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href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B0%D1%9E%D1%81%D0%BA%D1%96_%D0%B7%D0%B0%D1%80%D0%B0%D0%B4" title="Планкаўскі зарад — belorusa" lang="be" hreflang="be" data-title="Планкаўскі зарад" data-language-autonym="Беларуская" data-language-local-name="belorusa" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%A0rrega_de_Planck" title="Càrrega de Planck — kataluna" lang="ca" hreflang="ca" data-title="Càrrega de Planck" data-language-autonym="Català" data-language-local-name="kataluna" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Planck%C5%AFv_n%C3%A1boj" title="Planckův náboj — ĉeĥa" lang="cs" hreflang="cs" data-title="Planckův náboj" data-language-autonym="Čeština" data-language-local-name="ĉeĥa" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Planck_charge" title="Planck charge — angla" lang="en" hreflang="en" data-title="Planck charge" data-language-autonym="English" data-language-local-name="angla" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Carga_de_Planck" title="Carga de Planck — hispana" lang="es" hreflang="es" data-title="Carga de Planck" data-language-autonym="Español" data-language-local-name="hispana" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Planckin_varaus" title="Planckin varaus — finna" lang="fi" hreflang="fi" data-title="Planckin varaus" data-language-autonym="Suomi" data-language-local-name="finna" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Charge_de_Planck" title="Charge de Planck — franca" lang="fr" hreflang="fr" data-title="Charge de Planck" data-language-autonym="Français" data-language-local-name="franca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%98%D7%A2%D7%9F_%D7%A4%D7%9C%D7%90%D7%A0%D7%A7" title="מטען פלאנק — hebrea" lang="he" hreflang="he" data-title="מטען פלאנק" data-language-autonym="עברית" data-language-local-name="hebrea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Planck-t%C3%B6lt%C3%A9s" title="Planck-töltés — hungara" lang="hu" hreflang="hu" data-title="Planck-töltés" data-language-autonym="Magyar" data-language-local-name="hungara" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%AC%D5%A1%D5%B6%D5%AF%D5%AB_%D5%AC%D5%AB%D6%81%D6%84" title="Պլանկի լիցք — armena" lang="hy" hreflang="hy" data-title="Պլանկի լիցք" data-language-autonym="Հայերեն" data-language-local-name="armena" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Carica_di_Planck" title="Carica di Planck — itala" lang="it" hreflang="it" data-title="Carica di Planck" data-language-autonym="Italiano" data-language-local-name="itala" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%A9%E3%83%B3%E3%82%AF%E9%9B%BB%E8%8D%B7" title="プランク電荷 — japana" lang="ja" hreflang="ja" data-title="プランク電荷" data-language-autonym="日本語" data-language-local-name="japana" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%8C%EB%9E%91%ED%81%AC_%EC%A0%84%ED%95%98" title="플랑크 전하 — korea" lang="ko" hreflang="ko" data-title="플랑크 전하" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Onus_electricum_Planckianum" title="Onus electricum Planckianum — latino" lang="la" hreflang="la" data-title="Onus electricum Planckianum" data-language-autonym="Latina" data-language-local-name="latino" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%81adunek_Plancka" title="Ładunek Plancka — pola" lang="pl" hreflang="pl" data-title="Ładunek Plancka" data-language-autonym="Polski" data-language-local-name="pola" 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/Carga_de_Planck" title="Carga de Planck — portugala" lang="pt" hreflang="pt" data-title="Carga de Planck" data-language-autonym="Português" data-language-local-name="portugala" 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%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9_%D0%B7%D0%B0%D1%80%D1%8F%D0%B4" title="Планковский заряд — rusa" lang="ru" hreflang="ru" data-title="Планковский заряд" data-language-autonym="Русский" data-language-local-name="rusa" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Carica_di_Planck" title="Carica di Planck — sicilia" lang="scn" hreflang="scn" data-title="Carica di Planck" data-language-autonym="Sicilianu" data-language-local-name="sicilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Planckov_n%C3%A1boj" title="Planckov