span> og har dimensjon A⋅m<sup>2</sup> i <a href="/wiki/SI-systemet" title="SI-systemet">SI-systemet</a>. </p><p>En sylinderformet stavmagnet med magnetiseringen <b>M</b> rettet langs aksen vil ha nærliggende Ampère-strømmene inni magneten som kansellerer slik at man står igjen med en makroskopisk strøm langs sylinderoverflaten. De gir opphav til et <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetisk felt</a> <b>B</b> som inni magneten er rettet langs dens akse. Dette kan regnes ut fra <a href="/wiki/Biot-Savarts_lov" title="Biot-Savarts lov">Biot-Savarts lov</a>. Beregningen blir den samme som for en strømførende <a href="/wiki/Spole_(induktans)" title="Spole (induktans)">spole</a> som leder en strøm per lengdeenhet på overflaten lik med <i>M</i>. Utenfor magneten ser feltet ut som fra en <a href="/wiki/Magnetisk_dipol" title="Magnetisk dipol">magnetisk dipol</a> <span class="nowrap"><b>m</b> = <b>M</b><i>V</i></span> når dens volum <i>V</i> er lite nok. </p><p>Man kan alternativt tenke seg en slik magnetisk dipol sammensatt av en positiv og en negativ magnetisk ladning ±<i>q<sub>m</sub></i> i dens endepunkt. Hvis avstanden mellom dem er gitt ved vektoren <b>d</b>, vil de da sammen utgjøre en magnetisk dipol med moment <b>m</b> = <i>q<sub>m</sub></i> <b>d</b> helt analogt med en <a href="/wiki/Elektrisk_felt#Dipolfeltet" title="Elektrisk felt">elektrisk dipol</a>. Selv om slike magnetiske ladninger ikke finnes, kan denne modellen til Gilbert ofte gi en nyttig forståelse av magnetiske krefter. </p> <div class="mw-heading mw-heading2"><h2 id="Magnetiske_felt">Magnetiske felt</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=6" title="Rediger avsnitt: Magnetiske felt" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=6" title="Rediger kildekoden til seksjonen Magnetiske felt"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Utenfor en magnet finnes det et <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetisk induksjonsfelt</a> <b>B</b> som kan beregnes ved å anta at den er beskrevet ved et magnetisk dipolmoment <b>m</b>. Som for en <a href="/wiki/Elektrisk_felt#Dipolfeltet" title="Elektrisk felt">elektrisk dipol</a> plassert origo kan det skrives som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} (\mathbf {r} )={\mu _{0} \over 4\pi r^{3}}{\Big [}3(\mathbf {m} \cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}-\mathbf {m} {\Big ]}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">[</mo> </mrow> </mrow> <mn>3</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} (\mathbf {r} )={\mu _{0} \over 4\pi r^{3}}{\Big [}3(\mathbf {m} \cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}-\mathbf {m} {\Big ]}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66d79e4a82c61780cc0f8f5a8f373d7dc2f37242" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:29.808ex; height:5.176ex;" alt="{\displaystyle \mathbf {B} (\mathbf {r} )={\mu _{0} \over 4\pi r^{3}}{\Big [}3(\mathbf {m} \cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}-\mathbf {m} {\Big ]}}"></span></dd></dl> <p>når man benytter enhetsvektoren <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {\mathbf {r} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {\mathbf {r} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9740464b71653e12932278ee944540be8caa5b96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.343ex;" alt="{\displaystyle {\hat {\mathbf {r} }}}"></span> = <b>r</b>/<i>r</i> som angir retningen til feltpunktet i <b>r</b>. Ligger magnetens akse langs <i>x</i>-aksen, vil feltet lenger ut på denne aksen peke i samme retning og ha størrelse </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 B={\mu _{0}m \over 2\pi x^{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>m</mi> </mrow> <mrow> <mn>2</mn> <mi>π</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\mu _{0}m \over 2\pi x^{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e88f718d795f57d94de73d3229bbbbd005d55015" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.577ex; height:5.176ex;" alt="{\displaystyle B={\mu _{0}m \over 2\pi x^{3}}}"></span></dd></dl> <p>I et punkt på <i>y</i>-aksen er feltet motsatt rettet og har halvparten av denne verdien for samme avstand til magneten. </p><p>Dette resultatet kan man også komme frem til ved å beskrive magneten i Gilberts modell som bestående av to magnetiske ladninger <span class="nowrap">±<i>q<sub>m</sub></i></span> i avstand <i>d</i>. Bruk av Coulombs lov gir da det resulterende feltet fra disse to ladningene som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B={\mu _{0}q_{m} \over 4\pi }{\Big (}{1 \over x^{2}}-{1 \over (x+d)^{2}}{\Big )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>d</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\mu _{0}q_{m} \over 4\pi }{\Big (}{1 \over x^{2}}-{1 \over (x+d)^{2}}{\Big )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d424022fa00aee097becae1c4cc34c727095fc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.788ex; height:6.009ex;" alt="{\displaystyle B={\mu _{0}q_{m} \over 4\pi }{\Big (}{1 \over x^{2}}-{1 \over (x+d)^{2}}{\Big )}}"></span></dd></dl> <p>Når <i>x</i> >> <i>d</i>, kan innholdet av parentesen settes likt 2<i>d/x<sup>3</sup> </i> som da gir det samme resultatet når det magnetiske momentet <span class="nowrap"><i>m</i> = <i>q<sub>m</sub> d</i></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Magnetens_indre">Magnetens indre</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=7" title="Rediger avsnitt: Magnetens indre" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=7" title="Rediger kildekoden til seksjonen Magnetens indre"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:VFPt_magnets_BH_charges%2Bcurrents.