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n-noktasal_yuk.html
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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/n-noktasal_yuk.html><link rel=prev href=coulomb.html><link rel=next href=elek_alan.html><link rel=icon href=assets/favicon.png><meta name=generator content="mkdocs-1.5.3, mkdocs-material-9.5.10"><title>n adet noktasal yük - 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=#n-adet-noktasal-yukun-kuvveti 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> n adet noktasal yük </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 href=javascript:void(0) class="md-search__icon md-icon" title=Paylaş aria-label=Paylaş data-clipboard data-clipboard-text data-md-component=search-share tabindex=-1> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg> </a> <button type=reset class="md-search__icon md-icon" title=Temizle aria-label=Temizle tabindex=-1> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg> </button> </nav> <div class=md-search__suggest data-md-component=search-suggest></div> </form> <div 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 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> n adet noktasal yük </span> <span class="md-nav__icon md-icon"></span> </label> <a href=n-noktasal_yuk.html class="md-nav__link md-nav__link--active"> <span class=md-ellipsis> n adet noktasal yük </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=#uygulama-1 class=md-nav__link> <span class=md-ellipsis> Uygulama 1 </span> </a> </li> </ul> </nav> </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> <a href=yuk_dagilim.html class=md-nav__link> <span class=md-ellipsis> Yük Dağılımları </span> </a> </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 href=setup/adding-a-git-repository.html class=md-nav__link> <span class=md-ellipsis> Adding a git repository </span> </a> </li> <li class=md-nav__item> <a href=setup/adding-a-comment-system.html class=md-nav__link> <span class=md-ellipsis> Adding a comment system </span> </a> </li> <li class=md-nav__item> <a href=setup/building-an-optimized-site.html class=md-nav__link> <span class=md-ellipsis> Building an optimized site </span> </a> </li> <li class=md-nav__item> <a href=setup/building-for-offline-usage.html class=md-nav__link> <span class=md-ellipsis> Building for offline usage </span> </a> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-nav__toggle md-toggle " type=checkbox id=__nav_3_20> <div class="md-nav__link md-nav__container"> <a href=setup/extensions/index.html class="md-nav__link "> <span class=md-ellipsis> Extensions </span> </a> <label class="md-nav__link " for=__nav_3_20 id=__nav_3_20_label tabindex=0> <span class="md-nav__icon md-icon"></span> </label> </div> <nav class=md-nav data-md-level=2 aria-labelledby=__nav_3_20_label aria-expanded=false> <label class=md-nav__title for=__nav_3_20> <span class="md-nav__icon md-icon"></span> Extensions </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=setup/extensions/python-markdown.html class=md-nav__link> <span class=md-ellipsis> Python Markdown </span> </a> </li> <li class=md-nav__item> <a href=setup/extensions/python-markdown-extensions.html class=md-nav__link> <span class=md-ellipsis> Python Markdown Extensions </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_4> <div class="md-nav__link md-nav__container"> <a href=plugins/index.html class="md-nav__link "> <span 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href=dersv/index.html class=md-nav__link> <span class=md-ellipsis> Ders Videoları </span> </a> </li> </ul> </nav> </div> </div> </div> <div class="md-sidebar md-sidebar--secondary" data-md-component=sidebar data-md-type=toc> <div 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=#uygulama-1 class=md-nav__link> <span class=md-ellipsis> Uygulama 1 </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/n-noktasal_yuk.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/n-noktasal_yuk.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=n-adet-noktasal-yukun-kuvveti><span class=arithmatex>\(n\)</span> adet noktasal yükün kuvveti<a class=headerlink href=#n-adet-noktasal-yukun-kuvveti title="Permanent link">¶</a></h1> <p><span class=arithmatex>\(n\)</span> adet noktasal yükün bir noktasal yüke uyguladıkları toplam kuvvetin ifadesi aşağıdaki gibi yazılır.