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Update 2022-02-14 06:33

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Jean-Sébastien
2022-02-14 06:33:37 +01:00
parent f8446c1405
commit 4cfe8cef59
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build/emsm_msm_fmo_bc.html
+9 -7
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-10 Thu 08:32 -->
<!-- 2022-02-13 Sun 21:20 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1608,7 +1608,7 @@ 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="org1a25112">
<div class="main div" id="org86bd6f7">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} \int_{\cal V} d\tau' ~\frac{{\bf M} ({\bf r}') \times ({\bf r} - {\bf r}')}{|{\bf r} - {\bf r}'|^3}
@@ -1650,7 +1650,7 @@ Problem 1.61 b) (p.56): leads to
\]
Reinterpretation: first term: potential from volume current,
</p>
<div class="main div" id="org6bf98e0">
<div class="main div" id="org2d491ac">
<p>
\[
{\bf J}_b = {\boldsymbol \nabla} \times {\bf M}
@@ -1662,7 +1662,7 @@ Reinterpretation: first term: potential from volume current,
<p>
second term: potential from surface current,
</p>
<div class="main div" id="org78d77b5">
<div class="main div" id="org67395f8">
<p>
\[
{\bf K}_b = {\bf M} \times \hat{\bf n}
@@ -1674,7 +1674,7 @@ second term: potential from surface current,
<p>
With these definitions,
</p>
<div class="main div" id="org2c27e9b">
<div class="main div" id="org2145099">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} ∫_{\cal V} dτ' \frac{{\bf J}_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1695,7 +1695,7 @@ in the volume and surface of the material.
<div class="example div" id="orgc52afa7">
<div class="example div" id="org6d7ec15">
<p>
\paragraph{Example 6.1:} find field of uniformly magnetized sphere.
\paragraph{Solution:} put z axis along \({\bf M}\).
@@ -1726,6 +1726,8 @@ inside sphere, whereas outside: pure dipole field, with
<br><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>
<br>
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
@@ -1739,7 +1741,7 @@ 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: 2022-02-10 Thu 08:32</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="validation"></p>
</div>