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/VFPt_magnets_BH_charges%2Bcurrents.svg/220px-VFPt_magnets_BH_charges%2Bcurrents.svg.png" decoding="async" width="220" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/VFPt_magnets_BH_charges%2Bcurrents.svg/330px-VFPt_magnets_BH_charges%2Bcurrents.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/VFPt_magnets_BH_charges%2Bcurrents.svg/440px-VFPt_magnets_BH_charges%2Bcurrents.svg.png 2x" data-file-width="600" data-file-height="720" /></a><figcaption>Ampères modell for <b>B</b> og Gilberts modell for <b>H</b> gir samme resultat utenfor magneten, men ulike felt i dens indre.</figcaption></figure> <p>Utenfor magneten er det ikke noen magnetisering <b>M</b> slik at induksjonsfeltet kan uttrykkes på den vanlig måten <b>B</b> = <i>μ</i><sub>0</sub><b>H</b> ved det <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetiske feltet</a> <b>H</b>. Men inni magneten vil disse to være ganske forskjellige og i alminnelighet forbundet ved definisjonen<sup id="cite_ref-PS_7-0" class="reference"><a href="#cite_note-PS-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} =\mu _{0}(\mathbf {H} +\mathbf {M} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} =\mu _{0}(\mathbf {H} +\mathbf {M} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b90d8529e8a1b7b9a42e87880bb848af6b71ee1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.734ex; height:2.843ex;" alt="{\displaystyle \mathbf {B} =\mu _{0}(\mathbf {H} +\mathbf {M} )}"></span></dd></dl> <p>Mens <b>B</b> kan beregnes fra de makroskopiske Ampère-strømmene på magnetens sideflater, er feltet <b>H</b> gitt ved de makroskopiske <a href="/wiki/Magnetisering" title="Magnetisering">Gilbert-ladningene</a> på magnetens endeflater. De tilsvarende <a href="/wiki/Feltlinje" title="Feltlinje">feltlinjene</a> går ut fra de positive ladningene (N-pol) og ender opp på de negative ladningene (S-pol). Da feltlinjene for <b>B</b>-feltet alltid er lukkete kurver, betyr det at inni magneten har <b>B</b> og <b>H</b> motsatt retning. </p><p>Har magneten endelig utstrekning og dens endeflater er plane, kan <b>H</b>-feltet like utenfor beregnes på samme måte som det elektrisk feltet utenfor en plan <a href="/wiki/Elektrisk_felt#plan_disk" title="Elektrisk felt">skive</a>, nå med konstant magnetisk flateladningstetthet <span class="nowrap"><i>σ<sub>m</sub></i> = <i>M</i></span>. Like utenfor endeflaten står <b>H</b>-feltet <a href="/wiki/Vinkelrett" title="Vinkelrett">normalt</a> på endeflaten med tilnærmet størrelse <span class="nowrap"><i>H = M</i>/2</span>. Er denne magneten lang og tynn (kompassnål), bidrar ikke ladningene fra den motsatte enden og det magnetiske fluksfeltet som passerer endeflaten er derfor med god nøyaktig <span class="nowrap"><i>B</i> = <i>μ</i><sub>0</sub><i>M</i>/2</span>. Et punkt inni magneten som er langt borte fra begge endeflatene, vil ha <span class="nowrap"><i>H</i> = 0 </span> og derfor <span class="nowrap"><i>B</i> = <i>μ</i><sub>0</sub><i>M</i> </span> i en slik tilnærmet betraktning. </p><p>I det motsatte tilfellet for en veldig kort magnet som ser ut som en skive med en konstant magnetisering <b>M</b> langs aksen, vil <b>H</b>-feltene fra de to endeflatene kansellere utenfor magneten og der gi <i>B</i> = 0. Inni magneten vil de ha samme retning slik at <i>H = - M</i>. Dette er analogt med det elektriske feltet fra en <a href="/wiki/Elektrisk_felt#Kondensator" title="Elektrisk felt">plan kondensator</a>. <b>B</b>-feltet inni magneten er derfor null i denne approksimative beskrivelsen. </p> <div class="mw-heading mw-heading3"><h3 id="Beregning_av_indre_felt">Beregning av indre felt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=8" title="Rediger avsnitt: Beregning av indre felt" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=8" title="Rediger kildekoden til seksjonen Beregning av indre felt"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I en sylinderformet stavmagnet med lenge <i>L</i> og radius <i>a</i> som har en uniform magnetisering <i>M</i>  langs aksen, har hver endeflate med areal <span class="nowrap"><i>A = π</i> <i>r</i><sup> 2</sup> </span> en magnetisk ladning <span class="nowrap"><i>Q<sub>m</sub></i> = <i>σ<sub>m</sub> A</i></span> da den magnetiske ladningstettheten på hver av dem er <span class="nowrap"><i>σ<sub>m</sub></i> = ±<i>M</i></span>. Størrelsen av <b>H</b>-feltet på midten av magneten kan da finnes fra Coulombs lov anvendt på disse fiktive ladningene, </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 H_{L/2}=2\cdot {Q_{m} \over 4\pi (L/2)^{2}}=2{a^{2} \over L^{2}}M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow> <mn>4</mn> <mi>π</mi> <mo stretchy="false">(</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{L/2}=2\cdot {Q_{m} \over 4\pi (L/2)^{2}}=2{a^{2} \over L^{2}}M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d211f42295f7b3dfc8e3157b9ce3dbd6b079afd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:31.145ex; height:6.509ex;" alt="{\displaystyle H_{L/2}=2\cdot {Q_{m} \over 