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Update 2022-03-01 08:15

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Jean-Sébastien
2022-03-01 08:15:26 +01:00
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commit ac1e628013
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build/emsm_msm_m_fdi.html
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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>
@@ -1624,30 +1624,60 @@ Table of contents
<p>
Torque on magnetic dipole:
</p>
<div class="core div" id="orgbfd8f14">
<div class="core div" id="org970f504">
<div class="eqlabel" id="org46270e7">
<p>
<a id="NmB"></a><a href="./emsm_msm_m_fdi.html#NmB"><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="org4beb1cd">
<ul class="org-ul">
<li>Gr (6.1)</li>
</ul>
</div>
</div>
<p>
\[
{\bf N} = {\bf m} \times {\bf B}
\label{Gr(6.1)}
\]
{\bf N} = {\bf m} \times {\bf B}
\tag{NmB}\label{NmB}
\]
</p>
</div>
<p>
Tends to align magnetic dipoles with field. Accounts for paramagnetism.
Exact for extended dipole in uniform field, or for point dipole in non-uniform field.
Similar to electric analogue, \ref{Gr(4.4)}, \({\bf N} = {\bf p} \times {\bf E}\).
Similar to electric analogue, <a href="./emsm_esm_mE_o.html#di_N">di_N</a>, \({\bf N} = {\bf p} \times {\bf E}\).
</p>
<p>
In a non-uniform field: (to be done in Problem 6.4):
In a non-uniform field:
</p>
<div class="main div" id="orgf1c66bf">
<div class="main div" id="org8f7a1e1">
<div class="eqlabel" id="org2e3369f">
<p>
<a id="FgradmB"></a><a href="./emsm_msm_m_fdi.html#FgradmB"><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="orge5458ea">
<ul class="org-ul">
<li>Gr (6.3)</li>
</ul>
</div>
</div>
<p>
\[
{\bf F} = {\boldsymbol \nabla} ({\bf m} \cdot {\bf B})
\label{Gr(6.3)}
\]
{\bf F} = {\boldsymbol \nabla} ({\bf m} \cdot {\bf B})
\tag{FgradmB}\label{FgradmB}
\]
</p>
</div>
@@ -1671,7 +1701,7 @@ 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>