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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/ems_ms_dcB_BS.html
+14 -10
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1646,7 +1650,7 @@ we get
But \({\bf J}\) depends only on \({\bf r}'\) so \({\boldsymbol \nabla} \times {\bf J} ({\bf r}') = 0\), and since
the curl of a gradient always vanishes, we obtain
</p>
<div class="core div" id="orgdf5fc3e">
<div class="core div" id="org8f6dda2">
<p>
\[
{\boldsymbol \nabla} \cdot {\bf B} = 0
@@ -1714,7 +1718,7 @@ at infinity), and in the third step we have used the assumption of steady-state
<p>
We thus obtain in total
</p>
<div class="core div" id="org3da2f25">
<div class="core div" id="orga0245b5">
<p>
<b>Ampère's law</b>
\[
@@ -1731,7 +1735,7 @@ We thus obtain in total
\]
so
</p>
<div class="core div" id="org5aa5f70">
<div class="core div" id="orgdbc9d47">
<p>
\[
\oint_{\cal P} {\bf B} \cdot d{\bf l} = \mu_0 I_{enc} \hspace{2cm}
@@ -1753,7 +1757,7 @@ Sign ambiguity: resolved by right-hand rule as usual.
Ampère's law in magnetostatics takes a parallel role to Gauss's law in electrostatics.
</p>
<div class="example div" id="orgc846872">
<div class="example div" id="orge2cd1ba">
<p>
\paragraph{Example 5.7:} same as Example 5.5, but now with Ampère.
\paragraph{Solution:} by symmetry, \({\bf B}\) is circumferential and can only depend on \(s\). Then,
@@ -1765,7 +1769,7 @@ choosing an amperian loop at a fixed radius \(s\), we get
</div>
<div class="example div" id="org1c375de">
<div class="example div" id="orgf268569">
<p>
\paragraph{Example 5.8:} uniform surface current \({\bf K} = K \hat{\bf x}\) flowing in \(xy\) plane.
\paragraph{Solution:} Biot-Savart: \({\bf B}\) must be perpendicular to \({\bf K}\). Intuition:
@@ -1782,7 +1786,7 @@ and along \(\hat{\bf y}\) for \(z &lt; 0\). Amperian loop of width \(l\) punchi
</div>
<div class="example div" id="orgc3e6b98">
<div class="example div" id="org5e0a2eb">
<p>
\paragraph{Example 5.9:} solenoid along \(\hat{\bf z}\), wire carrying current \(I\) doing \(n\) turns per unit length on cylinder of radius \(R\).
\paragraph{Solution:} by symmetry, \({\bf B}\) must be along axis of solenoid. Outside: infinitely far away, \({\bf B}\) must vanish.
@@ -1803,7 +1807,7 @@ Amperian loop of length \(l\), half-inside and half-outside:
i) infinite straight lines, ii) infinite planes, iii) infinite solenoids, iv) toroids.
</p>
<div class="example div" id="orgb302b1e">
<div class="example div" id="org2a86e5f">
<p>
\paragraph{Example 5.10:} toroidal coil (no matter the shape, as long as it is rotationally symmetric).
\paragraph{Solution:} magnetic field is circumferential everywhere. Outside coil, field again zero.
@@ -1823,7 +1827,7 @@ Amperian loop half inside, half outside:
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</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>
</div>