4\pi (L/2)^{2}}=2{a^{2} \over L^{2}}M}"></span></dd></dl> <p>der faktoren 2 skyldes at begge endeflatene bidrar med like mye. Samme resultat fås ved å benytte beregningen av det elektrisk feltet utenfor en <a href="/wiki/Elektrisk_felt#plan_disk" title="Elektrisk felt">plan disk</a> med radius <span class="nowrap"><i>a</i> << <i>L</i></span>. Dette <b>H</b>-feltet er motsatt rettet magnetiseringen <b>M</b> slik at <span class="nowrap"><b>B</b> = <i>μ</i><sub>0</sub>(<b>H</b> + <b>M</b>) </span> har størrelsen </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 B(L/2)=\mu _{0}M{\Big (}1-2{a^{2} \over L^{2}}{\Big )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo stretchy="false">(</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B(L/2)=\mu _{0}M{\Big (}1-2{a^{2} \over L^{2}}{\Big )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71de37365f6b8ecef49b99170592e6fe1243026b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.892ex; height:5.843ex;" alt="{\displaystyle B(L/2)=\mu _{0}M{\Big (}1-2{a^{2} \over L^{2}}{\Big )}}"></span></dd></dl> <p>midt inni magneten. </p><p>På samme måte kan også feltet like utenfor en av endeflatene beregnes. Her vil ladningen på platen selv bidra med <i>M</i>/2 til <b>H</b>-feltet, mens bidraget fra den motsatte endeflaten i avstand <i>L</i> igjen kan finnes fra Coulombs lov som nå gir </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 H_{L}={Q_{m} \over 4\pi L^{2}}={a^{2} \over 4L^{2}}M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{L}={Q_{m} \over 4\pi L^{2}}={a^{2} \over 4L^{2}}M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d7c179ab41f878e4cb53a6aa050d2a4bb2472d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.525ex; height:6.009ex;" alt="{\displaystyle H_{L}={Q_{m} \over 4\pi L^{2}}={a^{2} \over 4L^{2}}M}"></span></dd></dl> <p>og virker i motsatt retning. Da <span class="nowrap"><b>M</b> = 0</span> utenfor magneten, blir derfor fluksfeltet der <span class="nowrap"><i>B</i> = <i>μ</i><sub>0</sub><i>H</i> </span> eller </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 B(L)={1 \over 2}\mu _{0}M{\Big (}1-{a^{2} \over 2L^{2}}{\Big )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo stretchy="false">(</mo> <mi>L</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B(L)={1 \over 2}\mu _{0}M{\Big (}1-{a^{2} \over 2L^{2}}{\Big )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd75a9f7a6a53ccfa7258922163239c38b95094c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.565ex; height:5.843ex;" alt="{\displaystyle B(L)={1 \over 2}\mu _{0}M{\Big (}1-{a^{2} \over 2L^{2}}{\Big )}}"></span></dd></dl> <p>Dette er også verdien på <b>B</b>-feltet like innenfor endeflatene. </p> <div class="mw-heading mw-heading3"><h3 id="Magnetisk_hysterese">Magnetisk hysterese</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=9" title="Rediger avsnitt: Magnetisk hysterese" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=9" title="Rediger kildekoden til seksjonen Magnetisk hysterese"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fil:Hysteresiskurve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Hysteresiskurve.svg/320px-Hysteresiskurve.svg.png" decoding="async" width="320" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Hysteresiskurve.svg/480px-Hysteresiskurve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Hysteresiskurve.svg/640px-Hysteresiskurve.svg.png 2x" data-file-width="500" data-file-height="280" /></a><figcaption>Typisk hysteresekurve for <a href="/wiki/Ferromagnetisme" title="Ferromagnetisme">ferromagnet</a>.</figcaption></figure> <p>Virkelige magneter er vanligvis laget av <a href="/wiki/Ferromagnetisme" title="Ferromagnetisme">ferromagnetisk materiale</a>. Dette inneholder små domener hvor magnetiseringen er konstant. Utsettes dette materialet for et ytre magnetfelt <b>H</b>, vil disse rette seg inn i samme retning ved økende feltstyrke. Den makroskopiske magnetiseringen <b>M</b> vil øke med økende <b>H</b>, men denne forandringen er ikke <a href="/wiki/Line%C3%A6r" class="mw-redirect" title="Lineær">lineær</a>. Dette uttrykkes ved fenomenologisk ved en ikke-lineær relasjon <i>B</i> = <i>B</i>(<i>H</i>) som tilsvarer variabel <a href="/wiki/Permeabilitet" class="mw-disambig" title="Permeabilitet">permeabilitet</a> for magnetmaterialet. Når <i>H</i> er blitt tilstrekkelig stor, peker magnetiseringen i alle domenene langs dette feltet, og det resulterende fluksfeltet <i>B</i> sies å ha gått i <i>metning</i>. </p><p>Hvis nå det ytre feltet <i>H</i> reduseres til null, vil fluksfeltet få et litt annet forløp uttrykt ved en modifikasjon av funksjonen <span class="nowrap"><i>B</i>(<i>H</i>)</span>. Når <span class="nowrap"><i>H</i> = 0</span>, vil det fremdeles være et fluksfelt <span class="nowrap"><i>B<sub>r</sub></i> = <i>μ</i><sub>0</sub><i>M<sub>r</sub> </i></span> i materialet hvor <i>M<sub>r</sub> </i> er den <a href="/wiki/Remanens" title="Remanens">remanente magnetiseringen</a>. For å få den ned til null, må det ytre feltet øke i motsatt retning til verdien <i>H<sub>c</sub></i> som angir materialets <i>koersivitet</i>. Ved å øke <i>H</i> ytterligere, går materialet i metning i motsatt retning. Hvis man så reverserer prosessen og øker <i>H</i> igjen, vil <i>B</i>-feltet få et nytt forløp <span class="nowrap"><i>B</i>(<i>H</i>)</span> før det igjen går i metning i den opprinnelige