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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 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 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1620,13 +1624,13 @@ Table of contents
<div class="outline-text-5" id="text-emsm_esm_di_ld">
</div>
<div id="outline-container-emsm_esm_d_ld_sp" class="outline-6">
<h6 id="emsm_esm_d_ld_sp"><a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a></h6>
<div class="outline-text-6" id="text-emsm_esm_d_ld_sp">
<div id="outline-container-emsm_esm_di_ld_sp" class="outline-6">
<h6 id="emsm_esm_di_ld_sp"><a href="#emsm_esm_di_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a></h6>
<div class="outline-text-6" id="text-emsm_esm_di_ld_sp">
<p>
For many substances: polarization is proportional to field, if the latter isn't too strong:
</p>
<div class="main div" id="org5882cee">
<div class="main div" id="org7e24b64">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1656,7 +1660,7 @@ In linear dielectrics:
\]
so
</p>
<div class="main div" id="orga3558f5">
<div class="main div" id="org5a85a00">
<p>
\[
{\bf D} = \varepsilon {\bf E}
@@ -1678,7 +1682,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}.
<div class="example div" id="org2c914e3">
<div class="example div" id="org2569277">
<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).
@@ -1734,7 +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="orgfebd47e">
<div class="example div" id="orgabbee42">
<p>
\paragraph{Example 4.6:} parallel-plate capacitor filled with insulating material of
dielectric constant \(\varepsilon_r\). What is the effect on the capacitance ?
@@ -1769,7 +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="orgb605e6c">
<div class="main div" id="orgfd85680">
<p>
\[
\varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f
@@ -1781,7 +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="orgf35ca50">
<div class="main div" id="org3294941">
<p>
\[
\varepsilon_{above} \frac{\partial V_{above}}{\partial n} -
@@ -1794,7 +1798,7 @@ or in terms of the potential,
<p>
Potential itself is continuous,
</p>
<div class="main div" id="org5c553e0">
<div class="main div" id="org1881d42">
<p>
\[
V_{above} = V_{below}
@@ -1806,7 +1810,7 @@ Potential itself is continuous,
<div class="example div" id="orgf527756">
<div class="example div" id="org197c783">
<p>
\paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\).
Find electric field inside sphere.
@@ -1864,7 +1868,7 @@ Thus,
<div class="example div" id="orgaa2beb6">
<div class="example div" id="org312cdc8">
<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.
@@ -1968,7 +1972,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\),
\]
Total work done:
</p>
<div class="main div" id="org9a3cd32">
<div class="main div" id="org1d22441">
<p>
\[
W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E}
@@ -2059,7 +2063,7 @@ so like before but with the correct sign.
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</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>
</div>