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<!doctype html><html lang=tr class=no-js> <head><meta charset=utf-8><meta name=viewport content="width=device-width,initial-scale=1"><meta name=description content="Python çözümlemeleri"><meta name=author content="Ali İhsan Çanakoğlu"><link rel=canonical href=https://ferahfeza.github.io/Elektromanyetik-Teori/yuk_dagilim.html><link rel=prev href=elek_alan.html><link rel=next href=setup/index.html><link rel=icon href=assets/favicon.png><meta name=generator content="mkdocs-1.5.3, mkdocs-material-9.5.10"><title>Yük Dağılımları - Elektromanyetik Alan Teorisi</title><link rel=stylesheet href=assets/stylesheets/main.7e359304.min.css><link rel=stylesheet href=assets/stylesheets/palette.06af60db.min.css><link rel=preconnect href=https://fonts.gstatic.com crossorigin><link rel=stylesheet href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback"><style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style><link rel=stylesheet href=assets/_markdown_exec_pyodide.css><link rel=stylesheet href=assets/_markdown_exec_ansi.css><link rel=stylesheet href=assets/css/custom.css><script>__md_scope=new URL(".",location),__md_hash=e=>[...e].reduce((e,_)=>(e<<5)-e+_.charCodeAt(0),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script><link rel=stylesheet href=assets/stylesheets/custom.00c04c01.min.css></head> <body dir=ltr data-md-color-scheme=default data-md-color-primary=indigo data-md-color-accent=indigo> <input class=md-toggle data-md-toggle=drawer type=checkbox id=__drawer autocomplete=off> <input class=md-toggle data-md-toggle=search type=checkbox id=__search autocomplete=off> <label class=md-overlay for=__drawer></label> <div data-md-component=skip> <a href=#yuk-daglmlar class=md-skip> Ana içeriğe geç </a> </div> <div data-md-component=announce> </div> <header class=md-header data-md-component=header> <nav class="md-header__inner md-grid" aria-label=Başlık> <a href=index.html title="Elektromanyetik Alan Teorisi" class="md-header__button md-logo" aria-label="Elektromanyetik Alan Teorisi" data-md-component=logo> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 89 89"> <path d=M3.136,17.387l0,42.932l42.932,21.467l-42.932,-64.399Z /> <path d=M21.91,8l42.933,64.398l-18.775,9.388l-42.932,-64.399l18.774,-9.387Z style="fill-opacity: 0.5"/> <path d=M67.535,17.387l-27.262,18.156l21.878,32.818l5.384,2.691l0,-53.665Z /> <path d=M67.535,17.387l0,53.666l18.774,-9.388l0,-53.665l-18.774,9.387Z style="fill-opacity: 0.25"/> </svg> </a> <label class="md-header__button md-icon" for=__drawer> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg> </label> <div class=md-header__title data-md-component=header-title> <div class=md-header__ellipsis> <div class=md-header__topic> <span class=md-ellipsis> Elektromanyetik Alan Teorisi </span> </div> <div class=md-header__topic data-md-component=header-topic> <span class=md-ellipsis> Yük Dağılımları </span> </div> </div> </div> <form class=md-header__option data-md-component=palette> <input class=md-option data-md-color-media=(prefers-color-scheme) data-md-color-scheme=default data-md-color-primary=indigo data-md-color-accent=indigo aria-label="Switch to light mode" type=radio name=__palette id=__palette_0> <label class="md-header__button md-icon" title="Switch to light mode" for=__palette_1 hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7a5 5 0 0 0-5 5 5 5 0 0 0 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1M8 13h8v-2H8v2m9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1 0 1.71-1.39 3.1-3.1 3.1h-4V17h4a5 5 0 0 0 5-5 5 5 0 0 0-5-5Z"/></svg> </label> <input class=md-option data-md-color-media="(prefers-color-scheme: light)" data-md-color-scheme=default data-md-color-primary=indigo data-md-color-accent=indigo aria-label="Switch to dark mode" type=radio name=__palette id=__palette_1> <label class="md-header__button md-icon" title="Switch to dark mode" for=__palette_2 hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M17 7H7a5 5 0 0 0-5 5 5 5 0 0 0 5 5h10a5 5 0 0 0 5-5 5 5 0 0 0-5-5m0 