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Jean-Sébastien
2022-02-21 10:35:02 +01:00
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<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-17 Thu 08:42 -->
<!-- 2022-02-21 Mon 10:33 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -602,11 +602,11 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
</li>
<li>
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
</li>
@@ -614,21 +614,12 @@ Table of contents
</details>
</li>
<li>
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
<details>
<summary>
</li>
<li>
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
</summary>
<ul>
<li>
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
</li>
</ul>
</details>
</li>
<li>
@@ -640,11 +631,15 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
</li>
<li>
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
</li>
<li>
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
</li>
@@ -661,6 +656,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
</li>
<li>
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
</li>
@@ -698,10 +697,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
</li>
<li>
<details>
<summary>
@@ -1435,7 +1430,7 @@ Table of contents
</li>
<li>
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
</li>
<li>
@@ -1597,24 +1592,61 @@ Table of contents
<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><span class="headline-id">ems.ms.vp.comp</span></h5>
<div class="outline-text-5" id="text-ems_ms_vp_comp">
\begin{tabular}{ll}
\mbox{Electrostatics:} \hspace{10mm}&amp;
$\begin{array}{ll}
{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0} \hspace{5mm} &amp; \mbox{Gauss's law} \\
{\boldsymbol \nabla} \times {\bf E} = 0 &amp; \mbox{[nameless]}
\end{array}$ \\ \\
\mbox{Magnetostatics:} &amp;
$\begin{array}{ll}
{\boldsymbol \nabla} \cdot {\bf B} = 0 &amp; \mbox{[nameless]} \\
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} &amp; \mbox{Ampère's law}
\end{array}$ \\ \\
\end{tabular}
<table>
<colgroup>
<col class="org-left">
<col class="org-left">
<col class="org-left">
<col class="org-left">
<col class="org-left">
</colgroup>
<tbody>
<tr>
<td class="org-left">Electrostatics</td>
<td class="org-left"> </td>
<td class="org-left">\({\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0}\)</td>
<td class="org-left"> </td>
<td class="org-left">Gauss's law</td>
</tr>
<tr>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">\({\boldsymbol \nabla} \times {\bf E} = 0\)</td>
<td class="org-left"> </td>
<td class="org-left">[nameless]</td>
</tr>
<tr>
<td class="org-left">Magnetostatics</td>
<td class="org-left"> </td>
<td class="org-left">\({\boldsymbol \nabla} \cdot {\bf B} = 0\)</td>
<td class="org-left"> </td>
<td class="org-left">[nameless]</td>
</tr>
<tr>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">\({\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J}\)</td>
<td class="org-left"> </td>
<td class="org-left">Ampère's law</td>
</tr>
</tbody>
</table>
</div>
</div>
<br><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ms_vp_me.html">Multipole Expansion of the Vector Potential&emsp;<small>[ems.ms.vp.me]</small></a></li><li>Next:&nbsp;<a href="ems_ms_vp_LC.html">The Levi-Civita Symbol&emsp;<small>[ems.ms.vp.LC]</small></a></li><li>Up:&nbsp;<a href="ems_ms_vp.html">The Vector Potential&emsp;<small>[ems.ms.vp]</small></a></li></ul>
<br>
<hr>
@@ -1630,7 +1662,7 @@ 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: 2022-02-17 Thu 08:42</p>
<p class="date">Created: 2022-02-21 Mon 10:33</p>
<p class="validation"></p>
</div>