</p> <div class="admonition note"> <p class=admonition-title>Süperpozisyon</p> <p> $$\mathbf{F}_T=\frac{q_1q}{4\pi\varepsilon_0 D_1^2}\mathbf{a}_{D_1}+\frac{q_2q}{4\pi\varepsilon_0 D_2^2}\mathbf{a}_{D_2}+\cdots +\frac{q_nq}{4\pi\varepsilon_0 D_n^2}\mathbf{a}_{D_n}$$ $$\mathbf{F}_T=\dfrac{q}{4\pi\varepsilon_0}\sum_{i=1}^n \dfrac{q_i}{D_i^2}\mathbf{a}_{D_i}$$ </p> </div> <h3 id=uygulama-1>Uygulama 1<a class=headerlink href=#uygulama-1 title="Permanent link">¶</a></h3> <div class="admonition note"> <p class=admonition-title>İki adet noktasal yükün tek yüke uyguladıkları kuvvet</p> <p> Kartezyen koordinat sisteminde $P_1(3,0,0)$ ve $P_2(-3,0,0)$ noktalarına yerleştirilmiş $q$ değerlikli noktasal yüklerin $P(0,4,0)$ noktasına yerleştirilmiş $q$ noktasal yüküne uyguladıkları toplam kuvveti hesaplayınız. <hr color=white> <ins>Çözüm:</ins><br> <center><img src=assets/images/iki_noktasal.jpg width=400 height=400></center> $$\mathbf{F}_T=2×\frac{q\ q}{4\pi\varepsilon_0 D^2}\cos \alpha\ \mathbf{a}_y$$ $$D= \sqrt{3^2+4^2}=5,\, \cos α=\frac{4}{5}$$ $$\mathbf{F}_T=\dfrac{72\ q^2}{125}\times 10^{9}\ \mathbf{a}_y\quad \text{(N)} $$ <p><u>Python Kod:</u></p> <div class="language-python highlight"><pre><span></span><code><span id=__span-0-1><a id=__codelineno-0-1 name=__codelineno-0-1 href=#__codelineno-0-1></a><span class=kn>import</span> <span class=nn>numpy</span> <span class=k>as</span> <span class=nn>np</span>
</span><span id=__span-0-2><a id=__codelineno-0-2 name=__codelineno-0-2 href=#__codelineno-0-2></a><span class=kn>from</span> <span class=nn>numpy</span> <span class=kn>import</span> <span class=n>linalg</span> <span class=k>as</span> <span class=n>LA</span>
</span><span id=__span-0-3><a id=__codelineno-0-3 name=__codelineno-0-3 href=#__codelineno-0-3></a>
</span><span id=__span-0-4><a id=__codelineno-0-4 name=__codelineno-0-4 href=#__codelineno-0-4></a><span class=n>eps0</span> <span class=o>=</span> <span class=mf>1E-9</span><span class=o>/</span><span class=p>(</span><span class=mi>36</span> <span class=o>*</span> <span class=n>np</span><span class=o>.</span><span class=n>pi</span><span class=p>)</span>
</span><span id=__span-0-5><a id=__codelineno-0-5 name=__codelineno-0-5 href=#__codelineno-0-5></a><span class=n>Q1</span><span class=p>,</span> <span class=n>Q2</span><span class=p>,</span> <span class=n>Q3</span> <span class=o>=</span> <span class=mf>1E-9</span><span class=p>,</span> <span class=mf>1E-9</span><span class=p>,</span> <span class=mf>1E-9</span> <span class=c1>#Noktasal Yüklerin Değerleri</span>
</span><span id=__span-0-6><a id=__codelineno-0-6 name=__codelineno-0-6 href=#__codelineno-0-6></a><span class=n>Q1P</span> <span class=o>=</span> <span class=p>[</span><span class=mi>3</span><span class=p>,</span><span class=mi>0</span><span class=p>,</span><span class=mi>0</span><span class=p>]</span>
</span><span id=__span-0-7><a id=__codelineno-0-7 name=__codelineno-0-7 href=#__codelineno-0-7></a><span class=n>Q2P</span> <span class=o>=</span> <span class=p>[</span><span class=o>-</span><span class=mi>3</span><span class=p>,</span><span class=mi>0</span><span class=p>,</span><span class=mi>0</span><span class=p>]</span>
</span><span id=__span-0-8><a id=__codelineno-0-8 name=__codelineno-0-8 href=#__codelineno-0-8></a><span class=n>Q3P</span> <span class=o>=</span> <span class=p>[</span><span class=mi>0</span><span class=p>,</span><span class=mi>4</span><span class=p>,</span><span class=mi>0</span><span class=p>]</span>
</span><span id=__span-0-9><a id=__codelineno-0-9 name=__codelineno-0-9 href=#__codelineno-0-9></a><span class=n>D1</span> <span class=o>=</span> <span class=n>np</span><span class=o>.</span><span class=n>subtract</span><span class=p>(</span><span class=n>Q3P</span><span class=p>,</span><span class=n>Q1P</span><span class=p>)</span>
</span><span id=__span-0-10><a id=__codelineno-0-10 name=__codelineno-0-10 href=#__codelineno-0-10></a><span class=n>D2</span> <span class=o>=</span> <span class=n>np</span><span class=o>.</span><span class=n>subtract</span><span class=p>(</span><span class=n>Q3P</span><span class=p>,</span><span class=n>Q2P</span><span class=p>)</span>