8a3 3 0 0 1-3-3 3 3 0 0 1 3-3 3 3 0 0 1 3 3 3 3 0 0 1-3 3Z"/></svg> </label> <input class=md-option data-md-color-media="(prefers-color-scheme: dark)" data-md-color-scheme=slate data-md-color-primary=black data-md-color-accent=indigo aria-label="Switch to system preference" type=radio name=__palette id=__palette_2> <label class="md-header__button md-icon" title="Switch to system preference" for=__palette_0 hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M17 7H7a5 5 0 0 0-5 5 5 5 0 0 0 5 5h10a5 5 0 0 0 5-5 5 5 0 0 0-5-5M7 15a3 3 0 0 1-3-3 3 3 0 0 1 3-3 3 3 0 0 1 3 3 3 3 0 0 1-3 3Z"/></svg> </label> </form> <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script> <label class="md-header__button md-icon" for=__search> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg> </label> <div class=md-search data-md-component=search role=dialog> <label class=md-search__overlay for=__search></label> <div class=md-search__inner role=search> <form class=md-search__form name=search> <input type=text class=md-search__input name=query aria-label=Ara placeholder=Ara autocapitalize=off autocorrect=off autocomplete=off spellcheck=false data-md-component=search-query required> <label class="md-search__icon md-icon" for=__search> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg> </label> <nav class=md-search__options aria-label=Ara> <a 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class=md-search__output> <div class=md-search__scrollwrap data-md-scrollfix> <div class=md-search-result data-md-component=search-result> <div class=md-search-result__meta> Arama başlatılıyor </div> <ol class=md-search-result__list role=presentation></ol> </div> </div> </div> </div> </div> <div class=md-header__source> <a href=https://github.com/ferahfeza/Elektromanyetik-Teori title="Depoya git" class=md-source data-md-component=source> <div class="md-source__icon md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 448 512"><!-- Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M439.55 236.05 244 40.45a28.87 28.87 0 0 0-40.81 0l-40.66 40.63 51.52 51.52c27.06-9.14 52.68 16.77 43.39 43.68l49.66 49.66c34.23-11.8 61.18 31 35.47 56.69-26.49 26.49-70.21-2.87-56-37.34L240.22 199v121.85c25.3 12.54 22.26 41.85 9.08 55a34.34 34.34 0 0 1-48.55 0c-17.57-17.6-11.07-46.91 11.25-56v-123c-20.8-8.51-24.6-30.74-18.64-45L142.57 101 8.45 235.14a28.86 28.86 0 0 0 0 40.81l195.61 195.6a28.86 28.86 0 0 0 40.8 0l194.69-194.69a28.86 28.86 0 0 0 0-40.81z"/></svg> </div> <div class=md-source__repository> Github </div> </a> </div> </nav> </header> <div class=md-container data-md-component=container> <nav class=md-tabs aria-label=Sekmeler data-md-component=tabs> <div class=md-grid> <ul class=md-tabs__list> <li class=md-tabs__item> <a href=index.html class=md-tabs__link> Ana Sayfa </a> </li> <li class="md-tabs__item md-tabs__item--active"> <a href=yuk.html class=md-tabs__link> Elektrostatik Alanlar </a> </li> <li class=md-tabs__item> <a href=setup/index.html class=md-tabs__link> Setup </a> </li> <li class=md-tabs__item> <a href=plugins/index.html class=md-tabs__link> Plugins </a> </li> <li class=md-tabs__item> <a href=reference/index.html class=md-tabs__link> Reference </a> </li> <li class=md-tabs__item> <a href=insiders/index.html class=md-tabs__link> Insiders </a> </li> <li class=md-tabs__item> <a href=blog/index.html class=md-tabs__link> Blog </a> </li> <li class=md-tabs__item> <a href=dersv/index.html class=md-tabs__link> Ders Videoları </a> </li> </ul> </div> </nav> <main class=md-main data-md-component=main> <div class="md-main__inner md-grid"> <div class="md-sidebar md-sidebar--primary" data-md-component=sidebar data-md-type=navigation> <div class=md-sidebar__scrollwrap> <div class=md-sidebar__inner> <nav class="md-nav md-nav--primary md-nav--lifted" aria-label=Navigasyon data-md-level=0> <label class=md-nav__title for=__drawer> <a href=index.html title="Elektromanyetik Alan Teorisi" class="md-nav__button md-logo" aria-label="Elektromanyetik Alan Teorisi" data-md-component=logo> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 