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

Update 2022-02-09 07:44

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
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

21
build/a.html
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>Next:&nbsp;<a href="a_l.html">Literature&emsp;<small>[a.l]</small></a></li></ul>
<ul class="breadcrumbs"><li>Appendices</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="a_l.html">Literature&emsp;<small>[a.l]</small></a></li></ul>
<h2 id="a">Appendices<a class="headline-permalink" href="./a.html#a"><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"/>
@ -1631,10 +1631,21 @@ Table of contents
<li><a href="a_l.html">Literature</a><span class="headline-id">a.l</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>

21
build/a_l.html
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="a.html">Appendices&emsp;<small>[a]</small></a></li><li>Next:&nbsp;<a href="c.html">Compendium&emsp;<small>[c]</small></a></li><li>Up:&nbsp;<a href="a.html">Appendices&emsp;<small>[a]</small></a></li></ul><div id="outline-container-a_l" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="a.html">Appendices</a></li><li>Literature</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="a.html">Appendices&emsp;<small>[a]</small></a></li><li>Next:&nbsp;<a href="c.html">Compendium&emsp;<small>[c]</small></a></li><li>Up:&nbsp;<a href="a.html">Appendices&emsp;<small>[a]</small></a></li></ul><div id="outline-container-a_l" class="outline-3">
<h3 id="a_l">Literature<a class="headline-permalink" href="./a_l.html#a_l"><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"/>
@ -1714,10 +1714,21 @@ Wiley, 1986 [2nd edition]
</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>

21
build/c.html
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>Next:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li>Compendium</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h2 id="c">Compendium<a class="headline-permalink" href="./c.html#c"><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"/>
@ -1631,10 +1631,21 @@ Table of contents
<li><a href="c_m.html">Mathematics</a><span class="headline-id">c.m</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>

21
build/c_m.html
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="c.html">Compendium&emsp;<small>[c]</small></a></li><li>Next:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li><li>Up:&nbsp;<a href="c.html">Compendium&emsp;<small>[c]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li>Mathematics</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c.html">Compendium&emsp;<small>[c]</small></a></li><li>Next:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li><li>Up:&nbsp;<a href="c.html">Compendium&emsp;<small>[c]</small></a></li></ul>
<h3 id="c_m">Mathematics<a class="headline-permalink" href="./c_m.html#c_m"><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"/>
@ -1637,10 +1637,21 @@ Table of contents
<li><a href="c_m_uf.html">Useful Formulas</a><span class="headline-id">c.m.uf</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>

21
build/c_m_cs.html
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="c_m_ic_ip.html">Integration by Parts&emsp;<small>[c.m.ic.ip]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Coordinate Systems</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_ip.html">Integration by Parts&emsp;<small>[c.m.ic.ip]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_cs">Coordinate Systems<a class="headline-permalink" href="./c_m_cs.html#c_m_cs"><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"/>
@ -1633,10 +1633,21 @@ Table of contents
<li><a href="c_m_cs_hyp.html">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</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>

33
build/c_m_cs_cyl.html
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="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_cs.html">Coordinate Systems</a></li><li>Cylindrical Coordinates</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5">
<h5 id="c_m_cs_cyl">Cylindrical Coordinates<a class="headline-permalink" href="./c_m_cs_cyl.html#c_m_cs_cyl"><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"/>
@ -1668,14 +1668,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
<h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
<div class="eqlabel" id="orgc4b6bac">
<div class="eqlabel" id="org397e9ce">
<p>
<a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><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"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgdcdbcb4">
<div class="alteqlabels" id="org3648e8a">
<ul class="org-ul">
<li>Gr4(1.79)</li>
</ul>
@ -1696,14 +1696,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_div">
<div class="eqlabel" id="orgf9d0262">
<div class="eqlabel" id="orgb76ebc0">
<p>
<a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><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"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgd456be1">
<div class="alteqlabels" id="orgc052c68">
<ul class="org-ul">
<li>Gr4(2.21)</li>
</ul>
@ -1724,14 +1724,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
<div class="eqlabel" id="orgeb922d3">
<div class="eqlabel" id="orgaaf2c4a">
<p>
<a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><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"/>
</svg></a>
</p>
<div class="alteqlabels" id="org66ae846">
<div class="alteqlabels" id="orgcf0b798">
<ul class="org-ul">
<li>Gr4(2.21)</li>
</ul>
@ -1765,10 +1765,21 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<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>

21
build/c_m_cs_hyp.html
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="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Next:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_hyp" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_cs.html">Coordinate Systems</a></li><li>Hyperbolic Coordinates</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Next:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_hyp" class="outline-5">
<h5 id="c_m_cs_hyp">Hyperbolic Coordinates<a class="headline-permalink" href="./c_m_cs_hyp.html#c_m_cs_hyp"><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"/>
@ -1626,10 +1626,21 @@ Table of contents
</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>