retningen. Den fulle variasjonen av de to magnetfeltene er beskrevet ved en lukket «hysteresekurve» i <i>BH</i> - diagrammet. </p> <div class="mw-heading mw-heading3"><h3 id="Permanent_magnetisering">Permanent magnetisering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=10" title="Rediger avsnitt: Permanent magnetisering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=10" title="Rediger kildekoden til seksjonen Permanent magnetisering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hysteresekurvene er karakteristiske for materialet som benyttes i magneten, men uavhengig av hvordan den ser ut. Men den geometriske formen bestemmer hvor stor dens magnetisering blir. Hvis den er lang og tynn (kompassnål), er <i>H</i> = 0 i dens midte. Dens magnetisering er derfor gitt ved den <a href="/wiki/Remanens" title="Remanens">remanente magnetiseringen</a> <span class="nowrap"><i>M<sub>r</sub></i> = <i>B<sub>r</sub> </i>/<i>μ</i><sub>0</sub>.</span> For en magnetisert kule er derimot de interne feltene relatert ved <span class="nowrap"><i>B</i> = -2<i>μ</i><sub>0</sub><i>H</i></span>.<sup id="cite_ref-PS_7-1" class="reference"><a href="#cite_note-PS-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Dette beskriver en rett linje i <i>BH</i> - diagrammet med <a href="/wiki/Stigningstall" title="Stigningstall">stigningstall</a> -2. De resulterende verdiene for <i>B</i> og <i>H</i> finnes fra dens skjæringspunkt med hysteresekurven. Magnetiseringen følger så fra <span class="nowrap"><i>M</i> = <i>B</i> /<i>μ</i><sub>0</sub> - <i>H</i>.</span> </p> <div class="mw-heading mw-heading2"><h2 id="Magnetiske_krefter">Magnetiske krefter</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=11" title="Rediger avsnitt: Magnetiske krefter" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=11" title="Rediger kildekoden til seksjonen Magnetiske krefter"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den enkleste utgave av en magnet er en <a href="/wiki/Magnetisk_dipol" title="Magnetisk dipol">magnetisk dipol</a>. Det fysiske bildet av denne er en liten strømsløyfe som omslutter et areal <i>A</i>. Er strømmen i sløyfen <i>I</i>, har den et <a href="/wiki/Magnetisk_moment" title="Magnetisk moment">magnetisk moment</a> med størrelse <i>m = IA</i> og rettet vinkelrett til sløyfens plan. Plasseres dipolen et ytre magnetfelt <b>B</b>, vil den påvirkes av en <a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">magnetisk kraft</a> gitt ved <a href="/wiki/Lorentz-kraft" title="Lorentz-kraft">Lorentz-kraften</a>. Resultatet er at den vil påvirkes av et <a href="/wiki/Dreiemoment" title="Dreiemoment">dreiemoment</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {T} =\mathbf {m} \times \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} =\mathbf {m} \times \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f9e1e8957da35db55303a5bd7896a5456d3e9cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.925ex; height:2.176ex;" alt="{\displaystyle \mathbf {T} =\mathbf {m} \times \mathbf {B} }"></span></dd></dl> <p>som vil prøve å rette inn dipolen etter feltet. Denne rotasjonskraften tilsvarer den <a href="/wiki/Magnetfelt#Magnetisk_energi" title="Magnetfelt">potensielle energien</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=-\mathbf {m} \cdot \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=-\mathbf {m} \cdot \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35075c58be33d65693f054ea34011e114c0d5449" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.5ex; height:2.343ex;" alt="{\displaystyle V=-\mathbf {m} \cdot \mathbf {B} }"></span></dd></dl> <p>Disse to uttrykkene er av samme form som for en <a href="/wiki/Elektrisk_felt#Dipolfeltet" title="Elektrisk felt">elektrisk dipol</a> i et elektrisk felt og kan utledes på samme måte ved å bruke Gilbert-modellen med to motsatte, magnetiske ladninger for dipolen. </p><p>Hvis magnetfeltet har en romlig variasjon <b>B</b>(<b>r</b>), vil dipolen også bli utsatt for en ekstra kraft </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =(\mathbf {m} \cdot {\boldsymbol {\nabla }})\mathbf {B} =m_{x}{\partial \mathbf {B} \over \partial x}+m_{y}{\partial \mathbf {B} \over \partial y}+m_{z}{\partial \mathbf {B} \over \partial z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">∇</mi> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =(\mathbf {m} \cdot {\boldsymbol {\nabla }})\mathbf {B} =m_{x}{\partial \mathbf {B} \over \partial x}+m_{y}{\partial \mathbf {B} \over \partial y}+m_{z}{\partial \mathbf {B} \over \partial z}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07334482290ad788be27ded41b53377073f4b3dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:44.913ex; height:6.009ex;" alt="{\displaystyle \mathbf {F} =(\mathbf {m} \cdot {\boldsymbol {\nabla }})\mathbf {B} =m_{x}{\partial \mathbf {B} \over \partial x}+m_{y}{\partial \mathbf {B} \over \partial y}+m_{z}{\partial \mathbf {B} \over \partial z}}"></span></dd></dl> <p>som prøver å flytte den. Dette uttrykket kan alternativt skrives som <b>F</b> = -<b>∇</b> <i>V</i> da man har <b>∇</b> × <b>B</b> = 0 i denne situasjonen. Denne translatoriske kraften kan også utledes ved å betrakte dipolen som en strømsløyfe.