89 89"> <path d=M3.136,17.387l0,42.932l42.932,21.467l-42.932,-64.399Z /> <path d=M21.91,8l42.933,64.398l-18.775,9.388l-42.932,-64.399l18.774,-9.387Z style="fill-opacity: 0.5"/> <path d=M67.535,17.387l-27.262,18.156l21.878,32.818l5.384,2.691l0,-53.665Z /> <path d=M67.535,17.387l0,53.666l18.774,-9.388l0,-53.665l-18.774,9.387Z style="fill-opacity: 0.25"/> </svg> </a> Elektromanyetik Alan Teorisi </label> <div class=md-nav__source> <a href=https://github.com/ferahfeza/Elektromanyetik-Teori title="Depoya git" class=md-source data-md-component=source> <div class="md-source__icon md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 448 512"><!-- Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M439.55 236.05 244 40.45a28.87 28.87 0 0 0-40.81 0l-40.66 40.63 51.52 51.52c27.06-9.14 52.68 16.77 43.39 43.68l49.66 49.66c34.23-11.8 61.18 31 35.47 56.69-26.49 26.49-70.21-2.87-56-37.34L240.22 199v121.85c25.3 12.54 22.26 41.85 9.08 55a34.34 34.34 0 0 1-48.55 0c-17.57-17.6-11.07-46.91 11.25-56v-123c-20.8-8.51-24.6-30.74-18.64-45L142.57 101 8.45 235.14a28.86 28.86 0 0 0 0 40.81l195.61 195.6a28.86 28.86 0 0 0 40.8 0l194.69-194.69a28.86 28.86 0 0 0 0-40.81z"/></svg> </div> <div class=md-source__repository> Github </div> </a> </div> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=index.html class=md-nav__link> <span class=md-ellipsis> Ana Sayfa </span> </a> </li> <li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested"> <input class="md-nav__toggle md-toggle " type=checkbox id=__nav_2 checked> <label class=md-nav__link for=__nav_2 id=__nav_2_label tabindex> <span class=md-ellipsis> Elektrostatik Alanlar </span> <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav data-md-level=1 aria-labelledby=__nav_2_label aria-expanded=true> <label class=md-nav__title for=__nav_2> <span class="md-nav__icon md-icon"></span> Elektrostatik Alanlar </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=yuk.html class=md-nav__link> <span class=md-ellipsis> Yük Kavramı </span> </a> </li> <li class=md-nav__item> <a href=coulomb.html class=md-nav__link> <span class=md-ellipsis> Coulomb Kanunu </span> </a> </li> <li class=md-nav__item> <a href=n-noktasal_yuk.html class=md-nav__link> <span class=md-ellipsis> n adet noktasal yük </span> </a> </li> <li class=md-nav__item> <a href=elek_alan.html class=md-nav__link> <span class=md-ellipsis> Elektrik Alan Şiddeti </span> </a> </li> <li class="md-nav__item md-nav__item--active"> <input class="md-nav__toggle md-toggle" type=checkbox id=__toc> <label class="md-nav__link md-nav__link--active" for=__toc> <span class=md-ellipsis> Yük Dağılımları </span> <span class="md-nav__icon md-icon"></span> </label> <a href=yuk_dagilim.html class="md-nav__link md-nav__link--active"> <span class=md-ellipsis> Yük Dağılımları </span> </a> <nav class="md-nav md-nav--secondary" aria-label=İçindekiler> <label class=md-nav__title for=__toc> <span class="md-nav__icon md-icon"></span> İçindekiler </label> <ul class=md-nav__list data-md-component=toc data-md-scrollfix> <li class=md-nav__item> <a href=#diferansiyel-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Diferansiyel elektrik alan şiddeti vektörü: </span> </a> </li> <li class=md-nav__item> <a href=#cizgisel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Çizgisel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> <nav class=md-nav aria-label="Çizgisel yük dağılımının elektrik alan şiddeti vektörü:"> <ul class=md-nav__list> <li class=md-nav__item> <a href=#uygulama class=md-nav__link> <span class=md-ellipsis> Uygulama </span> </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=#yuzeysel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Yüzeysel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> </li> <li class=md-nav__item> <a href=#hacimsel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Hacimsel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> </li> </ul> </nav> </li> </ul> </nav> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-nav__toggle md-toggle " type=checkbox id=__nav_3> <div