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Update 2022-02-09 07:44

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Jean-Sébastien
2022-02-09 07:44:58 +01:00
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build/emsm_msm_fmo_bc.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 17:21 -->
<!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1616,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_msm_fmo.html">The Field of a Magnetized Object&emsp;<small>[emsm.msm.fmo]</small></a></li><li>Next:&nbsp;<a href="emsm_msm_fmo_pibc.html">Physical Interpretation of Bound Currents&emsp;<small>[emsm.msm.fmo.pibc]</small></a></li><li>Up:&nbsp;<a href="emsm_msm_fmo.html">The Field of a Magnetized Object&emsp;<small>[emsm.msm.fmo]</small></a></li></ul><div id="outline-container-emsm_msm_fmo_bc" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emsm.html">Electromagnetostatics in matter</a></li><li><a class="breadcrumb-link"href="emsm_msm.html">Magnetostatics in matter</a></li><li><a class="breadcrumb-link"href="emsm_msm_fmo.html">The Field of a Magnetized Object</a></li><li>Bound Currents</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_msm_fmo.html">The Field of a Magnetized Object&emsp;<small>[emsm.msm.fmo]</small></a></li><li>Next:&nbsp;<a href="emsm_msm_fmo_pibc.html">Physical Interpretation of Bound Currents&emsp;<small>[emsm.msm.fmo.pibc]</small></a></li><li>Up:&nbsp;<a href="emsm_msm_fmo.html">The Field of a Magnetized Object&emsp;<small>[emsm.msm.fmo]</small></a></li></ul><div id="outline-container-emsm_msm_fmo_bc" class="outline-5">
<h5 id="emsm_msm_fmo_bc">Bound Currents<a class="headline-permalink" href="./emsm_msm_fmo_bc.html#emsm_msm_fmo_bc"><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"/>
@@ -1633,7 +1633,7 @@ For a single dipole: refer to \ref{Gr(5.83)} (vector potential of single dipole
For a chunk of material with local magnetization \({\bf M} ({\bf r})\),
by the principle of superposition we thus have:
</p>
<div class="main div" id="orge334af5">
<div class="main div" id="orgb364767">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} \int_{\cal V} d\tau' ~\frac{{\bf M} ({\bf r}') \times ({\bf r} - {\bf r}')}{|{\bf r} - {\bf r}'|^3}
@@ -1675,7 +1675,7 @@ Problem 1.61 b) (p.56): leads to
\]
Reinterpretation: first term: potential from volume current,
</p>
<div class="main div" id="org6918802">
<div class="main div" id="org9e75531">
<p>
\[
{\bf J}_b = {\boldsymbol \nabla} \times {\bf M}
@@ -1687,7 +1687,7 @@ Reinterpretation: first term: potential from volume current,
<p>
second term: potential from surface current,
</p>
<div class="main div" id="org4df5f2f">
<div class="main div" id="org8ca26d2">
<p>
\[
{\bf K}_b = {\bf M} \times \hat{\bf n}
@@ -1699,7 +1699,7 @@ second term: potential from surface current,
<p>
With these definitions,
</p>
<div class="main div" id="orge6fb0a7">
<div class="main div" id="orgd150a70">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} ∫_{\cal V} dτ' \frac{{\bf J}_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1720,7 +1720,7 @@ in the volume and surface of the material.
<div class="example div" id="org61adab0">
<div class="example div" id="orgf06e27d">
<p>
\paragraph{Example 6.1:} find field of uniformly magnetized sphere.
\paragraph{Solution:} put z axis along \({\bf M}\).
@@ -1751,10 +1751,21 @@ inside sphere, whereas outside: pure dipole field, with
<hr><div id="postamble" class="status">
<hr>
<div class="license">
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target="_blank" class="m-2">
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src="https://licensebuttons.net/l/by/4.0/80x15.png"/>
</a>
Except where otherwise noted, all content is licensed under a
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
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: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"></p>
</div>