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Update 2022-02-14 06:33

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Jean-Sébastien
2022-02-14 06:33:37 +01:00
parent f8446c1405
commit 4cfe8cef59
204 changed files with 1839 additions and 941 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>
<!-- 2022-02-10 Thu 08:32 -->
<!-- 2022-02-13 Sun 21:20 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1605,7 +1605,7 @@ 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="org6ac9560">
<div class="main div" id="org795f182">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1635,7 +1635,7 @@ In linear dielectrics:
\]
so
</p>
<div class="main div" id="orgd8cb3ab">
<div class="main div" id="orgb295c77">
<p>
\[
{\bf D} = \varepsilon {\bf E}
@@ -1657,7 +1657,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}.
<div class="example div" id="org29b4ca7">
<div class="example div" id="orgf14e981">
<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).
@@ -1713,7 +1713,7 @@ 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="orgd710a3a">
<div class="example div" id="org4613192">
<p>
\paragraph{Example 4.6:} parallel-plate capacitor filled with insulating material of
dielectric constant \(\varepsilon_r\). What is the effect on the capacitance ?
@@ -1748,7 +1748,7 @@ 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="org78d2d1f">
<div class="main div" id="org52f5ae7">
<p>
\[
\varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f
@@ -1760,7 +1760,7 @@ 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="orgc1815c1">
<div class="main div" id="org7daea21">
<p>
\[
\varepsilon_{above} \frac{\partial V_{above}}{\partial n} -
@@ -1773,7 +1773,7 @@ or in terms of the potential,
<p>
Potential itself is continuous,
</p>
<div class="main div" id="orgdda22c8">
<div class="main div" id="orgfab7e78">
<p>
\[
V_{above} = V_{below}
@@ -1785,7 +1785,7 @@ Potential itself is continuous,
<div class="example div" id="org6d6fcc0">
<div class="example div" id="org0f118b9">
<p>
\paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\).
Find electric field inside sphere.
@@ -1843,7 +1843,7 @@ Thus,
<div class="example div" id="org1f1cffb">
<div class="example div" id="orgc38f4b8">
<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.
@@ -1947,7 +1947,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\),
\]
Total work done:
</p>
<div class="main div" id="orgafaaf7a">
<div class="main div" id="orgacdadfe">
<p>
\[
W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E}
@@ -2036,6 +2036,8 @@ so like before but with the correct sign.
</div>
<br><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>
<br>
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
@@ -2049,7 +2051,7 @@ 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: 2022-02-10 Thu 08:32</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="validation"></p>
</div>