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class="vector-toc-numb">2</span> <span>Point charge</span> </div> </a> <ul id="toc-Point_charge-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_quantum_mechanics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>In quantum mechanics</span> </div> </a> <ul id="toc-In_quantum_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_and_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_and_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notes and references</span> </div> </a> <button aria-controls="toc-Notes_and_references-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>Toggle Notes and references subsection</span> </button> <ul id="toc-Notes_and_references-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" 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particle</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="Go to an article in another language. Available in 37 languages" > <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-37" 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">37 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Puntdeeltjie" title="Puntdeeltjie – Afrikaans" lang="af" hreflang="af" data-title="Puntdeeltjie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%B3%D9%8A%D9%85_%D9%86%D9%82%D8%B7%D9%8A" title="جسيم نقطي – Arabic" lang="ar" hreflang="ar" data-title="جسيم نقطي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%81_%E0%A6%95%E0%A6%A3%E0%A6%BE" title="বিন্দু কণা – Bangla" lang="bn" hreflang="bn" data-title="বিন্দু কণা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D1%80%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BF%D1%83%D0%BD%D0%BA%D1%82" title="Матэрыяльны пункт – Belarusian" lang="be" hreflang="be" data-title="Матэрыяльны пункт" data-language-autonym="Беларуская" data-language-local-name="Belarusian" 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%D1%82%D1%8D%D1%80%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BF%D1%83%D0%BD%D0%BA%D1%82" title="Матэрыяльны пункт – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Матэрыяльны пункт" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D0%B8%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%BE%D1%87%D0%BA%D0%B0" title="Материална точка – Bulgarian" lang="bg" hreflang="bg" data-title="Материална точка" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Part%C3%ADcula_puntual" title="Partícula puntual – Catalan" lang="ca" hreflang="ca" data-title="Partícula puntual" data-language-autonym="Català" data-language-local-name="Catalan" 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%99%C4%83%D0%BC%D0%BB%C4%83%D1%85%D0%BB%D0%B0_%D0%BF%C4%83%D0%BD%D1%87%C4%83" title="Йăмлăхла пăнчă – Chuvash" lang="cv" hreflang="cv" data-title="Йăмлăхла пăнчă" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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/Bodov%C3%A1_%C4%8D%C3%A1stice" title="Bodová částice – Czech" lang="cs" hreflang="cs" data-title="Bodová částice" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CE%BB%CE%B9%CE%BA%CF%8C_%CF%83%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF" title="Υλικό σημείο – Greek" lang="el" hreflang="el" data-title="Υλικό σημείο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Punto_material" title="Punto material – Spanish" lang="es" hreflang="es" data-title="Punto material" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B0%D8%B1%D9%87_%D9%86%D9%82%D8%B7%D9%87%E2%80%8C%D8%A7%DB%8C" title="ذره نقطه‌ای – Persian" lang="fa" hreflang="fa" data-title="ذره نقطه‌ای" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Particule_ponctuelle" title="Particule ponctuelle – French" lang="fr" hreflang="fr" data-title="Particule ponctuelle" data-language-autonym="Français" data-language-local-name="French" 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/Ponc-ch%C3%A1ithn%C3%ADn" title="Ponc-cháithnín – Irish" lang="ga" hreflang="ga" data-title="Ponc-cháithnín" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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/Punto_material" title="Punto material – Galician" lang="gl" hreflang="gl" data-title="Punto material" data-language-autonym="Galego" data-language-local-name="Galician" 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%A0%90%EC%9E%85%EC%9E%90" title="점입자 – Korean" lang="ko" hreflang="ko" data-title="점입자" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Partikel_titik" title="Partikel titik – Indonesian" lang="id" hreflang="id" data-title="Partikel titik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Punto_materiale" title="Punto materiale – Italian" lang="it" hreflang="it" data-title="Punto materiale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Materi%C4%81ls_punkts" title="Materiāls punkts – Latvian" lang="lv" hreflang="lv" data-title="Materiāls