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Update 2022-02-09 07:44

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Jean-Sébastien
2022-02-09 07:44:58 +01:00
parent 84531d125a
commit 3c40f5bfe8
209 changed files with 3663 additions and 1367 deletions
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build/emsm_esm_di_ld.html
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@@ -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_msm.html">Magnetostatics in matter&emsp;<small>[emsm.msm]</small></a></li><li>Up:&nbsp;<a href="emsm_esm_di.html">Dielectrics&emsp;<small>[emsm.esm.di]</small></a></li></ul><div id="outline-container-emsm_esm_di_ld" class="outline-5">
<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><a class="breadcrumb-link"href="emsm_esm_di.html">Dielectrics</a></li><li>Linear Dielectrics</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_msm.html">Magnetostatics in matter&emsp;<small>[emsm.msm]</small></a></li><li>Up:&nbsp;<a href="emsm_esm_di.html">Dielectrics&emsp;<small>[emsm.esm.di]</small></a></li></ul><div id="outline-container-emsm_esm_di_ld" class="outline-5">
<h5 id="emsm_esm_di_ld">Linear Dielectrics<a class="headline-permalink" href="./emsm_esm_di_ld.html#emsm_esm_di_ld"><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"/>
@@ -1630,7 +1630,7 @@ Table of contents
<p>
For many substances: polarization is proportional to field, if the latter isn't too strong:
</p>
<div class="main div" id="org7e24b64">
<div class="main div" id="org0c6bf2b">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1660,7 +1660,7 @@ In linear dielectrics:
\]
so
</p>
<div class="main div" id="org5a85a00">
<div class="main div" id="org355774c">
<p>
\[
{\bf D} = \varepsilon {\bf E}
@@ -1682,7 +1682,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}.
<div class="example div" id="org2569277">
<div class="example div" id="orga6bc510">
<p>
\paragraph{Example 4.5:} metal sphere of radius \(a\) carrying charge \(Q\), surrounded out to radius \(b\) by
a linear dielectric material of permittivity \(\varepsilon\). Find potential at center (relative to infinity).
@@ -1738,7 +1738,7 @@ of {\it e.g.} \({\bf P}\) would not vanish.
Only case where parallel works: space entirely filled with homogeneous linear dielectric.
</p>
<div class="example div" id="orgabbee42">
<div class="example div" id="org501f05d">
<p>
\paragraph{Example 4.6:} parallel-plate capacitor filled with insulating material of
dielectric constant \(\varepsilon_r\). What is the effect on the capacitance ?
@@ -1773,7 +1773,7 @@ If \(\rho = 0\), any net charge is on surface, potential then obeys Laplace.
<p>
Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr(4.26)},
</p>
<div class="main div" id="orgfd85680">
<div class="main div" id="org19119e6">
<p>
\[
\varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f
@@ -1785,7 +1785,7 @@ Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr
<p>
or in terms of the potential,
</p>
<div class="main div" id="org3294941">
<div class="main div" id="org2db8669">
<p>
\[
\varepsilon_{above} \frac{\partial V_{above}}{\partial n} -
@@ -1798,7 +1798,7 @@ or in terms of the potential,
<p>
Potential itself is continuous,
</p>
<div class="main div" id="org1881d42">
<div class="main div" id="org9779897">
<p>
\[
V_{above} = V_{below}
@@ -1810,7 +1810,7 @@ Potential itself is continuous,
<div class="example div" id="org197c783">
<div class="example div" id="orgea2ac3a">
<p>
\paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\).
Find electric field inside sphere.
@@ -1868,7 +1868,7 @@ Thus,
<div class="example div" id="org312cdc8">
<div class="example div" id="org4fcf560">
<p>
\paragraph{Example 4.8:} suppose region below \(z = 0\) is filled with uniform linear dielectric with susceptibility \(\chi_e\).
Calculate force on point charge \(q\) situated a distance \(d\) above origin.
@@ -1972,7 +1972,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\),
\]
Total work done:
</p>
<div class="main div" id="org1d22441">
<div class="main div" id="orgd18dfe7">
<p>
\[
W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E}
@@ -2061,10 +2061,21 @@ so like before but with the correct sign.
</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>