<sup id="cite_ref-RPF_8-0" class="reference"><a href="#cite_note-RPF-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Da <a href="/wiki/Gradient" title="Gradient">gradientene</a> til magnetfeltet rundt en stavpunkt er størst rundt dens ender, vil fritt bevegelig jernfilspon i størst grad samles der. Et konstant magnetfelt kan dreie, men ikke flytte en magnetisk gjenstand. </p> <div class="mw-heading mw-heading3"><h3 id="Dipol-dipol_kraft">Dipol-dipol kraft</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=12" title="Rediger avsnitt: Dipol-dipol kraft" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=12" title="Rediger kildekoden til seksjonen Dipol-dipol kraft"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:VFPt_cylindrical_magnets_attracting.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VFPt_cylindrical_magnets_attracting.svg/300px-VFPt_cylindrical_magnets_attracting.svg.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VFPt_cylindrical_magnets_attracting.svg/450px-VFPt_cylindrical_magnets_attracting.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VFPt_cylindrical_magnets_attracting.svg/600px-VFPt_cylindrical_magnets_attracting.svg.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Feltlinjer rundt to stavmagneter som tiltrekker hverandre.</figcaption></figure> <p>Kraften mellom to magneter i tilstrekkelig stor avstand fra hverandre, kan beregnes ved å betrakte dem begge som <a href="/wiki/Magnetisk_dipol" title="Magnetisk dipol">magnetiske dipoler</a> med momenter <b>m</b><sub>1</sub> og <b>m</b><sub>2</sub> ved bruk av formelen <span class="nowrap">(<b>m</b><sub>2</sub>⋅<b>∇</b>)<b>B</b><sub>1</sub></span>. Plasseres <b>m</b><sub>1</sub> i origo, er dens felt <b>B</b><sub>1</sub> gitt ved den vanlige dipoluttrykket. Med <b>m</b><sub>2</sub> i posisjon <b>r</b> finnes da kraften mellom magnetene som </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} ={\frac {3\mu _{0}}{4\pi r^{4}}}{\Big [}(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{2}+(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{1}+(\mathbf {m} _{1}\cdot \mathbf {m} _{2}){\hat {\mathbf {r} }}-5(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}{\Big ]}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">[</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>−</mo> <mn>5</mn> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} ={\frac {3\mu _{0}}{4\pi r^{4}}}{\Big [}(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{2}+(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{1}+(\mathbf {m} _{1}\cdot \mathbf {m} _{2}){\hat {\mathbf {r} }}-5(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}{\Big ]}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1f200ea708b3f5a62e6065206ce73ab89cb9260" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:72.753ex; height:5.676ex;" alt="{\displaystyle \mathbf {F} ={\frac {3\mu _{0}}{4\pi r^{4}}}{\Big [}(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{2}+(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }})\mathbf {m} _{1}+(\mathbf {m} _{1}\cdot \mathbf {m} _{2}){\hat {\mathbf {r} }}-5(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}{\Big ]}}"></span></dd></dl> <p>Den avtar med fjerde potens av avstanden og har som forventet en komplisert avhengighet av den relative orienteringen av de to dipolene. Det kan forstås som resultatet av de fire magnetiske Coulomb-kreftene som virker mellom de to polene på den ene magneten og de to polene til den andre magneten.<sup id="cite_ref-Zangwill_9-0" class="reference"><a href="#cite_note-Zangwill-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>I det spesielle tilfellet at begge magnetene ligger langs <i>x</i>-aksen med samme retning slik at N-polen på den ene magneten er hovedsakelig tiltrukket av S-polen på den andre, tar denne kraften en enkel form. Den kan i dette spesielle tilfellet beregnes mer direkte fra </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\Big (}m_{2}{d \over dx}{\Big )}{\mu _{0}m_{1} \over 2\pi x^{3}}=-{\frac {3\mu _{0}}{2\pi }}{\frac {m_{1}m_{2}}{x^{4}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mi>π</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <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>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\Big (}m_{2}{d \over dx}{\Big )}{\mu _{0}m_{1} \over 2\pi x^{3}}=-{\frac {3\mu _{0}}{2\pi }}{\frac {m_{1}m_{2}}{x^{4}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9003ec44e93fa66c2d67d37be43ccd8ede1a9c63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:36.864ex; height:5.676ex;" alt="{\displaystyle F={\Big (}m_{2}{d \over dx}{\Big )}{\mu _{0}m_{1} \over 2\pi x^{3}}=-{\frac {3\mu _{0}}{2\pi }}{\frac {m_{1}m_{2}}{x^{4}}}}"></span></dd></dl> <p>hvor minustegnet bekrefter at magneten tiltrekker hverandre. Kraften mellom magnetene avtar med avstanden i fjerde potens som er mye raskere enn kraften mellom to isolerte ladninger. </p><p>Denne dipolantagelsen bryter sammen når magnetene er nær hverandre. Da vil den generelle formelen bare gi et approksimativt svar. Men hvis begge magnetene er kuleformete og uniformt magnetiserte, er feltet utenfor hver av dem gitt nøyaktig som for en ideell dipol plassert i kulenes sentrum. </p> <div class="mw-heading mw-heading3"><h3 id="Maxwell-spenning">Maxwell-spenning</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=13" title="Rediger avsnitt: Maxwell-spenning" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=13" title="Rediger kildekoden til seksjonen