punkts" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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/Materialus_ta%C5%A1kas" title="Materialus taškas – Lithuanian" lang="lt" hreflang="lt" data-title="Materialus taškas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%BE%D1%87%D0%BA%D0%B0" title="Материјална точка – Macedonian" lang="mk" hreflang="mk" data-title="Материјална точка" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%82%B9%E7%B2%92%E5%AD%90" title="点粒子 – Japanese" lang="ja" hreflang="ja" data-title="点粒子" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Punktpartikkel" title="Punktpartikkel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Punktpartikkel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Nuqtaviy_zarra" title="Nuqtaviy zarra – Uzbek" lang="uz" hreflang="uz" data-title="Nuqtaviy zarra" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" 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%AC%E0%A8%BF%E0%A9%B0%E0%A8%A6%E0%A9%82_%E0%A8%95%E0%A8%A3" title="ਬਿੰਦੂ ਕਣ – Punjabi" lang="pa" hreflang="pa" data-title="ਬਿੰਦੂ ਕਣ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Pont_material" title="Pont material – Piedmontese" lang="pms" hreflang="pms" data-title="Pont material" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Punkt_materialny" title="Punkt materialny – Polish" lang="pl" hreflang="pl" data-title="Punkt materialny" data-language-autonym="Polski" data-language-local-name="Polish" 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/Ponto_material" title="Ponto material – Portuguese" lang="pt" hreflang="pt" data-title="Ponto material" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%BE%D1%87%D0%BA%D0%B0" title="Материальная точка – Russian" lang="ru" hreflang="ru" data-title="Материальная точка" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%88%D8%B1%D8%AF%DB%8C%D9%84%DB%95%DB%8C_%D9%86%D9%88%D9%82%D8%AA%DB%95%DB%8C%DB%8C" title="وردیلەی نوقتەیی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="وردیلەی نوقتەیی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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%D1%82%D0%B5%D1%80%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%B0%D1%87%D0%BA%D0%B0" title="Материјална тачка – Serbian" lang="sr" hreflang="sr" data-title="Материјална тачка" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Materijalna_to%C4%8Dka" title="Materijalna točka – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Materijalna točka" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Nokta_par%C3%A7ac%C4%B1k" title="Nokta parçacık – Turkish" lang="tr" hreflang="tr" data-title="Nokta parçacık" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%82%D0%BE%D1%87%D0%BA%D0%B0" title="Матеріальна точка – Ukrainian" lang="uk" hreflang="uk" data-title="Матеріальна точка" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BA%A1t_%C4%91i%E1%BB%83m" title="Hạt điểm – Vietnamese" lang="vi" hreflang="vi" data-title="Hạt điểm" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%BB%9E%E7%B2%92%E5%AD%90" title="點粒子 – Cantonese" lang="yue" hreflang="yue" data-title="點粒子" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%BB%9E%E7%B2%92%E5%AD%90" title="點粒子 – Chinese" lang="zh" hreflang="zh" data-title="點粒子" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1068091#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</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="Namespaces"> <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 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data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </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">From Wikipedia, the free encyclopedia</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="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Idealised model of a particle in physics</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Collage_of_point_particles.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Collage_of_point_particles.png/300px-Collage_of_point_particles.png" decoding="async" width="300" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Collage_of_point_particles.png/450px-Collage_of_point_particles.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Collage_of_point_particles.png/600px-Collage_of_point_particles.png 2x" data-file-width="1000" data-file-height="800" /></a><figcaption>Examples of point particles: <em>(counterclockwise from top left)</em> point mass for <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a>, point particles to measure distance between two charged particles, <a href="/wiki/Pendulum" title="Pendulum">simple pendulum</a> (point mass attached to the end of a massless string), <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gas</a> particles devoid of interactions (no collisions, gravitational force, or <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's force</a> between particles)</figcaption></figure> <p class="mw-empty-elt"> </p><p>A <b>point particle</b>, <b>ideal particle</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or <b>point-like particle</b> (often spelled <b>pointlike particle</b>) is an <a href="/wiki/Idealization_(science_philosophy)" class="mw-redirect" title="Idealization (science philosophy)">idealization</a> of <a href="/wiki/Particle" title="Particle">particles</a> heavily used in <a href="/wiki/Physics" title="Physics">physics</a>. Its defining feature is that it lacks spatial <a href="/wiki/Extension_(metaphysics)" title="Extension (metaphysics)">extension</a>; being dimensionless, it does not take up <a href="/wiki/Space" title="Space">space</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. Point masses and point charges, discussed below, are two common cases. When a point particle has an additive property, such as mass or charge, it is often represented mathematically by a <a href="/wiki/Dirac_delta_function" title="Dirac delta function">Dirac delta function</a>. In classical mechanics there is usually no concept of rotation of point particles about their "center". </p><p>In <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, the concept of a point particle is complicated by the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Heisenberg uncertainty principle</a>, because even an <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particle</a>, with no internal structure, occupies a nonzero volume. For example, the <a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic orbit</a> of an <a href="/wiki/Electron" title="Electron">electron</a> in the <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atom</a> occupies a volume of ~<span class="nowrap"><span data-sort-value="6970100000000000000♠"></span>10<sup>−30</sup> m<sup>3</sup></span>. There is nevertheless a distinction between elementary particles such as <a href="/wiki/Electron" title="Electron">electrons</a> or <a href="/wiki/Quark" title="Quark">quarks</a>, which have no known internal structure, and <a href="/wiki/Composite_particle" class="mw-redirect" title="Composite particle">composite particles</a> such as <a href="/wiki/Proton" title="Proton">protons</a> and neutrons, whose internal structures are made up of quarks. Elementary particles are sometimes called "point particles" in reference to their lack of internal structure, but this is in a different sense than that discussed herein. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Point_mass">Point mass</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=1" title="Edit section: Point mass"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Point mass</b> (<b>pointlike mass</b>) is the concept, for example in <a href="/wiki/Classical_physics" title="Classical physics">classical physics</a>, of a physical object (typically <a href="/wiki/Matter" title="Matter">matter</a>) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as) <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a> (infinitely small) in its volume or <a href="/wiki/Length" title="Length">linear dimensions</a>. In the theory of <a href="/wiki/Gravity" title="Gravity">gravity</a>, extended objects can behave as point-like even in their immediate vicinity. For example, spherical objects interacting in <a href="/wiki/3-dimensional_space" class="mw-redirect" title="3-dimensional space">3-dimensional space</a> whose interactions are described by the <a href="/wiki/Law_of_universal_gravitation" class="mw-redirect" title="Law of universal gravitation">Newtonian gravitation</a> behave, as long as they do not touch each other, in such a way as if all their matter were concentrated in their <a href="/wiki/Center_of_mass" title="Center of mass">centers of mass</a>.<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> In fact, this is true for all fields described by an <a href="/wiki/Inverse_square_law" class="mw-redirect" title="Inverse square law">inverse square law</a>.<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><sup id="cite_ref-NewtonMotteMachin1_5-0" class="reference"><a href="#cite_note-NewtonMotteMachin1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Point_charge">Point charge</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=2" title="Edit section: Point charge"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Scalar_potential_of_a_point_charge.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Scalar_potential_of_a_point_charge.jpg/220px-Scalar_potential_of_a_point_charge.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Scalar_potential_of_a_point_charge.jpg/330px-Scalar_potential_of_a_point_charge.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Scalar_potential_of_a_point_charge.jpg/440px-Scalar_potential_of_a_point_charge.jpg 2x" data-file-width="898" data-file-height="898" /></a><figcaption>Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right.