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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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@@ -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>
@@ -1637,18 +1637,18 @@ We thus obtain
\]
Recognizing the proper velocity, we thus get that charge density and current density can together form the
</p>
<div class="core div" id="org94723ec">
<div class="core div" id="org4a23d61">
<p>
<b>Current density 4-vector</b>
</p>
<div class="eqlabel" id="org479bb40">
<div class="eqlabel" id="org8494a4a">
<p>
<a id="Jmu"></a><a href="./red_rem_Me.html#Jmu"><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="org324820b">
<div class="alteqlabels" id="org63c21fa">
</div>
@@ -1665,18 +1665,18 @@ J^\mu = \left( c\rho, J_x, J_y, J_z \right)
<p>
The continuity equation <a href="./ems_ms_ce.html#conteq">conteq</a> takes the simple form
</p>
<div class="core div" id="org5885f61">
<div class="core div" id="org2a3444b">
<p>
<b>Continuity equation</b>
</p>
<div class="eqlabel" id="org52b2d08">
<div class="eqlabel" id="org2db5045">
<p>
<a id="conteq_rel"></a><a href="./red_rem_Me.html#conteq_rel"><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="org8386e2d">
<div class="alteqlabels" id="org830511b">
</div>
@@ -1692,18 +1692,18 @@ The continuity equation <a href="./ems_ms_ce.html#conteq">conteq</a> takes the s
<p>
while similarly the notation simplifies for
</p>
<div class="main div" id="orgdb33787">
<div class="main div" id="org0816f0a">
<p>
<b>Maxwell's equations</b>
</p>
<div class="eqlabel" id="org26adf05">
<div class="eqlabel" id="org3cc1fa8">
<p>
<a id="Max_rel"></a><a href="./red_rem_Me.html#Max_rel"><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="orge69d726">
<div class="alteqlabels" id="org77d9519">
</div>
@@ -1722,18 +1722,18 @@ while similarly the notation simplifies for
<p>
In terms of \(F^{\mu \nu}\) and the proper velocity \(\eta^\mu\), we also have the
</p>
<div class="main div" id="org1aadbdc">
<div class="main div" id="orge8ec801">
<p>
<b>Minkowski force on a charge</b> \(q\)
</p>
<div class="eqlabel" id="org8ed30ad">
<div class="eqlabel" id="org467f39b">
<p>
<a id="MinkF_rel"></a><a href="./red_rem_Me.html#MinkF_rel"><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="org4770a30">
<div class="alteqlabels" id="orgf90a88d">
</div>
@@ -1782,14 +1782,14 @@ We can now exploit gauge invariance
which leaves \(F^{\mu \nu}\) invariant. In particular, we can choose
the Lorenz gauge <a href="./emf_g_Lg.html#LorenzG">LorenzG</a> here expressed as
</p>
<div class="eqlabel" id="org02fe36f">
<div class="eqlabel" id="org6a52a14">
<p>
<a id="LorenzG_4v"></a><a href="./red_rem_Me.html#LorenzG_4v"><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="org162a638">
<div class="alteqlabels" id="orgf61a44d">
</div>
@@ -1802,15 +1802,15 @@ the Lorenz gauge <a href="./emf_g_Lg.html#LorenzG">LorenzG</a> here expressed as
Using the d'Alembertian operator introduced in <a href="./emf_g_Lg.html#dAl">dAl</a>
here rewritten as
</p>
<div class="main div" id="org4189168">
<div class="eqlabel" id="org347c7ab">
<div class="main div" id="orgf152aad">
<div class="eqlabel" id="orgf826c45">
<p>
<a id="dAl_4v"></a><a href="./red_rem_Me.html#dAl_4v"><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="org373726e">
<div class="alteqlabels" id="orgea79545">
</div>
@@ -1827,18 +1827,18 @@ here rewritten as
we obtain the final form of
</p>
<div class="core div" id="org1c23781">
<div class="core div" id="org7a7f039">
<p>
<b>Maxwell's equations</b> <i>(Lorenz gauge, 4-vector notation)</i>
</p>
<div class="eqlabel" id="org7c865aa">
<div class="eqlabel" id="org5b1a56e">
<p>
<a id="Max_Lor_4v"></a><a href="./red_rem_Me.html#Max_Lor_4v"><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="org5e9be4d">
<div class="alteqlabels" id="orga66f820">
</div>
@@ -1874,7 +1874,7 @@ 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>