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

Update 2022-02-09 22:41

Browse Source
This commit is contained in:
Jean-Sébastien
2022-02-09 22:41:42 +01:00
parent 3c40f5bfe8
commit f3c2446d19
208 changed files with 1583 additions and 12916 deletions
Download Patch File Download Diff File Expand all files Collapse all files
build/emsm_esm_di_ld.html
+13 -38
View File
@@ -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>
@@ -1630,7 +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="org0c6bf2b">
<div class="main div" id="orga3278d6">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1660,7 +1635,7 @@ In linear dielectrics:
\]
so
</p>
<div class="main div" id="org355774c">
<div class="main div" id="org78784fd">
<p>
\[
{\bf D} = \varepsilon {\bf E}
@@ -1682,7 +1657,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}.
<div class="example div" id="orga6bc510">
<div class="example div" id="org85c03d5">
<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 +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="org501f05d">
<div class="example div" id="orgc0d8c4c">
<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 +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="org19119e6">
<div class="main div" id="org738acac">
<p>
\[
\varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f
@@ -1785,7 +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="org2db8669">
<div class="main div" id="org6a5bb81">
<p>
\[
\varepsilon_{above} \frac{\partial V_{above}}{\partial n} -
@@ -1798,7 +1773,7 @@ or in terms of the potential,
<p>
Potential itself is continuous,
</p>
<div class="main div" id="org9779897">
<div class="main div" id="org00bd1e4">
<p>
\[
V_{above} = V_{below}
@@ -1810,7 +1785,7 @@ Potential itself is continuous,
<div class="example div" id="orgea2ac3a">
<div class="example div" id="orgf22ddc4">
<p>
\paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\).
Find electric field inside sphere.
@@ -1868,7 +1843,7 @@ Thus,
<div class="example div" id="org4fcf560">
<div class="example div" id="org3d34c22">
<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 +1947,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\),
\]
Total work done:
</p>
<div class="main div" id="orgd18dfe7">
<div class="main div" id="org4c9c303">
<p>
\[
W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E}
@@ -2074,7 +2049,7 @@ 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>