</figcaption></figure> <p>Similar to point masses, in <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> physicists discuss a <b><style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="point_charge"></span><span id="POINT_CHARGE"></span><span class="vanchor-text">point charge</span></span></b>, a point particle with a nonzero <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a>.<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> The fundamental <a href="/wiki/Equation" title="Equation">equation</a> of <a href="/wiki/Electrostatics" title="Electrostatics">electrostatics</a> is <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a>, which describes the electric force between two point charges. Another result, <a href="/wiki/Earnshaw%27s_theorem" title="Earnshaw's theorem">Earnshaw's theorem</a>, states that a collection of point charges cannot be maintained in a static <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">equilibrium</a> configuration solely by the electrostatic interaction of the charges. The <a href="/wiki/Electric_field" title="Electric field">electric field</a> associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero, which suggests that the model is no longer accurate in this limit. </p> <div class="mw-heading mw-heading2"><h2 id="In_quantum_mechanics">In quantum mechanics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=3" title="Edit section: In quantum mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Quark_structure_proton.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Quark_structure_proton.svg/200px-Quark_structure_proton.svg.png" decoding="async" width="200" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Quark_structure_proton.svg/300px-Quark_structure_proton.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Quark_structure_proton.svg/400px-Quark_structure_proton.svg.png 2x" data-file-width="673" data-file-height="695" /></a><figcaption>A proton is a combination of two <a href="/wiki/Up_quark" title="Up quark">up quarks</a> and one <a href="/wiki/Down_quark" title="Down quark">down quark</a>, held together by <a href="/wiki/Gluon" title="Gluon">gluons</a>.</figcaption></figure> <p>In <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, there is a distinction between an <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particle</a> (also called "point particle") and a <a href="/wiki/Composite_particle" class="mw-redirect" title="Composite particle">composite particle</a>. An elementary particle, such as an <a href="/wiki/Electron" title="Electron">electron</a>, <a href="/wiki/Quark" title="Quark">quark</a>, or <a href="/wiki/Photon" title="Photon">photon</a>, is a particle with no known internal structure. Whereas a composite particle, such as a <a href="/wiki/Proton" title="Proton">proton</a> or <a href="/wiki/Neutron" title="Neutron">neutron</a>, has an internal structure. However, neither elementary nor composite particles are spatially localized, because of the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Heisenberg uncertainty principle</a>. The particle <a href="/wiki/Wavepacket" class="mw-redirect" title="Wavepacket">wavepacket</a> always occupies a nonzero volume. For example, see <a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic orbital</a>: The electron is an elementary particle, but its quantum states form three-dimensional patterns. </p><p>Nevertheless, there is good reason that an elementary particle is often called a point particle. Even if an elementary particle has a delocalized wavepacket, the wavepacket can be represented as a <a href="/wiki/Quantum_superposition" title="Quantum superposition">quantum superposition</a> of <a href="/wiki/Quantum_state" title="Quantum state">quantum states</a> wherein the particle is exactly localized. Moreover, the <i>interactions</i> of the particle can be represented as a superposition of interactions of individual states which are localized. This is not true for a composite particle, which can never be represented as a superposition of exactly-localized quantum states. It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero. </p><p>For example, for the electron, experimental evidence shows that the size of an electron is less than <span class="nowrap"><span data-sort-value="6982100000000000000♠"></span>10<sup>−18</sup> m</span>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This is consistent with the expected value of exactly zero. (This should not be confused with the <a href="/wiki/Classical_electron_radius" title="Classical electron radius">classical electron radius</a>, which, despite the name, is unrelated to the actual size of an electron.) </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Test_particle" title="Test particle">Test particle</a></li> <li class="mw-empty-elt"></li> <li><a href="/wiki/Brane" title="Brane">Brane</a></li> <li><a href="/wiki/Charge_(physics)" title="Charge (physics)">Charge (physics)</a> (general concept, not limited to <i><a href="/wiki/Electric_charge" title="Electric charge">electric charge</a></i>)</li> <li><a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> of particle physics</li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_and_references">Notes and references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=5" title="Edit section: Notes and references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=6" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output 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no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFOhanianMarkert2007" class="citation book cs1">Ohanian, H. C.; Markert, J. T. (2007). <i>Physics for Engineers and Scientists</i>. Vol. 1 (3rd ed.). <a href="/wiki/W._W._Norton_%26_Company" title="W. W. Norton & Company">Norton</a>. p. 3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-93003-0" title="Special:BookSources/978-0-393-93003-0"><bdi>978-0-393-93003-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Engineers+and+Scientists&rft.pages=3&rft.edition=3rd&rft.pub=Norton&rft.date=2007&rft.isbn=978-0-393-93003-0&rft.aulast=Ohanian&rft.aufirst=H.+C.&rft.au=Markert%2C+J.+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUdwadiaKalaba2007" class="citation book cs1">Udwadia, F. E.; Kalaba, R. E. (2007). <i>Analytical Dynamics: A New Approach</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-04833-0" title="Special:BookSources/978-0-521-04833-0"><bdi>978-0-521-04833-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analytical+Dynamics%3A+A+New+Approach&rft.pages=1&rft.pub=Cambridge+University+Press&rft.date=2007&rft.isbn=978-0-521-04833-0&rft.aulast=Udwadia&rft.aufirst=F.+E.&rft.au=Kalaba%2C+R.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFowlesCassiday" class="citation book cs1">Fowles, Grant R; Cassiday, George L. <i>Analytical Mechanics</i>. §6.2 Gravitational Force between a Uniform Sphere and a Particle.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analytical+Mechanics&rft.pages=%C2%A76.2+Gravitational+Force+between+a+Uniform+Sphere+and+a+Particle&rft.aulast=Fowles&rft.aufirst=Grant+R&rft.au=Cassiday%2C+George+L&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1999" class="citation book cs1">Newton, I. (1999). <i>The Principia: Mathematical Principles of Natural Philosophy</i>. Translated by Cohen, I. B.; Whitman, A. <a href="/wiki/University_of_California_Press" title="University of California Press">University of California Press</a>. p. 956 (Proposition 75, Theorem 35). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-520-08817-4" title="Special:BookSources/0-520-08817-4"><bdi>0-520-08817-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principia%3A+Mathematical+Principles+of+Natural+Philosophy&rft.pages=p.+956+%28Proposition+75%2C+Theorem+35%29&rft.pub=University+of+California+Press&rft.date=1999&rft.isbn=0-520-08817-4&rft.aulast=Newton&rft.aufirst=I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-NewtonMotteMachin1-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-NewtonMotteMachin1_5-0">^</a></b></span> <span class="reference-text">I. Newton, A. Motte, J. Machin (1729), p. 270–271.<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, I. (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ"><i>The Mathematical Principles of Natural Philosophy</i></a>. Translated by Motte, A.; Machin, J. <a href="/wiki/Benjamin_Motte" title="Benjamin Motte">Benjamin Motte</a>. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n354">270</a>–271.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy&rft.pages=270-271&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=I.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSnieder2001" class="citation book cs1">Snieder, R. (2001). <i>A Guided Tour of Mathematical Methods for the Physical Sciences</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. pp. 196–198. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-78751-3" title="Special:BookSources/0-521-78751-3"><bdi>0-521-78751-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Guided+Tour+of+Mathematical+Methods+for+the+Physical+Sciences&rft.pages=196-198&rft.pub=Cambridge+University+Press&rft.date=2001&rft.isbn=0-521-78751-3&rft.aulast=Snieder&rft.aufirst=R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://cerncourier.com/cws/article/cern/29724">"Precision pins down the electron's magnetism"</a>. 4 October 2006.