náboj — slovaka" lang="sk" hreflang="sk" data-title="Planckov náboj" data-language-autonym="Slovenčina" data-language-local-name="slovaka" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Planckov_naboj" title="Planckov naboj — slovena" lang="sl" hreflang="sl" data-title="Planckov naboj" data-language-autonym="Slovenščina" data-language-local-name="slovena" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Planckladdning" title="Planckladdning — sveda" lang="sv" hreflang="sv" data-title="Planckladdning" data-language-autonym="Svenska" data-language-local-name="sveda" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Planck_y%C3%BCk%C3%BC" title="Planck yükü — turka" lang="tr" hreflang="tr" data-title="Planck yükü" data-language-autonym="Türkçe" data-language-local-name="turka" 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%9F%D0%BB%D0%B0%D0%BD%D0%BA%D1%96%D0%B2%D1%81%D1%8C%D0%BA%D0%B8%D0%B9_%D0%B7%D0%B0%D1%80%D1%8F%D0%B4" title="Планківський заряд — ukraina" lang="uk" hreflang="uk" data-title="Планківський заряд" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E8%8D%B7" title="普朗克電荷 — ĉina" lang="zh" hreflang="zh" data-title="普朗克電荷" data-language-autonym="中文" data-language-local-name="ĉina" 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/Q249439#sitelinks-wikipedia" title="Redakti interlingvajn ligilojn" class="wbc-editpage">Redakti ligilojn</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="Nomspacoj"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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class="mw-content-ltr mw-parser-output" lang="eo" dir="ltr"><p>En <a href="/wiki/Fiziko" title="Fiziko">fiziko</a>, la <b>elektra ŝargo de Planck</b> <i>q<sub>P</sub></i> estas la <a href="/wiki/Mezurunuo" title="Mezurunuo">mezurunuo</a> de <a href="/wiki/Elektra_%C5%9Dargo" title="Elektra ŝargo">elektra ŝargo</a> en sistemo de <a href="/w/index.php?title=Naturaj_unuoj&action=edit&redlink=1" class="new" title="Naturaj unuoj (paĝo ne ekzistas)">naturaj unuoj</a> <a href="/wiki/Unuoj_de_Planck" title="Unuoj de Planck">origine proponitaj</a> de germana fizikisto <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>. </p><p>Ĝi egalas al </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{P}={\sqrt {4\pi \epsilon _{0}\hbar c}}={\sqrt {2ch\epsilon _{0}}}={\frac {e}{\sqrt {\alpha }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>c</mi> <mi>h</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>e</mi> <msqrt> <mi>α</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{P}={\sqrt {4\pi \epsilon _{0}\hbar c}}={\sqrt {2ch\epsilon _{0}}}={\frac {e}{\sqrt {\alpha }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0958483dd7a30ee15d856cdb6a23097e22cf3f3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:33.019ex; height:5.676ex;" alt="{\displaystyle q_{P}={\sqrt {4\pi \epsilon _{0}\hbar c}}={\sqrt {2ch\epsilon _{0}}}={\frac {e}{\sqrt {\alpha }}}}"></span></dd></dl> <p>kie <i>c</i> estas <a href="/wiki/Lumrapideco" class="mw-redirect" title="Lumrapideco">lumrapideco</a> en vakuo; </p> <dl><dd><i>h</i> estas <a href="/wiki/Konstanto_de_Planck" title="Konstanto de Planck">konstanto de Planck</a>;</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar ={\frac {h}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar ={\frac {h}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df05180652a87fe1af83af4bba3402117bd18466" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.736ex; height:5.343ex;" alt="{\displaystyle \hbar ={\frac {h}{2\pi }}}"></span> estas <a href="/wiki/Malpligrandigita_konstanto_de_Planck" class="mw-redirect" title="Malpligrandigita konstanto de Planck">malpligrandigita konstanto de Planck</a>;</dd> <dd><i>ε<sub>0</sub></i> estas <a href="/wiki/Elektra_konstanto" title="Elektra konstanto">elektra konstanto</a>;</dd> <dd><i>e</i> ≈ 1,602176487(40) · 10<sup>−19</sup> <a href="/wiki/Kulombo" class="mw-redirect" title="Kulombo">C</a> estas la <a href="/wiki/Elementa_elektra_%C5%9Dargo" title="Elementa elektra ŝargo">elementa elektra ŝargo</a>;</dd> <dd><i>α</i> ≈ 7,297352569(5) · 10<sup>−3</sup> ≈ (137,035999084)<sup>−1</sup> estas <a href="/wiki/Konstanto_de_maldika_strukturo" class="mw-redirect" title="Konstanto de maldika strukturo">konstanto de maldika strukturo</a>.