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Update 2022-02-09 22:41

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Jean-Sébastien
2022-02-09 22:41:42 +01:00
parent 3c40f5bfe8
commit f3c2446d19
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build/emsm_esm_fpo.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-09 Wed 07:31 -->
<!-- 2022-02-09 Wed 22:40 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -408,17 +408,13 @@ Table of contents
<li>
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
</li>
<li>
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
</li>
<li>
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
</li>
<li>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
</li>
<li>
@@ -430,29 +426,8 @@ Table of contents
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary>
<ul>
<li>
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
</li>
<li>
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
</li>
<li>
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
</li>
</ul>
</details>
</li>
<li>
@@ -1666,7 +1641,7 @@ V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \oint_{\cal S} d{\bf a}' ⋅ \frac{{\bf
\]
Interpretation: first terms is like contribution of a surface charge,
</p>
<div class="main div" id="orga0c2c2c">
<div class="main div" id="org6345609">
<p>
\[
\sigma_b({\bf r}) = {\bf P} ({\bf r}) \cdot \hat{\bf n}
@@ -1678,7 +1653,7 @@ Interpretation: first terms is like contribution of a surface charge,
<p>
and second term looks like contribution of a volume charge,
</p>
<div class="main div" id="org50b0298">
<div class="main div" id="org53483c6">
<p>
\[
\rho_b ({\bf r}) = -{\boldsymbol \nabla} \cdot {\bf P} ({\bf r})
@@ -1690,7 +1665,7 @@ and second term looks like contribution of a volume charge,
<p>
Using these definitions,
</p>
<div class="main div" id="org89e541d">
<div class="main div" id="org71e319e">
<p>
\[
V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \oint_{\cal S} d{\bf a}' ⋅ \frac{σ_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1709,7 +1684,7 @@ These {\bf bound charges} faithfully represent the object's sources for electric
</p>
<div class="example div" id="org6d1dc9b">
<div class="example div" id="orgea10cb1">
<p>
\paragraph{Example 4.2:} electric field produced by uniformly polarized sphere of radius \(R\).
\paragraph{Solution:} put \(z\) axis along \({\bf P}\). Since \({\bf P}\) is uniform, \(\rho_b = 0\).
@@ -1766,7 +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: 2022-02-09 Wed 07:31</p>
<p class="date">Created: 2022-02-09 Wed 22:40</p>
<p class="validation"></p>
</div>