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Jean-Sébastien
2022-03-01 08:15:26 +01:00
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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>
@@ -1624,28 +1624,77 @@ Table of contents
<p>
In para/diamagnets: when \({\bf B}\) is removed, \({\bf M}\) disappears. For not too strong
fields, proportionality. Custom (slightly different than for dielectrics):
{\bf magnetic susceptibility} \(\chi_m\) defined as
<b>magnetic susceptibility</b> \(\chi_m\) defined as
</p>
<div class="core div" id="org96397c4">
<div class="core div" id="orgc733cbb">
<div class="eqlabel" id="orgbcc985e">
<p>
<a id="chim"></a><a href="./emsm_msm_lnlm_sp.html#chim"><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="org9f42e67">
<ul class="org-ul">
<li>Gr (6.29)</li>
</ul>
</div>
</div>
<p>
\[
{\bf M} = \chi_m {\bf H}
\label{Gr(6.29)}
\]
{\bf M} = \chi_m {\bf H}
\tag{chim}\label{chim}
\]
</p>
</div>
<p>
(and <b>not</b> \({\bf M} = \frac{1}{\mu_0} \chi_m {\bf B}\) had the electrostatics parallel
been followed historically). Materials that obey this are called <i>linear media</i>. Then,
</p>
<div class="eqlabel" id="org3de4f86">
<p>
<a id="BHM"></a><a href="./emsm_msm_lnlm_sp.html#BHM"><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="org44c0f44">
<ul class="org-ul">
<li>Gr (6.30)</li>
</ul>
</div>
</div>
<p>
\[
{\bf B} = \mu_0 ({\bf H} + {\bf M}) = \mu_0 (1 + \chi_m) {\bf H}
\label{Gr(6.30)}
\tag{BHM}\label{BHM}
\]
and thus
</p>
<div class="eqlabel" id="org131dc97">
<p>
<a id="BH"></a><a href="./emsm_msm_lnlm_sp.html#BH"><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="org6db2344">
<ul class="org-ul">
<li>Gr (6.31)</li>
</ul>
</div>
</div>
<p>
\[
{\bf B} = \mu {\bf H}, \hspace{1cm} \mu \equiv \mu_0 (1 + \chi_m)
\label{Gr(6.31)}
\tag{BH}\label{BH}
\]
where \(\mu\) is called the {\bf permeability} of the material.
</p>
@@ -1658,10 +1707,27 @@ have nonzero divergence.
<p>
In linear medium: bound volume current proportional to free current,
</p>
<div class="eqlabel" id="org601b8db">
<p>
<a id="JbchimJf"></a><a href="./emsm_msm_lnlm_sp.html#JbchimJf"><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="org5a5795b">
<ul class="org-ul">
<li>Gr (6.33)</li>
</ul>
</div>
</div>
<p>
\[
{\bf J}_b = {\boldsymbol \nabla} \times {\bf M} = {\boldsymbol \nabla} \times (\chi_m {\bf H})
= \chi_m {\bf J}_f.
\label{Gr(6.33)}
\tag{JbchimJf}\label{JbchimJf}
\]
</p>
</div>
@@ -1684,7 +1750,7 @@ 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>