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Jean-Sébastien
2022-03-24 08:43:21 +01:00
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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>
@@ -1617,14 +1617,14 @@ 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="org2f67ed9">
<div class="eqlabel" id="orgf612a79">
<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="org8bc9595">
<div class="alteqlabels" id="orgd462050">
<ul class="org-ul">
<li>Gr (6.17)</li>
</ul>
@@ -1644,15 +1644,15 @@ Ampère's law:
\]
so we can define
</p>
<div class="core div" id="org1215d01">
<div class="eqlabel" id="orgd5d9468">
<div class="core div" id="orgb005d3f">
<div class="eqlabel" id="orge90374d">
<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="org9ba5a4d">
<div class="alteqlabels" id="org7acbd07">
<ul class="org-ul">
<li>Gr (6.18)</li>
</ul>
@@ -1671,15 +1671,15 @@ so we can define
<p>
and rewrite Ampère's law as
</p>
<div class="core div" id="org18518e4">
<div class="eqlabel" id="orga0d403e">
<div class="core div" id="org498380a">
<div class="eqlabel" id="orgacd7c31">
<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="orgec3bba4">
<div class="alteqlabels" id="org1a7220e">
<ul class="org-ul">
<li>Gr (6.19)</li>
</ul>
@@ -1698,15 +1698,15 @@ and rewrite Ampère's law as
<p>
or in integral form,
</p>
<div class="core div" id="org288c4e9">
<div class="eqlabel" id="orgccd63b9">
<div class="core div" id="org77499d2">
<div class="eqlabel" id="orgf374008">
<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="org9025220">
<div class="alteqlabels" id="org9cbba67">
<ul class="org-ul">
<li>Gr (6.20)</li>
</ul>
@@ -1727,7 +1727,7 @@ 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="org2556e80">
<div class="example div" id="orgec3bc1c">
<p>
<b>Example: copper rod</b>
</p>
@@ -1746,14 +1746,14 @@ 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="orga2d5f0f">
<div class="eqlabel" id="org645df4c">
<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="org6c30162">
<div class="alteqlabels" id="orgd07686f">
<ul class="org-ul">
<li>Gr (6.21)</li>
</ul>
@@ -1768,14 +1768,14 @@ 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="org3469141">
<div class="eqlabel" id="org01a6ad4">
<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="org617ce83">
<div class="alteqlabels" id="org8d46f2c">
<ul class="org-ul">
<li>Gr (6.22)</li>
</ul>
@@ -1801,14 +1801,14 @@ 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="org9d34023">
<div class="eqlabel" id="org75b7450">
<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="orgd156a25">
<div class="alteqlabels" id="org4360dd3">
<ul class="org-ul">
<li>Gr (6.23)</li>
</ul>
@@ -1869,14 +1869,14 @@ 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="orge31639d">
<div class="eqlabel" id="org0d19976">
<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="orga7ad559">
<div class="alteqlabels" id="org23f8b3d">
<ul class="org-ul">
<li>Gr (6.24)</li>
</ul>
@@ -1891,14 +1891,14 @@ 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="org8258597">
<div class="eqlabel" id="orgb5a3e26">
<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="org086a72c">
<div class="alteqlabels" id="org43a8e56">
<ul class="org-ul">
<li>Gr (6.25)</li>
</ul>
@@ -1943,7 +1943,7 @@ 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>