Maxwell-spenning"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hvis begge endene til en stavmagnet bøyes slik at dens N-pol står direkte overfor sin egen S-pol, ville disse to polene trekkes mot hverandre med en magnetisk kraft. Er endeflatene plane, kan man anta at de etter bøyningen igjen er parallelle med hverandre slik at feltet i luftgapet mellom dem er homogent. Kraften mellom disse to magnetpolene kan da ikke beregnes i samme dipolapproksimasjon, men derimot som kraften mellom de to platene i en ladet <a href="/wiki/Elektrisk_felt#Kondensator" title="Elektrisk felt">plan kondensator</a>. Hvis magneten har magnetiseringen <i>M</i>, er den magnetiske ladningen på den ene endeplaten <span class="nowrap"><i>Q<sub>m</sub> = AM</i> </span> hvor <i>A</i> er arealet til denne platen. Det magnetiske feltet fra den andre er <span class="nowrap"><i>B' </i> = <i>μ</i><sub>0</sub><i>M</i>/2 </span> slik at kraften mellom endeflatene blir </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=Q_{m}B'={1 \over 2}\mu _{0}AM^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <msup> <mi>B</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>A</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=Q_{m}B'={1 \over 2}\mu _{0}AM^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1af0dca29a890e2429b157887435898495451bc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.65ex; height:5.176ex;" alt="{\displaystyle F=Q_{m}B'={1 \over 2}\mu _{0}AM^{2}}"></span></dd></dl> <p>Men nå er det totale, magnetiske feltet i luftgapet <i>B</i> = 2<i>B' = μ</i><sub>0</sub><i>M</i>  da ladningene på begge endeflatene bidrar til det. Attraktiv kraft per flateenhet er derfor det negative trykket </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 P={F \over A}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>A</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>B</mi> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={F \over A}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae1ddc733ce6bd92cc69a0ec2cfa1f09e3488772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.901ex; height:6.176ex;" alt="{\displaystyle P={F \over A}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}"></span></dd></dl> <p>da <i>B = μ</i><sub>0</sub><i>H</i>  i luftgapet. Dette kalles en «Maxwell-spenning» og har samme form som den tilsvarende spenningen i et <a href="/wiki/Elektrostatikk#Maxwells_spenningstensor" title="Elektrostatikk">elektrisk felt</a>. De inngår begge som komponenter i <a href="/w/index.php?title=Maxwells_spenningstensor&action=edit&redlink=1" class="new" title="Maxwells spenningstensor (ikke skrevet ennå)">Maxwells spenningstensor</a> som kan benyttes til å beregne elektriske og magnetiske krefter på utstrakte legemer uten å kjenne direkte til de elektriske ladningene og strømmene som de inneholder. </p> <div class="mw-heading mw-heading3"><h3 id="Regneeksempel">Regneeksempel</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=14" title="Rediger avsnitt: Regneeksempel" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=14" title="Rediger kildekoden til seksjonen Regneeksempel"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ved å bruke verdien </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mu _{0} \over 4\pi }=10^{-7}{\mbox{N}}/{\mbox{A}}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>7</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>N</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>A</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mu _{0} \over 4\pi }=10^{-7}{\mbox{N}}/{\mbox{A}}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97de12ab813c3a514767f933ce20d12c2ca306ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.79ex; height:4.843ex;" alt="{\displaystyle {\mu _{0} \over 4\pi }=10^{-7}{\mbox{N}}/{\mbox{A}}^{2}}"></span></dd></dl> <p>for den <a href="/wiki/Permeabilitet_(fysikk)" title="Permeabilitet (fysikk)">magnetiske konstanten</a>, finner man for et magnetfelt <span class="nowrap"><i>B</i> = 1 <a href="/wiki/Tesla" title="Tesla">tesla</a></span> = <span class="nowrap">1 N/Am</span> et Maxwell-trykk av størrelse <span class="nowrap"><i>P</i> = 4⋅10<sup>5</sup> N/m<sup>2</sup></span>. Dette tilsvarer fire ganger normalt <a href="/wiki/Atmosf%C3%A6risk_trykk" title="Atmosfærisk trykk">lufttrykk</a> som kan resultere i store krefter. </p><p>Det er denne effekten som gjøres bruk av når en hesteskomagnet benyttes til å løfte tunge metallgjenstander. I dette tilfellet går den magnetiske fluksen fra N-polen, gjennom jernet tilbake til S-polen i en <a href="/wiki/Magnetisk_krets" title="Magnetisk krets">magnetisk krets</a>. Ved å anta at magnetpolene har sirkulære endeflater med diameter på <span class="nowrap">5 cm</span>, finner man en kraft <span class="nowrap"><i>F</i> = 800 <a href="/wiki/Newton_(enhet)" title="Newton (enhet)">N</a></span> fra hver pol. For hesteskomagneten med to slike luftgap blir derfor den totale kraften av størrelse <span class="nowrap">1600 N</span>. Dette er nok til å løfte et stykke jern med en masse rundt <span class="nowrap">160 kg</span>. </p> <div class="mw-heading mw-heading3"><h3 id="Magnetisk_feltenergi">Magnetisk feltenergi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=15" title="Rediger avsnitt: Magnetisk feltenergi" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=15" title="Rediger kildekoden til seksjonen Magnetisk