jscaux/pqed_html
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update 2022-02-09 07:44

Browse Source
This commit is contained in:
Jean-Sébastien
2022-02-09 07:44:58 +01:00
parent 84531d125a
commit 3c40f5bfe8
209 changed files with 3663 additions and 1367 deletions
Download Patch File Download Diff File Expand all files Collapse all files
build/emsm_esm_fpo.html
+20 -9
View File
@@ -1,7 +1,7 @@
<!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="emsm_esm_di.html">Dielectrics&emsp;<small>[emsm.esm.di]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_fpo_pibc.html">Physical Interpretation of Bound Charges&emsp;<small>[emsm.esm.fpo.pibc]</small></a></li><li>Up:&nbsp;<a href="emsm_esm.html">Electrostatics in matter&emsp;<small>[emsm.esm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emsm.html">Electromagnetostatics in matter</a></li><li><a class="breadcrumb-link"href="emsm_esm.html">Electrostatics in matter</a></li><li>The Field of a Polarized Object</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_esm_di.html">Dielectrics&emsp;<small>[emsm.esm.di]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_fpo_pibc.html">Physical Interpretation of Bound Charges&emsp;<small>[emsm.esm.fpo.pibc]</small></a></li><li>Up:&nbsp;<a href="emsm_esm.html">Electrostatics in matter&emsp;<small>[emsm.esm]</small></a></li></ul>
<h4 id="emsm_esm_fpo">The Field of a Polarized Object<a class="headline-permalink" href="./emsm_esm_fpo.html#emsm_esm_fpo"><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"/>
@@ -1666,7 +1666,7 @@ 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="org0db0ed1">
<div class="main div" id="orga0c2c2c">
<p>
\[
\sigma_b({\bf r}) = {\bf P} ({\bf r}) \cdot \hat{\bf n}
@@ -1678,7 +1678,7 @@ 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="orgf6835b7">
<div class="main div" id="org50b0298">
<p>
\[
\rho_b ({\bf r}) = -{\boldsymbol \nabla} \cdot {\bf P} ({\bf r})
@@ -1690,7 +1690,7 @@ and second term looks like contribution of a volume charge,
<p>
Using these definitions,
</p>
<div class="main div" id="orgaff40e6">
<div class="main div" id="org89e541d">
<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 +1709,7 @@ These {\bf bound charges} faithfully represent the object's sources for electric
</p>
<div class="example div" id="orgd5d2cc0">
<div class="example div" id="org6d1dc9b">
<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, \(\rho_b = 0\).
@@ -1753,10 +1753,21 @@ where the total dipole moment is simply the integral over the polarization,
<li><a href="emsm_esm_fpo_fid.html">The Field Inside a Dielectric</a><span class="headline-id">emsm.esm.fpo.fid</span></li>
</ul>
<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>