class="md-nav__link md-nav__container"> <a href=setup/index.html class="md-nav__link "> <span class=md-ellipsis> Setup </span> </a> <label class="md-nav__link " for=__nav_3 id=__nav_3_label tabindex=0> <span class="md-nav__icon md-icon"></span> </label> </div> <nav class=md-nav data-md-level=1 aria-labelledby=__nav_3_label aria-expanded=false> <label class=md-nav__title for=__nav_3> <span class="md-nav__icon md-icon"></span> Setup </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=setup/changing-the-colors.html class=md-nav__link> <span class=md-ellipsis> Changing the colors </span> </a> </li> <li class=md-nav__item> <a href=setup/changing-the-fonts.html class=md-nav__link> <span class=md-ellipsis> Changing the fonts </span> </a> </li> <li class=md-nav__item> <a href=setup/changing-the-language.html class=md-nav__link> <span class=md-ellipsis> Changing the language </span> </a> </li> <li class=md-nav__item> <a href=setup/changing-the-logo-and-icons.html class=md-nav__link> <span class=md-ellipsis> Changing the logo and icons </span> </a> </li> <li class=md-nav__item> <a href=setup/ensuring-data-privacy.html class=md-nav__link> <span class=md-ellipsis> Ensuring data privacy </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-navigation.html class=md-nav__link> <span class=md-ellipsis> Setting up navigation </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-site-search.html class=md-nav__link> <span class=md-ellipsis> Setting up site search </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-site-analytics.html class=md-nav__link> <span class=md-ellipsis> Setting up site analytics </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-social-cards.html class=md-nav__link> <span class=md-ellipsis> Setting up social cards </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-a-blog.html class=md-nav__link> <span class=md-ellipsis> Setting up a blog </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-tags.html class=md-nav__link> <span class=md-ellipsis> Setting up tags </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-versioning.html class=md-nav__link> <span class=md-ellipsis> Setting up versioning </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-the-header.html class=md-nav__link> <span class=md-ellipsis> Setting up the header </span> </a> </li> <li class=md-nav__item> <a href=setup/setting-up-the-footer.html class=md-nav__link> <span class=md-ellipsis> Setting up the footer </span> </a> </li> <li class=md-nav__item> <a 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class=md-sidebar__scrollwrap> <div class=md-sidebar__inner> <nav class="md-nav md-nav--secondary" aria-label=İçindekiler> <label class=md-nav__title for=__toc> <span class="md-nav__icon md-icon"></span> İçindekiler </label> <ul class=md-nav__list data-md-component=toc data-md-scrollfix> <li class=md-nav__item> <a href=#diferansiyel-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Diferansiyel elektrik alan şiddeti vektörü: </span> </a> </li> <li class=md-nav__item> <a href=#cizgisel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Çizgisel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> <nav class=md-nav aria-label="Çizgisel yük dağılımının elektrik alan şiddeti vektörü:"> <ul class=md-nav__list> <li class=md-nav__item> <a href=#uygulama class=md-nav__link> <span class=md-ellipsis> Uygulama </span> </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=#yuzeysel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Yüzeysel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> </li> <li class=md-nav__item> <a href=#hacimsel-yuk-daglmnn-elektrik-alan-siddeti-vektoru class=md-nav__link> <span class=md-ellipsis> Hacimsel yük dağılımının elektrik alan şiddeti vektörü: </span> </a> </li> </ul> </nav> </div> </div> </div> <div class=md-content data-md-component=content> <article class="md-content__inner md-typeset"> <a href=https://github.com/ferahfeza/Elektromanyetik-Teori/edit/master/docs/yuk_dagilim.md title=Düzenle class="md-content__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg> </a> <a