feltenergi"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Utvides luftgapet mellom de to magnetiske endeflatene med Δ<i>x</i>, må man utføre arbeidet <i>F</i>Δ<i>x</i>. Dette går med til å øke den magnetiske feltenergien i dette gapet. Har denne energitettheten <i>u<sub>B</sub></i>, vil det utførte arbeidet gå med til å øke denne med </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{B}\Delta V=F\Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi mathvariant="normal">Δ</mi> <mi>V</mi> <mo>=</mo> <mi>F</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{B}\Delta V=F\Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b45e95a2ec43db83753978c3a1905233214b534e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.637ex; height:2.509ex;" alt="{\displaystyle u_{B}\Delta V=F\Delta x}"></span></dd></dl> <p>der økningen i luftgapets volum er Δ<i>V</i> = <i>A</i>Δ<i>x</i>. Dette betyr at energitettheten i det magnetiske feltet er </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{B}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>B</mi> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{B}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d0b6fe1423b8f0bc2ff32f59cae1c58d89c5b4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.287ex; height:6.176ex;" alt="{\displaystyle u_{B}={B^{2} \over 2\mu _{0}}={1 \over 2}BH}"></span></dd></dl> <p>En mer <a href="/wiki/Magnetfelt#Magnetisk_energi" title="Magnetfelt">teoretisk betraktning</a> viser at dette resultatet også holder når magnetfeltet varierer <b>B</b>(<b>r</b>) i rommet. Mer generelt kan det utledes fra <a href="/wiki/Elektromagnetisk_felt#Poyntings_teorem" title="Elektromagnetisk felt">Poyntings teorem</a> som en direkte konsekvens av <a href="/wiki/Maxwells_ligninger" class="mw-redirect" title="Maxwells ligninger">Maxwells ligninger</a> når feltet i tillegg varierer med tiden.<sup id="cite_ref-Griffiths_10-0" class="reference"><a href="#cite_note-Griffiths-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Kjøleskapsmagnet"><span id="Kj.C3.B8leskapsmagnet"></span>Kjøleskapsmagnet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=16" title="Rediger avsnitt: Kjøleskapsmagnet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=16" title="Rediger kildekoden til seksjonen Kjøleskapsmagnet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fil:Fridge_Magnet_Halbach.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Fridge_Magnet_Halbach.svg/250px-Fridge_Magnet_Halbach.svg.png" decoding="async" width="250" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Fridge_Magnet_Halbach.svg/375px-Fridge_Magnet_Halbach.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Fridge_Magnet_Halbach.svg/500px-Fridge_Magnet_Halbach.svg.png 2x" data-file-width="440" data-file-height="100" /></a><figcaption>Magnetiske domener er regelmessig arrangert i en kjøleskapsmagnet.</figcaption></figure> <p>En kjøleskapsmagnet består av et tynt lag av ferromagnetisk materiale som på den ene siden har et belegg som kan brukes til bilder, tekst eller andre illustrasjoner. Magnetiseringen består av regelmessige <a href="/wiki/Ferromagnetisme" title="Ferromagnetisme">domener</a> som er arrangert slik at magnetfeltet på siden mot kjøleskapsdøren ser ut som en serie med små hesteskomagneter av samme størrelse som domenene og med vekselende polaritet. Denne siden kan derfor festes til en kjøleskapsdør med høy magnetisk <a href="/wiki/Permeabilitet_(fysikk)" title="Permeabilitet (fysikk)">permeabilitet</a> ved at det oppstår en attraktiv Maxwell-spenning i et tynt luftgap mellom døren og magneten.<sup id="cite_ref-Zangwill_9-1" class="reference"><a href="#cite_note-Zangwill-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>De regelmessig arrangerte domenene gir et netto magnetfelt som går raskt mot null utenfor magneten da de virker i motsatt retning. I en avstand som tilsvarer størrelsen av disse, kan det settes tilnærmet lik null. Tiltrekningen mot kjøleskapsdøren blir likevel sterk når luftgapet er svært lite da den er bestemt av magnetiseringen til hver domene og er uavhengig av retningen til denne i hver domene. </p> <div class="mw-heading mw-heading2"><h2 id="Se_også"><span id="Se_ogs.C3.A5"></span>Se også</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=17" title="Rediger avsnitt: Se også" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=17" title="Rediger kildekoden til seksjonen Se også"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elektromagnet" title="Elektromagnet">Elektromagnet</a></li> <li><a href="/wiki/Magnetisk_felt" class="mw-redirect" title="Magnetisk felt">Magnetisk felt</a></li> <li><a href="/wiki/Magnetisme" title="Magnetisme">Magnetisme</a></li> <li><a href="/wiki/Ferromagnetisme" title="Ferromagnetisme">Ferromagnetisme</a></li> <li><a href="/wiki/Paramagnetisme" title="Paramagnetisme">Paramagnetisme</a></li> <li><a href="/wiki/Diamagnetisme" title="Diamagnetisme">Diamagnetisme</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=18" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=18" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-EB-1"><b>^</b> <a href="#cite_ref-EB_1-0"><sup>a</sup></a> <a href="#cite_ref-EB_1-1"><sup>b</sup></a> <span class="reference-text"> <i>Encyclopedia Britannica</i>, 11th edition, Cambridge, England (1911).