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Update 2022-03-22 10:53

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Jean-Sébastien
2022-03-22 10:53:22 +01:00
parent f8fdc5f8b4
commit 2d1d8d39a4
209 changed files with 1240 additions and 1226 deletions
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build/emf_svp.html
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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>
@@ -1631,7 +1631,7 @@ Useful strategy: represent fields in terms of potentials.
Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
field as a pure curl (since its divergence always vanishes):
</p>
<div class="core div" id="orgb63eb69">
<div class="core div" id="org0868f0a">
<p>
\[
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
@@ -1648,15 +1648,15 @@ Putting this into Faraday's law <a href="./emd_Fl_Fl.html#Fl">Fl</a> gives
so this can be written as the gradient of a scalar.
Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
</p>
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<div class="eqlabel" id="org51cbd1b">
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<p>
<a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><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="org25412c6">
<div class="alteqlabels" id="orgc2e0dbe">
</div>
@@ -1673,15 +1673,15 @@ Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
<p>
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
</p>
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<p>
<a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><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>
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<div class="alteqlabels" id="org1b03eff">
</div>
@@ -1701,15 +1701,15 @@ whereas Ampère-Maxwell becomes
\]
which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
</p>
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<p>
<a id="LapA"></a><a href="./emf_svp.html#LapA"><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>
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<div class="alteqlabels" id="org9e9918d">
</div>
@@ -1744,7 +1744,7 @@ 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>