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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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<!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="ems_ms_BS.html">Steady Currents: the Biot-Savart Law&emsp;<small>[ems.ms.BS]</small></a></li><li>Next:&nbsp;<a href="ems_ms_dcB.html">Divergence and Curl of \({\bf B}\)&emsp;<small>[ems.ms.dcB]</small></a></li><li>Up:&nbsp;<a href="ems_ms_BS.html">Steady Currents: the Biot-Savart Law&emsp;<small>[ems.ms.BS]</small></a></li></ul><div id="outline-container-ems_ms_BS_sc" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li><a class="breadcrumb-link"href="ems_ms.html">Magnetostatics</a></li><li><a class="breadcrumb-link"href="ems_ms_BS.html">Steady Currents: the Biot-Savart Law</a></li><li>The Magnetic Field issuing from a Steady Current</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ms_BS.html">Steady Currents: the Biot-Savart Law&emsp;<small>[ems.ms.BS]</small></a></li><li>Next:&nbsp;<a href="ems_ms_dcB.html">Divergence and Curl of \({\bf B}\)&emsp;<small>[ems.ms.dcB]</small></a></li><li>Up:&nbsp;<a href="ems_ms_BS.html">Steady Currents: the Biot-Savart Law&emsp;<small>[ems.ms.BS]</small></a></li></ul><div id="outline-container-ems_ms_BS_sc" class="outline-5">
<h5 id="ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current<a class="headline-permalink" href="./ems_ms_BS_sc.html#ems_ms_BS_sc"><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"/>
@@ -1625,7 +1625,7 @@ Table of contents
<p>
This is given experimentally (around 1820) by the
</p>
<div class="core div" id="org420384a">
<div class="core div" id="org788e7e2">
<p>
{\bf Biot-Savart law}
\[
@@ -1647,7 +1647,7 @@ with the {\it henry} \(H = kg m^2 / s^2 A^2\) being the unit for inductance.
<p>
For surface and volume density currents:
</p>
<div class="main div" id="org09e6a02">
<div class="main div" id="org8dab1d8">
<p>
\[
{\bf B} ({\bf r}) = \frac{\mu_0}{4\pi} \int da' \frac{{\bf K} ({\bf r}') \times ({\bf r} - {\bf r}')}{|{\bf r} - {\bf r}'|^3},
@@ -1669,7 +1669,7 @@ The {\bf superposition principle} applies here as well: collection of currents
the vector sum of the fields generated by the individual currents.
</p>
<div class="example div" id="org8a3ac4c">
<div class="example div" id="org4f56ddc">
<p>
\paragraph{Example 5.5:} find \({\bf B}\) a distance \(s\) from a long straight wire carrying steady current \(I\).
\paragraph{Solution:} {\bf Gr Fig 5.18}:
@@ -1699,7 +1699,7 @@ f = \frac{\mu_0}{2\pi} \frac{I_1 I_2}{d}
(like currents attract).
</p>
<div class="example div" id="orgd6bf182">
<div class="example div" id="org80d2089">
<p>
\paragraph{Example 5.6:} find {\bf B} a distance \(z\) above the center of a circular loop of radius \(R\),
carrying a steady counterclockwise current \(I\).
@@ -1717,10 +1717,21 @@ carrying a steady counterclockwise current \(I\).
</div>
<hr><div id="postamble" class="status">
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank" class="m-2">
<img alt="Creative Commons License" style="border-width:0"
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>