</span> </li> <li id="cite_note-Blundell-2"><b><a href="#cite_ref-Blundell_2-0">^</a></b> <span class="reference-text"> S.J. Blundell, <i>Magnetism: A Very short introduction</i>, Oxford University Press, Oxford (2012). <a href="/wiki/Spesial:Bokkilder/9780199601202" class="internal mw-magiclink-isbn">ISBN 978-0-19-960120-2</a>.</span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.birmingham.ac.uk/Documents/college-eps/metallurgy/research/Magnetic-Materials-Background/Magnetic-Materials-Background-1-History.pdf">«Magnetic Materials: History»</a> <span style="font-size:85%;">(PDF)</span>. University of Birmingham<span class="reference-accessdate">. Besøkt 28. desember 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMagnet&rft.btitle=Magnetic+Materials%3A+History&rft.genre=unknown&rft.pub=University+of+Birmingham&rft_id=https%3A%2F%2Fwww.birmingham.ac.uk%2FDocuments%2Fcollege-eps%2Fmetallurgy%2Fresearch%2FMagnetic-Materials-Background%2FMagnetic-Materials-Background-1-History.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.apexmagnets.com/news-how-tos/magnets-last-100-years-alnico-neodymium/">«Magnets Over the Last 100 Years: From AlNiCo to Neodymium | Apex Magnets Blog»</a>. <i>www.apexmagnets.com</i> (på engelsk)<span class="reference-accessdate">. Besøkt 28. desember 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMagnet&rft.atitle=Magnets+Over+the+Last+100+Years%3A+From+AlNiCo+to+Neodymium+%7C+Apex+Magnets+Blog&rft.genre=unknown&rft.jtitle=www.apexmagnets.com&rft_id=https%3A%2F%2Fwww.apexmagnets.com%2Fnews-how-tos%2Fmagnets-last-100-years-alnico-neodymium%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Whittaker-5"><b><a href="#cite_ref-Whittaker_5-0">^</a></b> <span class="reference-text"> E.T. Whittaker, <a rel="nofollow" class="external text" href="https://archive.org/stream/historyoftheorie00whitrich#page/n5/mode/2up"><i>A History of the Theories of Aether and Electricity</i></a>, Longman, Green and Co, London (1910).</span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://idealmagnetsolutions.com/knowledge-base/samarium-cobalt-vs-neodymium-magnets/">«Samarium Cobalt vs Neodymium Magnets»</a>. <i>Ideal Magnet Solutions</i> (på engelsk). 15. mai 2019<span class="reference-accessdate">. Besøkt 28. desember 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AMagnet&rft.atitle=Samarium+Cobalt+vs+Neodymium+Magnets&rft.date=2019-05-15&rft.genre=unknown&rft.jtitle=Ideal+Magnet+Solutions&rft_id=https%3A%2F%2Fidealmagnetsolutions.com%2Fknowledge-base%2Fsamarium-cobalt-vs-neodymium-magnets%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-PS-7"><b>^</b> <a href="#cite_ref-PS_7-0"><sup>a</sup></a> <a href="#cite_ref-PS_7-1"><sup>b</sup></a> <span class="reference-text"> G.L. Pollack and D.R. Stump, <i>Electromagnetism</i>, Addison Wesley, San Fransisco (2002). <a href="/wiki/Spesial:Bokkilder/0805385673" class="internal mw-magiclink-isbn">ISBN 0-8053-8567-3</a>.</span> </li> <li id="cite_note-RPF-8"><b><a href="#cite_ref-RPF_8-0">^</a></b> <span class="reference-text">R.P. Feynman, <a rel="nofollow" class="external text" href="http://www.feynmanlectures.caltech.edu/II_15.html"><i>The Feynman Lectures on Physics</i></a>, Volume II, Chapter 15, <a href="/wiki/Caltech" class="mw-redirect" title="Caltech">Caltech</a>, Pasadena (2003).</span> </li> <li id="cite_note-Zangwill-9"><b>^</b> <a href="#cite_ref-Zangwill_9-0"><sup>a</sup></a> <a href="#cite_ref-Zangwill_9-1"><sup>b</sup></a> <span class="reference-text">A. Zangwill, <i>Modern Electrodynamics</i>, Cambridge University Press, Cambridge (2013). <a href="/wiki/Spesial:Bokkilder/9780521896979" class="internal mw-magiclink-isbn">ISBN 978-0-521-89697-9</a>.</span> </li> <li id="cite_note-Griffiths-10"><b><a href="#cite_ref-Griffiths_10-0">^</a></b> <span class="reference-text">D.J. Griffiths, <i>Introduction to Electrodynamics</i>, Prentice Hall, New Jersey (1999). <a href="/wiki/Spesial:Bokkilder/013805326X" class="internal mw-magiclink-isbn">ISBN 0-13-805326-X</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Eksterne_lenker">Eksterne lenker</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Magnet&veaction=edit&section=19" title="Rediger avsnitt: Eksterne lenker" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Magnet&action=edit&section=19" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>C. Blondel et B. Wolff, CNRS, <a rel="nofollow" class="external text" href="http://www.ampere.cnrs.fr/parcourspedagogique/zoom/coulomb/memoire/lois.php"><i>Les lois fondamentales de l'électricité et du magnétisme</i></a>, om Coulombs målinger av elektriske og magnetiske krefter.</li> <li>Trinity College, Dublin, <a rel="nofollow" class="external text" href="https://www.tcd.ie/Physics/research/groups/magnetism/teaching/">PY5006: <i>Magnetism and Magnetic Materials</i></a>, 15 forelesninger om magnetisme.</li> <li>W. Wang, University of Washington, <a rel="nofollow" class="external text" href="http://depts.washington.edu/mictech/optics/sensors/week2.pdf"><i>Magnetism</i></a>, tekniske anvendelser av magneter.</li> <li>D.P. Stern, <a rel="nofollow" class="external text" href="http://www.phy6.org/earthmag/dmglist.htm"><i>The Great Magnet, the Earth</i></a>, historie og mye annet om geomagnetisme.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23230704">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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