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Update 2022-03-01 08:15

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Jean-Sébastien
2022-03-01 08:15:26 +01:00
parent ead639cf67
commit ac1e628013
194 changed files with 1320 additions and 1022 deletions
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-21 Mon 20:41 -->
<!-- 2022-03-01 Tue 08:14 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1646,9 +1646,26 @@ W = \frac{1}{2} I \oint {\bf A} \cdot d{\bf l} = \frac{1}{2} \oint ({\bf A} \cdo
\label{Gr(7.30)}
\]
Generalization to volume currents:
</p>
<div class="eqlabel" id="org9fbfb9d">
<p>
<a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><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="org6b3d2a5">
<ul class="org-ul">
<li>gr (7.31)</li>
</ul>
</div>
</div>
<p>
\[
W = \frac{1}{2} \int_{\cal V} ({\bf A} \cdot {\bf J}) d\tau
\label{Gr(7.31)}
\tag{W_intAJ}\label{W_intAJ}
\]
Even better: use Ampère, \({\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J}\):
\[
@@ -1681,7 +1698,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
\]
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
</p>
<div class="core div" id="orgac0c4b7">
<div class="core div" id="org2f4a453">
<p>
\[
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
@@ -1702,7 +1719,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
\hspace{2cm} \mbox{(7.31 and 7.34)}
\end{align}
<div class="example div" id="org763563a">
<div class="example div" id="orgeb4514a">
<p>
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
Find energy stored in section of length \(l\).
@@ -1741,7 +1758,7 @@ 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: 2022-02-21 Mon 20:41</p>
<p class="date">Created: 2022-03-01 Tue 08:14</p>
<p class="validation"></p>
</div>