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Update 2022-03-22 10:53

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Jean-Sébastien
2022-03-22 10:53:22 +01:00
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commit 2d1d8d39a4
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-15 Tue 08:10 -->
<!-- 2022-03-22 Tue 10:52 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1617,15 +1617,15 @@ Table of contents
Since \({\boldsymbol \nabla} \cdot {\bf B} = 0\) in magnetostatics, following Helmholtz's theorem
(see <a href="./c_m_vf_helm.html#c_m_vf_helm">c_m_vf_helm</a>) we can write
</p>
<div class="core div" id="org0e39e79">
<div class="eqlabel" id="org373dcc3">
<div class="core div" id="org43892ce">
<div class="eqlabel" id="org3a3bc3a">
<p>
<a id="BcurlA"></a><a href="./ems_ms_vp_A.html#BcurlA"><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="org19a8207">
<div class="alteqlabels" id="orgb09d3b2">
<ul class="org-ul">
<li>Gr (5.61)</li>
</ul>
@@ -1661,18 +1661,18 @@ add any curlless function (said otherwise: the gradient of any scalar field) to
without changing the magnetic field. Making a specific choice is called making a <b>gauge choice</b>.
For example, we can always choose to eliminate the divergence of \({\bf A}\), giving us the example of the
</p>
<div class="main div" id="orgc170b1d">
<div class="main div" id="org6e595ac">
<p>
<b>Coulomb gauge</b>
</p>
<div class="eqlabel" id="org31d1543">
<div class="eqlabel" id="orgff30682">
<p>
<a id="CoulG"></a><a href="./ems_ms_vp_A.html#CoulG"><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="org3a1cdeb">
<div class="alteqlabels" id="org9e044e6">
<ul class="org-ul">
<li>Gr (5.63)</li>
</ul>
@@ -1711,15 +1711,15 @@ zero at infinity,
<p>
Under this gauge choice, Ampère's law becomes
</p>
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<div class="eqlabel" id="orgb96c94b">
<div class="main div" id="org764e2b0">
<div class="eqlabel" id="org3f693e5">
<p>
<a id="Amp_CoulG"></a><a href="./ems_ms_vp_A.html#Amp_CoulG"><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="org7571aa0">
<div class="alteqlabels" id="org74208de">
<ul class="org-ul">
<li>Gr (5.64)</li>
</ul>
@@ -1739,15 +1739,15 @@ Under this gauge choice, Ampère's law becomes
Again this is precisely like the Poisson equation, with one separate equation for each component.
For currents falling off sufficiently rapidly at infinity, we thus have
</p>
<div class="core div" id="org5ec98ad">
<div class="eqlabel" id="org0962fcb">
<div class="core div" id="orga51c6d0">
<div class="eqlabel" id="orgf1fa3d4">
<p>
<a id="A_CoulG"></a><a href="./ems_ms_vp_A.html#A_CoulG"><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="org8ff7eb6">
<div class="alteqlabels" id="org35d9537">
<ul class="org-ul">
<li>Gr (5.65)</li>
</ul>
@@ -1766,15 +1766,15 @@ For currents falling off sufficiently rapidly at infinity, we thus have
<p>
For line and surface currents,
</p>
<div class="main div" id="org602b0f8">
<div class="eqlabel" id="orgf1afc13">
<div class="main div" id="org6da036c">
<div class="eqlabel" id="orge6299eb">
<p>
<a id="A_CoulG_l"></a><a href="./ems_ms_vp_A.html#A_CoulG_l"><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="org7f3875b">
<div class="alteqlabels" id="orga10cfa7">
</div>
@@ -1785,14 +1785,14 @@ For line and surface currents,
\tag{A_CoulG_l}\label{A_CoulG_l}
\]
</p>
<div class="eqlabel" id="org805a994">
<div class="eqlabel" id="orgae969c5">
<p>
<a id="A_CoulG_s"></a><a href="./ems_ms_vp_A.html#A_CoulG_s"><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="orgfe08271">
<div class="alteqlabels" id="org3392659">
</div>
@@ -1807,7 +1807,7 @@ For line and surface currents,
</div>
<div class="example div" id="org5085a2c">
<div class="example div" id="org277d07b">
<p>
<b>Example: infinite solenoid</b>
</p>
@@ -1888,7 +1888,7 @@ 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: 2022-03-15 Tue 08:10</p>
<p class="date">Created: 2022-03-22 Tue 10:52</p>
<p class="validation"></p>
</div>