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Jean-Sébastien
2022-03-02 15:47:54 +01:00
parent ac1e628013
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-01 Tue 08:14 -->
<!-- 2022-03-02 Wed 15:45 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1625,14 +1625,14 @@ Table of contents
Nomenclature: as in electric case, we have bound currents, and everything else, which we call the <b>free current</b>.
Total current:
</p>
<div class="eqlabel" id="orga39b83a">
<div class="eqlabel" id="org57e3e26">
<p>
<a id="JbJf"></a><a href="./emsm_msm_H_A.html#JbJf"><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="orgc7c6653">
<div class="alteqlabels" id="org272e5cb">
<ul class="org-ul">
<li>Gr (6.17)</li>
</ul>
@@ -1652,15 +1652,15 @@ Ampère's law:
\]
so we can define
</p>
<div class="core div" id="org32c294e">
<div class="eqlabel" id="orgc06236c">
<div class="core div" id="orga2e1412">
<div class="eqlabel" id="org53f4990">
<p>
<a id="HBM"></a><a href="./emsm_msm_H_A.html#HBM"><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="org410c63d">
<div class="alteqlabels" id="orge72bef9">
<ul class="org-ul">
<li>Gr (6.18)</li>
</ul>
@@ -1679,15 +1679,15 @@ so we can define
<p>
and rewrite Ampère's law as
</p>
<div class="core div" id="org1ebd940">
<div class="eqlabel" id="org06d1eac">
<div class="core div" id="org7ea9009">
<div class="eqlabel" id="org19917b5">
<p>
<a id="curlHJf"></a><a href="./emsm_msm_H_A.html#curlHJf"><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="org7c7eb8e">
<div class="alteqlabels" id="org133cbf3">
<ul class="org-ul">
<li>Gr (6.19)</li>
</ul>
@@ -1706,15 +1706,15 @@ and rewrite Ampère's law as
<p>
or in integral form,
</p>
<div class="core div" id="orge1fd102">
<div class="eqlabel" id="orga535d4d">
<div class="core div" id="org7d4db58">
<div class="eqlabel" id="org8221106">
<p>
<a id="intHdl"></a><a href="./emsm_msm_H_A.html#intHdl"><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="org6d8451f">
<div class="alteqlabels" id="org86ffc5f">
<ul class="org-ul">
<li>Gr (6.20)</li>
</ul>
@@ -1735,9 +1735,9 @@ or in integral form,
rewrite Ampère's law in terms of free currents alone. Bound currents come along for the ride.
</p>
<div class="example div" id="org64362d6">
<div class="example div" id="org82ad7a0">
<p>
<b>Example</b>: copper rod
<b>Example: copper rod</b>
</p>
<p>
@@ -1754,14 +1754,14 @@ Bound currents antiparallel to \(I\) in bulk and parallel at surface. All curre
so \({\bf B}, {\bf M}, {\bf H}\) are circumferential. Apply integral form of Ampère's law with
radius \(s &lt; R\): \(H (2\pi s) = I_{f_{enc}} = I \frac{\pi s^2}{\pi R^2}\) so
</p>
<div class="eqlabel" id="org3874fab">
<div class="eqlabel" id="orgead6de3">
<p>
<a id="Hrod_in"></a><a href="./emsm_msm_H_A.html#Hrod_in"><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="org8615022">
<div class="alteqlabels" id="org95d4918">
<ul class="org-ul">
<li>Gr (6.21)</li>
</ul>
@@ -1776,14 +1776,14 @@ radius \(s &lt; R\): \(H (2\pi s) = I_{f_{enc}} = I \frac{\pi s^2}{\pi R^2}\) s
\]
Outside,
</p>
<div class="eqlabel" id="org2e8656f">
<div class="eqlabel" id="orga0a4526">
<p>
<a id="Hrod_out"></a><a href="./emsm_msm_H_A.html#Hrod_out"><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="orgfe04bd5">
<div class="alteqlabels" id="org4c6a005">
<ul class="org-ul">
<li>Gr (6.22)</li>
</ul>
@@ -1809,14 +1809,14 @@ There, \({\bf M} = 0\) so \({\bf B} = \mu_0 {\bf H}\).
Similarly to electric case: cannot assume that \({\bf H}\) is like \({\bf B}\).
\({\bf H}\) might have a divergence,
</p>
<div class="eqlabel" id="org1605cc8">
<div class="eqlabel" id="orgcec8c1f">
<p>
<a id="divH"></a><a href="./emsm_msm_H_A.html#divH"><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="org1693077">
<div class="alteqlabels" id="org3c06aa5">
<ul class="org-ul">
<li>Gr (6.23)</li>
</ul>
@@ -1877,14 +1877,14 @@ W_{mag} = \int_{all~space} d\tau \frac{1}{2} {\bf H} \cdot {\bf B}
<p>
Can rewrite BCs in terms of \({\bf H}\): from <a href="./emsm_msm_H_A.html#divH">divH</a>,
</p>
<div class="eqlabel" id="org9aec61c">
<div class="eqlabel" id="org93e0bea">
<p>
<a id="HdiscM"></a><a href="./emsm_msm_H_A.html#HdiscM"><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="orgf88a9a3">
<div class="alteqlabels" id="org8ee9ea6">
<ul class="org-ul">
<li>Gr (6.24)</li>
</ul>
@@ -1899,14 +1899,14 @@ H^{\perp}_{above} - H^{\perp}_{below} = -(M^{\perp}_{above} - M^{\perp}_{below})
<p>
while <a href="./emsm_msm_H_A.html#curlHJf">curlHJf</a> gives
</p>
<div class="eqlabel" id="org92fe64e">
<div class="eqlabel" id="org59d693a">
<p>
<a id="Hdisc"></a><a href="./emsm_msm_H_A.html#Hdisc"><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="org08361d0">
<div class="alteqlabels" id="org759b508">
<ul class="org-ul">
<li>Gr (6.25)</li>
</ul>
@@ -1951,7 +1951,7 @@ 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: 2022-03-01 Tue 08:14</p>
<p class="date">Created: 2022-03-02 Wed 15:45</p>
<p class="validation"></p>
</div>