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Precision+pins+down+the+electron%27s+magnetism&rft.date=2006-10-04&rft_id=http%3A%2F%2Fcerncourier.com%2Fcws%2Farticle%2Fcern%2F29724&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=7" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFC._Quigg2009" class="citation encyclopaedia cs1">C. Quigg (2009). <a rel="nofollow" class="external text" href="https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N">"Particle, Elementary"</a>. <i><a href="/wiki/Encyclopedia_Americana" title="Encyclopedia Americana">Encyclopedia Americana</a></i>. <a href="/wiki/Grolier" title="Grolier">Grolier Online</a>. Archived from <a rel="nofollow" class="external text" href="http://ea.grolier.com/article?id=0303750-00">the original</a> on 2013-04-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-07-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Particle%2C+Elementary&rft.btitle=Encyclopedia+Americana&rft.pub=Grolier+Online&rft.date=2009&rft.au=C.+Quigg&rft_id=http%3A%2F%2Fea.grolier.com%2Farticle%3Fid%3D0303750-00&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFS._L._Glashow2009" class="citation encyclopaedia cs1">S. L. Glashow (2009). <a rel="nofollow" class="external text" href="https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N">"Quark"</a>. <i><a href="/wiki/Encyclopedia_Americana" title="Encyclopedia Americana">Encyclopedia Americana</a></i>. <a href="/wiki/Grolier" title="Grolier">Grolier Online</a>. Archived from <a rel="nofollow" class="external text" href="http://ea.grolier.com/article?id=0325780-00">the original</a> on 2013-04-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-07-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Quark&rft.btitle=Encyclopedia+Americana&rft.pub=Grolier+Online&rft.date=2009&rft.au=S.+L.+Glashow&rft_id=http%3A%2F%2Fea.grolier.com%2Farticle%3Fid%3D0325780-00&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM._AlonsoE._J._Finn1968" class="citation book cs1">M. Alonso; E. J. Finn (1968). <i>Fundamental University Physics Volume III: Quantum and Statistical Physics</i>. <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-00262-0" title="Special:BookSources/0-201-00262-0"><bdi>0-201-00262-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamental+University+Physics+Volume+III%3A+Quantum+and+Statistical+Physics&rft.pub=Addison-Wesley&rft.date=1968&rft.isbn=0-201-00262-0&rft.au=M.+Alonso&rft.au=E.+J.+Finn&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCornish1965" class="citation journal cs1">Cornish, F. H. J. (1965). "Classical radiation theory and point charges". <i><a href="/wiki/Proceedings_of_the_Physical_Society" title="Proceedings of the Physical Society">Proceedings of the Physical Society</a></i>. <b>86</b> (3): 427–442. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965PPS....86..427C">1965PPS....86..427C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0370-1328%2F86%2F3%2F301">10.1088/0370-1328/86/3/301</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Physical+Society&rft.atitle=Classical+radiation+theory+and+point+charges&rft.volume=86&rft.issue=3&rft.pages=427-442&rft.date=1965&rft_id=info%3Adoi%2F10.1088%2F0370-1328%2F86%2F3%2F301&rft_id=info%3Abibcode%2F1965PPS....86..427C&rft.aulast=Cornish&rft.aufirst=F.+H.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJefimenko1994" class="citation journal cs1">Jefimenko, Oleg D. (1994). "Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity". <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>62</b> (1): 79–85. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994AmJPh..62...79J">1994AmJPh..62...79J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.17716">10.1119/1.17716</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Direct+calculation+of+the+electric+and+magnetic+fields+of+an+electric+point+charge+moving+with+constant+velocity&rft.volume=62&rft.issue=1&rft.pages=79-85&rft.date=1994&rft_id=info%3Adoi%2F10.1119%2F1.17716&rft_id=info%3Abibcode%2F1994AmJPh..62...79J&rft.aulast=Jefimenko&rft.aufirst=Oleg+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APoint+particle" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Point_particle&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Point_particle" class="extiw" title="commons:Category:Point particle">Point particle</a> at Wikimedia Commons</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Point_particle&oldid=1260526561">https://en.wikipedia.org/w/index.php?title=Point_particle&oldid=1260526561</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Concepts_in_physics" title="Category:Concepts in physics">Concepts in physics</a></li><li><a href="/wiki/Category:Classical_mechanics" title="Category:Classical mechanics">Classical mechanics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_American_English_from_February_2019" title="Category:Use American English from February 2019">Use American English from February 2019</a></li><li><a href="/wiki/Category:All_Wikipedia_articles_written_in_American_English" title="Category:All Wikipedia articles written in American English">All Wikipedia articles written in American English</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 1 December 2024, at 07:18<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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