</dd></dl> <p>Ĝia valoro estas </p> <dl><dd><i>q<sub>P</sub></i> ≈ 1,875545866(47) · 10<sup>−18</sup> <a href="/wiki/Kulombo" class="mw-redirect" title="Kulombo">kulomboj</a></dd></dl> <p>La <a href="/w/index.php?title=%C4%88eferarujo&action=edit&redlink=1" class="new" title="Ĉeferarujo (paĝo ne ekzistas)">ĉeferarujo</a> de la pritaksita valoro estas metita en krampoj. </p><p>Pli elvolvita formo de ĉi tiu lasta esprimo estas <i>q<sub>P</sub></i> = 1,875545870 · 10<sup>−18</sup> C ± 0,000000047 · 10<sup>−18</sup> C. </p><p>La ŝargo de Planck estas je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\sqrt {\alpha }}}\approx 11,7062376144(22)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mi>α</mi> </msqrt> </mfrac> </mrow> <mo>≈</mo> <mn>11</mn> <mo>,</mo> <mn>7062376144</mn> <mo stretchy="false">(</mo> <mn>22</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\sqrt {\alpha }}}\approx 11,7062376144(22)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5468c229204565e220419452d1e514a6816f1b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:26.476ex; height:6.176ex;" alt="{\displaystyle {\frac {1}{\sqrt {\alpha }}}\approx 11,7062376144(22)}"></span> fojoj pli granda ol la <a href="/wiki/Elementa_elektra_%C5%9Dargo" title="Elementa elektra ŝargo">elementa elektra ŝargo</a> <i>e</i>. Reen, la elementa elektra ŝargo mezurita en la ŝargoj de Planck estas </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e=q_{P}{\sqrt {\alpha }}\approx 0,085424543131(16)q_{P}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>α</mi> </msqrt> </mrow> <mo>≈</mo> <mn>0</mn> <mo>,</mo> <mn>085424543131</mn> <mo stretchy="false">(</mo> <mn>16</mn> <mo stretchy="false">)</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=q_{P}{\sqrt {\alpha }}\approx 0,085424543131(16)q_{P}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1eda141e1a05de0931906b5d05bae452a01f635c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.991ex; height:3.009ex;" alt="{\displaystyle e=q_{P}{\sqrt {\alpha }}\approx 0,085424543131(16)q_{P}}"></span></dd></dl> <p>Relativa necerteco de valoro de la ŝargo de Planck en kulomboj egalas al duono de relativa necerteco de <a href="/wiki/Konstanto_de_Planck" title="Konstanto de Planck">konstanto de Planck</a>, kaj relativa necerteco de la ŝargo de Planck en <a href="/wiki/Elementa_elektra_%C5%9Dargo" title="Elementa elektra ŝargo">elementaj elektraj ŝargoj</a> egalas al duono de relativa necerteco de la <a href="/wiki/Maldiko-struktura_konstanto" class="mw-redirect" title="Maldiko-struktura konstanto">maldiko-struktura konstanto</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Vidu_ankaŭ"><span id="Vidu_anka.C5.AD"></span>Vidu ankaŭ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektra_%C5%9Dargo_de_Planck&veaction=edit&section=1" title="Redakti sekcion: Vidu ankaŭ" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektra_%C5%9Dargo_de_Planck&action=edit&section=1" title="Redakti la fontkodo de la sekcio: Vidu ankaŭ"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Unuoj_de_Planck" title="Unuoj de Planck">Unuoj de Planck</a></li> <li><a href="/w/index.php?title=Naturaj_unuoj&action=edit&redlink=1" class="new" title="Naturaj unuoj (paĝo ne ekzistas)">Naturaj unuoj</a></li> <li><a href="/wiki/Elektra_%C5%9Dargo" title="Elektra ŝargo">Elektra ŝargo</a></li> <li><a href="/wiki/Elementa_elektra_%C5%9Dargo" title="Elementa elektra ŝargo">Elementa elektra ŝargo</a></li> <li><a href="/wiki/Elektra_kurento_de_Planck" title="Elektra kurento de Planck">Elektra kurento de Planck</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Eksteraj_ligiloj">Eksteraj ligiloj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elektra_%C5%9Dargo_de_Planck&veaction=edit&section=2" title="Redakti sekcion: Eksteraj ligiloj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elektra_%C5%9Dargo_de_Planck&action=edit&section=2" title="Redakti la fontkodo de la sekcio: Eksteraj ligiloj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://physics.nist.gov/cuu/Constants/index.html">NIST pri konstantoj kaj mezurunuoj</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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