href=https://github.com/ferahfeza/Elektromanyetik-Teori/raw/master/docs/yuk_dagilim.md title="Sayfanın kaynağını görüntüle" class="md-content__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M17 18c.56 0 1 .44 1 1s-.44 1-1 1-1-.44-1-1 .44-1 1-1m0-3c-2.73 0-5.06 1.66-6 4 .94 2.34 3.27 4 6 4s5.06-1.66 6-4c-.94-2.34-3.27-4-6-4m0 6.5a2.5 2.5 0 0 1-2.5-2.5 2.5 2.5 0 0 1 2.5-2.5 2.5 2.5 0 0 1 2.5 2.5 2.5 2.5 0 0 1-2.5 2.5M9.27 20H6V4h7v5h5v4.07c.7.08 1.36.25 2 .49V8l-6-6H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h4.5a8.15 8.15 0 0 1-1.23-2Z"/></svg> </a> <h1 id=yuk-daglmlar>Yük Dağılımları<a class=headerlink href=#yuk-daglmlar title="Permanent link">¶</a></h1> <h2 id=diferansiyel-elektrik-alan-siddeti-vektoru>Diferansiyel elektrik alan şiddeti vektörü:<a class=headerlink href=#diferansiyel-elektrik-alan-siddeti-vektoru title="Permanent link">¶</a></h2> <div class="admonition important"> <p class=admonition-title>Diferansiyel Elektrik Alan Şiddeti</p> <p> $$\mathrm{d}\mathbf{E}=\dfrac{\mathrm{d}q}{4\pi\varepsilon_0 D^2}\mathbf{a}_D\quad \text{(V/m)} $$ </p> </div> <h2 id=cizgisel-yuk-daglmnn-elektrik-alan-siddeti-vektoru>Çizgisel yük dağılımının elektrik alan şiddeti vektörü:<a class=headerlink href=#cizgisel-yuk-daglmnn-elektrik-alan-siddeti-vektoru title="Permanent link">¶</a></h2> <div class="admonition note"> <p class=admonition-title>Çizgisel yük dağılımı</p> <p> $$\mathbf{E}=\int_l \dfrac{\lambda\ \mathrm{d}\mathbf{l}}{4\pi\varepsilon_0 D^2}\mathbf{a}_D $$ </p> </div> <figure> <img alt="Image title" src=assets/images/cizgisel_yuk_elek_alan.png> </figure> <h3 id=uygulama>Uygulama<a class=headerlink href=#uygulama title="Permanent link">¶</a></h3> <div class="admonition note"> <p class=admonition-title>Uygulama</p> <p> Sonsuz uzun çizgisel yük dağılımı $x$ ekseni boyunca yerleşik ve üzerinde $\lambda\ \text{(C/m)}$'lik yük yoğunluğu vardır. $(0,d,0)$ noktasında oluşan elektrik alan şiddeti vektörünü hesaplayınız. <hr color=white> <ins>Çözüm:</ins><br> <img src=assets/images/sonsuz_uzun_uyg.png> $$dE=\frac {dq} {4πϵ_0D^2} e^{jθ}=\frac {λdx} {4πϵ_0(d^2+x^2)} e^{jθ}$$ $$ \begin{align} dE=dE_x+jdE_y \nonumber \\ dE_x=\frac {λdx} {4πϵ_0(d^2+x^2)} \cosθ \nonumber \\ dE_y=\frac {λdx} {4πϵ_0(d^2+x^2)} \sinθ \nonumber \end{align} $$ $$E=∫^∞_{−∞} \frac {λ} {4πϵ_0(d^2+x^2)} [\cosθ+j\sinθ]dx $$ $$\cosθ=\frac {x} {(x^2+d^2)^{1/2}} ; \sinθ=\frac {d} {(x^2+d^2)^{1/2}} $$ $$ \begin{align} E&=jE_y=j∫^∞_{−∞} \frac {λd} {4πϵ_0} \frac {dx} {(x^2+d^2)^{3/2}} \\ &=j\frac {λd} {4πϵ_0} \Bigg[\frac {x} {d^2(x^2+d^2)^{1/2}}\Bigg]^∞_{−∞} \\ &=j\frac {λd} {4πϵ_0} \Bigg[\frac 1 {d^2} + \frac 1 {d^2}\Bigg] = j\frac {λ} {2πϵ_0d} \\ E&=\frac λ {2πϵ_0d}\ \text{(V/m)} \nonumber \end{align} $$ </div> <p><a class=md-button href=Py%20Codes/sonsuz_uzun_int.html>İntegralin Python çözümü</a></p> <h2 id=yuzeysel-yuk-daglmnn-elektrik-alan-siddeti-vektoru>Yüzeysel yük dağılımının elektrik alan şiddeti vektörü:<a class=headerlink href=#yuzeysel-yuk-daglmnn-elektrik-alan-siddeti-vektoru title="Permanent link">¶</a></h2> <div class="admonition note"> <p class=admonition-title>Yüzeysel yük dağılımı</p> <p> $$\mathbf{E}=\int_S \dfrac{\sigma\ \mathrm{d}\mathbf{s}}{4\pi\varepsilon_0 D^2}\mathbf{a}_D $$ </p> </div> <figure> <img alt="Image title" src=assets/images/yuzeysel_yuk_elek_alan.png> </figure> <h2 id=hacimsel-yuk-daglmnn-elektrik-alan-siddeti-vektoru>Hacimsel yük dağılımının elektrik alan şiddeti vektörü:<a class=headerlink href=#hacimsel-yuk-daglmnn-elektrik-alan-siddeti-vektoru title="Permanent link">¶</a></h2> <div class="admonition note"> <p class=admonition-title>Hacimsel yük dağılımı</p> <p> $$\mathbf{E}=\int_v \dfrac{\rho\ \mathrm{d}v}{4\pi\varepsilon_0 D^2}\mathbf{a}_D $$ </p> </div> </article> </div> <script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script> </div> <button type=button class="md-top md-icon" data-md-component=top hidden> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M13 20h-2V8l-5.5 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