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Update 2022-03-24 08:43

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Jean-Sébastien
2022-03-24 08:43:21 +01:00
parent 1d852e7213
commit 50704eba07
211 changed files with 1506 additions and 3143 deletions
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build/ems_ca_me_a.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-22 Tue 10:52 -->
<!-- 2022-03-24 Thu 08:42 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
</summary>
<ul>
<li>
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
</li>
@@ -1628,14 +1628,14 @@ By Taylor expanding, we get
Formally, we could do this for any vector \({\bf r}_s\) such that \(|{\bf r}_s| &lt; |{\bf r}|\) by
Taylor expanding with the \({\boldsymbol \nabla}\) operator,
</p>
<div class="eqlabel" id="org7b106bc">
<div class="eqlabel" id="orgb48be32">
<p>
<a id="1or_grad"></a><a href="./ems_ca_me_a.html#1or_grad"><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="orgf9dea72">
<div class="alteqlabels" id="orge7c3a2e">
</div>
@@ -1653,14 +1653,14 @@ the potential takes the form of the general solution of Laplace's equation <a hr
Reading the parameters, we get \(A_l = 0\), \(B_l = r_s^l\). Putting back a generic angle
(the coefficients remain the same), we thus get
</p>
<div class="eqlabel" id="org68023ff">
<div class="eqlabel" id="orgf3ead78">
<p>
<a id="1or_Leg"></a><a href="./ems_ca_me_a.html#1or_Leg"><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="org593b10c">
<div class="alteqlabels" id="orga8fca88">
<ul class="org-ul">
<li>Gr(3.94)</li>
</ul>
@@ -1682,14 +1682,14 @@ we can expand the potential at a point \({\bf r}\) outside \({\cal V}\) accordin
(here, we put the origin of our coordinate system closer to all points in \({\cal V}\) than to \({\bf r}\)
to ensure convergence)
</p>
<div class="eqlabel" id="orgaf6dad4">
<div class="eqlabel" id="orgbced9c3">
<p>
<a id="p_Leg"></a><a href="./ems_ca_me_a.html#p_Leg"><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="org0904818">
<div class="alteqlabels" id="org24bf079">
<ul class="org-ul">
<li>Gr (3.95)</li>
</ul>
@@ -1752,14 +1752,14 @@ For \(r \gg d\), we can expand (immediately dropping terms of order \(d^2/r^2\))
Putting things together, the leading term in the expansion <a href="./ems_ca_me_a.html#p_Leg">p_Leg</a> for the
potential of the physical dipole is given by
</p>
<div class="eqlabel" id="org0b3de33">
<div class="eqlabel" id="orgfe4f1c4">
<p>
<a id="p_physdi"></a><a href="./ems_ca_me_a.html#p_physdi"><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="org1803e09">
<div class="alteqlabels" id="orgf15f43d">
<ul class="org-ul">
<li>Gr (3.90)</li>
</ul>
@@ -1806,7 +1806,7 @@ 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: 2022-03-22 Tue 10:52</p>
<p class="date">Created: 2022-03-24 Thu 08:42</p>
<p class="validation"></p>
</div>