</span><span id=__span-0-11><a id=__codelineno-0-11 name=__codelineno-0-11 href=#__codelineno-0-11></a><span class=n>D_gen_1</span> <span class=o>=</span> <span class=n>LA</span><span class=o>.</span><span class=n>norm</span><span class=p>(</span><span class=n>D1</span><span class=p>)</span>
</span><span id=__span-0-12><a id=__codelineno-0-12 name=__codelineno-0-12 href=#__codelineno-0-12></a><span class=n>D_gen_2</span> <span class=o>=</span> <span class=n>LA</span><span class=o>.</span><span class=n>norm</span><span class=p>(</span><span class=n>D2</span><span class=p>)</span>
</span><span id=__span-0-13><a id=__codelineno-0-13 name=__codelineno-0-13 href=#__codelineno-0-13></a><span class=n>F1</span> <span class=o>=</span> <span class=p>(</span><span class=n>Q1</span> <span class=o>*</span> <span class=n>Q3</span> <span class=o>*</span> <span class=n>D1</span><span class=p>)</span> <span class=o>/</span> <span class=p>(</span><span class=mi>4</span><span class=o>*</span><span class=n>np</span><span class=o>.</span><span class=n>pi</span><span class=o>*</span><span class=n>eps0</span><span class=o>*</span><span class=n>D_gen_1</span><span class=o>**</span><span class=mi>3</span><span class=p>)</span>
</span><span id=__span-0-14><a id=__codelineno-0-14 name=__codelineno-0-14 href=#__codelineno-0-14></a><span class=n>F2</span> <span class=o>=</span> <span class=p>(</span><span class=n>Q2</span> <span class=o>*</span> <span class=n>Q3</span> <span class=o>*</span> <span class=n>D2</span><span class=p>)</span> <span class=o>/</span> <span class=p>(</span><span class=mi>4</span><span class=o>*</span><span class=n>np</span><span class=o>.</span><span class=n>pi</span><span class=o>*</span><span class=n>eps0</span><span class=o>*</span><span class=n>D_gen_2</span><span class=o>**</span><span class=mi>3</span><span class=p>)</span>
</span><span id=__span-0-15><a id=__codelineno-0-15 name=__codelineno-0-15 href=#__codelineno-0-15></a><span class=n>F_T</span> <span class=o>=</span> <span class=n>F1</span> <span class=o>+</span> <span class=n>F2</span>
</span><span id=__span-0-16><a id=__codelineno-0-16 name=__codelineno-0-16 href=#__codelineno-0-16></a><span class=nb>print</span><span class=p>(</span><span class=s2>"$F_T=$ "</span><span class=p>,</span> <span class=n>F_T</span><span class=p>[</span><span class=mi>0</span><span class=p>],</span><span class=s2>"ax"</span><span class=p>,</span><span class=n>F_T</span><span class=p>[</span><span class=mi>1</span><span class=p>],</span><span class=s2>"ay"</span><span class=p>,</span><span class=n>F_T</span><span class=p>[</span><span class=mi>2</span><span class=p>],</span><span class=s2>"az"</span><span class=p>)</span>
</span></code></pre></div> <p><span class=arithmatex>\(F_T=\)</span> 0.0 ax 5.76e-10 ay 0.0 az (N)</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 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8v12Z"/></svg> Başa dön </button> </main> <footer class=md-footer> <nav class="md-footer__inner md-grid" aria-label=Altbilgi> <a href=coulomb.html class="md-footer__link md-footer__link--prev" aria-label="Önceki: Coulomb Kanunu"> <div class="md-footer__button md-icon"> <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> </div> <div class=md-footer__title> <span class=md-footer__direction> Önceki </span> <div class=md-ellipsis> Coulomb Kanunu </div> </div> </a> <a href=elek_alan.html class="md-footer__link md-footer__link--next" aria-label="Sonraki: Elektrik Alan Şiddeti"> <div class=md-footer__title> <span class=md-footer__direction> Sonraki </span> <div class=md-ellipsis> Elektrik Alan Şiddeti </div> </div> <div class="md-footer__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg> </div> </a> </nav> <div class="md-footer-meta md-typeset"> <div class="md-footer-meta__inner md-grid"> <div class=md-copyright> <div class=md-copyright__highlight> Copyright © 2024 Ali İhsan Çanakoğlu </div> Made with <a href=https://squidfunk.github.io/mkdocs-material/ target=_blank rel=noopener> Material for MkDocs </a> </div> <div class=md-social> <a href=https://github.com/ferahfeza target=_blank rel=noopener title=github.com class=md-social__link> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 496 512"><!-- Font Awesome Free 6.5.1 by @fontawesome - 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