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Update 2022-03-01 08:15

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Jean-Sébastien
2022-03-01 08:15:26 +01:00
parent ead639cf67
commit ac1e628013
194 changed files with 1320 additions and 1022 deletions
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build/ems_ms_BS.html
+16 -16
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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>
@@ -1625,18 +1625,18 @@ Table of contents
The magnetic field issuing from a steady surrent
is given experimentally (around 1820) by the
</p>
<div class="core div" id="orgf84cc6f">
<div class="core div" id="orgf3f2be1">
<p>
<b>Biot-Savart law</b>
</p>
<div class="eqlabel" id="org3281466">
<div class="eqlabel" id="orgd1bb68b">
<p>
<a id="BiotSavart"></a><a href="./ems_ms_BS.html#BiotSavart"><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="org7bf94e5">
<div class="alteqlabels" id="orgc933e6c">
<ul class="org-ul">
<li>FLS II (14.43)</li>
<li>Gr (5.34)</li>
@@ -1666,15 +1666,15 @@ with the <i>henry</i> \(H = kg ~m^2 / s^2 A^2\) being the unit for inductance.
<p>
For surface and volume density currents:
</p>
<div class="main div" id="org0fc8a2d">
<div class="eqlabel" id="org6473469">
<div class="main div" id="orgee80182">
<div class="eqlabel" id="orgc3e9918">
<p>
<a id="BiotSavart_s"></a><a href="./ems_ms_BS.html#BiotSavart_s"><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="org84dd95e">
<div class="alteqlabels" id="org9eee0f6">
</div>
@@ -1685,14 +1685,14 @@ For surface and volume density currents:
\tag{BiotSavart_s}\label{BiotSavart_s}
\]
</p>
<div class="eqlabel" id="org8947c4c">
<div class="eqlabel" id="org108f9a3">
<p>
<a id="BiotSavart_v"></a><a href="./ems_ms_BS.html#BiotSavart_v"><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="org75ae01b">
<div class="alteqlabels" id="orgcf3d52e">
</div>
@@ -1717,7 +1717,7 @@ The <b>superposition principle</b> applies here as well: a collection of curren
the vector sum of the fields generated by the individual currents.
</p>
<div class="example div" id="orgac81691">
<div class="example div" id="org958356a">
<p>
<b>Example: \({\bf B}\) from long straight wire</b>
</p>
@@ -1729,7 +1729,7 @@ the vector sum of the fields generated by the individual currents.
<p>
<b>Solution</b>:
\(dl {\bf I} \times ({\bf r} - {\bf r}')\) points out of the page, and has
magnitude \(dl' \sin \alpha = dl' \cos \theta\). But \(l' = r \tan \theta\) so \(dl' = \frac{r}{\cos^2 \theta} d\theta\),
magnitude \(dl' \cos \theta\). But \(l' = r \tan \theta\) so \(dl' = \frac{r}{\cos^2 \theta} d\theta\),
and \(r = |{\bf r} - {\bf r}'| \cos \theta\). Then,
</p>
@@ -1740,14 +1740,14 @@ B = \frac{\mu_0}{4\pi} I \int_{\theta_1}^{\theta_2} d\theta \cos \theta \frac{\c
\]
For infinite wire: \(\theta_1 = -\pi/2\), \(\theta_2 = \pi/2\), so
</p>
<div class="eqlabel" id="org72687b1">
<div class="eqlabel" id="orgf96305e">
<p>
<a id="Bwire1"></a><a href="./ems_ms_BS.html#Bwire1"><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="org772ccc6">
<div class="alteqlabels" id="org29f9b1d">
<ul class="org-ul">
<li>Gr (5.38)</li>
</ul>
@@ -1776,7 +1776,7 @@ f = \frac{\mu_0}{2\pi} \frac{I_1 I_2}{d}
(like currents attract).
</p>
<div class="example div" id="org433e75f">
<div class="example div" id="org575e184">
<p>
<b>Example: \({\bf B}\) above a circular loop</b>
</p>
@@ -1792,7 +1792,7 @@ carrying a steady counterclockwise current \(I\).
<p>
\[
B(z) = \frac{\mu_0 I}{4\pi} \int dl' \frac{\cos \theta}{|{\bf r} - {\bf r}'|}
B(z) = \frac{\mu_0 I}{4\pi} \int dl' \frac{\cos \theta}{|{\bf r} - {\bf r}'|^2}
= \frac{\mu_0 I}{4\pi} \frac{\cos \theta}{R^2 + z^2} \int dl' = \frac{\mu_0 I}{2} \frac{R^2}{(R^2 + z^2)^{3/2}}
\]
(since \(\cos \theta = R/\sqrt{R^2 + z^2}\)).
@@ -1820,7 +1820,7 @@ 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>