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Update 2022-02-09 07:44

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Jean-Sébastien
2022-02-09 07:44:58 +01:00
parent 84531d125a
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 17:21 -->
<!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1616,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_es_ef_ccd.html">Electrostatic Field of Continuous Charge Distributions&emsp;<small>[ems.es.ef.ccd]</small></a></li><li>Next:&nbsp;<a href="ems_es_ef_Gl.html">Gauss's Law: the divergence of \({\bf E}\)&emsp;<small>[ems.es.ef.Gl]</small></a></li><li>Up:&nbsp;<a href="ems_es_ef.html">Electrostatic Fields&emsp;<small>[ems.es.ef]</small></a></li></ul><div id="outline-container-ems_es_ef_cE" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li><a class="breadcrumb-link"href="ems_es.html">Electrostatics</a></li><li><a class="breadcrumb-link"href="ems_es_ef.html">Electrostatic Fields</a></li><li>The Curl of \({\bf E}\)</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_es_ef_ccd.html">Electrostatic Field of Continuous Charge Distributions&emsp;<small>[ems.es.ef.ccd]</small></a></li><li>Next:&nbsp;<a href="ems_es_ef_Gl.html">Gauss's Law: the divergence of \({\bf E}\)&emsp;<small>[ems.es.ef.Gl]</small></a></li><li>Up:&nbsp;<a href="ems_es_ef.html">Electrostatic Fields&emsp;<small>[ems.es.ef]</small></a></li></ul><div id="outline-container-ems_es_ef_cE" class="outline-5">
<h5 id="ems_es_ef_cE">The Curl of \({\bf E}\)<a class="headline-permalink" href="./ems_es_ef_cE.html#ems_es_ef_cE"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
@@ -1626,14 +1626,14 @@ Table of contents
Since the work done when moving on a closed path vanishes, we have
</p>
<div class="eqlabel" id="orga7e79ce">
<div class="eqlabel" id="org7fb5656">
<p>
<a id="ointE0"></a><a href="./ems_es_ef_cE.html#ointE0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org8ebbbb3">
<div class="alteqlabels" id="orgb185e6c">
<ul class="org-ul">
<li>Gr (2.19)</li>
</ul>
@@ -1641,7 +1641,7 @@ Since the work done when moving on a closed path vanishes, we have
</div>
</div>
<div class="core div" id="orgf093675">
<div class="core div" id="org6438325">
<p>
</p>
@@ -1659,14 +1659,14 @@ Since the work done when moving on a closed path vanishes, we have
which by <a href="./c_m_ic_stokes.html#Stokes">Stokes' theorem</a> implies that the electrostatic field is curlless,
</p>
<div class="eqlabel" id="org616e452">
<div class="eqlabel" id="orgdbe37df">
<p>
<a id="curlE0"></a><a href="./ems_es_ef_cE.html#curlE0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgc32cca9">
<div class="alteqlabels" id="orge173b52">
<ul class="org-ul">
<li>Gr (2.20)</li>
</ul>
@@ -1674,7 +1674,7 @@ which by <a href="./c_m_ic_stokes.html#Stokes">Stokes' theorem</a> implies that
</div>
</div>
<div class="core div" id="orgf430f99">
<div class="core div" id="org95becb2">
<p>
\[
{\boldsymbol \nabla} \times {\bf E} = 0.
@@ -1701,10 +1701,21 @@ falls off, has the property that the work done is independent of the path.
<hr><div id="postamble" class="status">
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank" class="m-2">
<img alt="Creative Commons License" style="border-width:0"
src="https://licensebuttons.net/l/by/4.0/80x15.png"/>
</a>
Except where otherwise noted, all content is licensed under a
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"></p>
</div>