21
build/c_m_cs_sph.html
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="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_cs.html">Coordinate Systems</a></li><li>Spherical Coordinates</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5">
<h5 id="c_m_cs_sph">Spherical Coordinates<a class="headline-permalink" href="./c_m_cs_sph.html#c_m_cs_sph"><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"/>
@ -1739,10 +1739,21 @@ Infinitesimal surface element: depends on situation.
<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>

21
build/c_m_dc.html
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="c_m_va_pds.html">Position, Displacement and Separation Vectors&emsp;<small>[c.m.va.pds]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_g.html">Gradient&emsp;<small>[c.m.dc.g]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Differential Calculus</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va_pds.html">Position, Displacement and Separation Vectors&emsp;<small>[c.m.va.pds]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_g.html">Gradient&emsp;<small>[c.m.dc.g]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_dc">Differential Calculus<a class="headline-permalink" href="./c_m_dc.html#c_m_dc"><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"/>
@ -1636,10 +1636,21 @@ Table of contents
<li><a href="c_m_dc_d2.html">Second Derivatives</a><span class="headline-id">c.m.dc.d2</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>

21
build/c_m_dc_curl.html
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="c_m_dc_div.html">The Divergence&emsp;<small>[c.m.dc.div]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_curl" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>The Curl</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_div.html">The Divergence&emsp;<small>[c.m.dc.div]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_curl" class="outline-5">
<h5 id="c_m_dc_curl">The Curl<a class="headline-permalink" href="./c_m_dc_curl.html#c_m_dc_curl"><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"/>
@ -1638,10 +1638,21 @@ v_x &amp; v_y &amp; v_z \end{array} \right| \nonumber \\
<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>

51
build/c_m_dc_d2.html
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="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Next:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Second Derivatives</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Next:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
<h5 id="c_m_dc_d2">Second Derivatives<a class="headline-permalink" href="./c_m_dc_d2.html#c_m_dc_d2"><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"/>
@ -1624,9 +1624,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2">
</div>
<div id="outline-container-org5fd48d1" class="outline-6">
<h6 id="org5fd48d1"><a href="#org5fd48d1">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-org5fd48d1">
<div id="outline-container-orga13f3ad" class="outline-6">
<h6 id="orga13f3ad"><a href="#orga13f3ad">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orga13f3ad">
<p>
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
@ -1635,36 +1635,36 @@ given by the Laplacian of the corresponding vector elements.
</div>
</div>
<div id="outline-container-org41a3448" class="outline-6">
<h6 id="org41a3448"><a href="#org41a3448">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org41a3448">
<div id="outline-container-orgf350618" class="outline-6">
<h6 id="orgf350618"><a href="#orgf350618">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-orgf350618">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org6c4b5a7" class="outline-6">
<h6 id="org6c4b5a7"><a href="#org6c4b5a7">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org6c4b5a7">
<div id="outline-container-orgb23671d" class="outline-6">
<h6 id="orgb23671d"><a href="#orgb23671d">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-orgb23671d">
<p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p>
</div>
</div>
<div id="outline-container-org68b62ab" class="outline-6">
<h6 id="org68b62ab"><a href="#org68b62ab">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org68b62ab">
<div id="outline-container-org0373292" class="outline-6">
<h6 id="org0373292"><a href="#org0373292">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org0373292">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org62690be" class="outline-6">
<h6 id="org62690be"><a href="#org62690be">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org62690be">
<div id="outline-container-org21d697e" class="outline-6">
<h6 id="org21d697e"><a href="#org21d697e">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org21d697e">
<p>
\[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@ -1676,10 +1676,21 @@ This always vanishes.
</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>

21
build/c_m_dc_del.html
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="c_m_dc_g.html">Gradient&emsp;<small>[c.m.dc.g]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_div.html">The Divergence&emsp;<small>[c.m.dc.div]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_del" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>The \({\boldsymbol \nabla}\) Operator</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_g.html">Gradient&emsp;<small>[c.m.dc.g]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_div.html">The Divergence&emsp;<small>[c.m.dc.div]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_del" class="outline-5">
<h5 id="c_m_dc_del">The \({\boldsymbol \nabla}\) Operator<a class="headline-permalink" href="./c_m_dc_del.html#c_m_dc_del"><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"/>
@ -1637,10 +1637,21 @@ The <b>del/grad/nabla operator</b> is defined as
<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>

21
build/c_m_dc_div.html
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="c_m_dc_del.html">The \({\boldsymbol \nabla}\) Operator&emsp;<small>[c.m.dc.del]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_curl.html">The Curl&emsp;<small>[c.m.dc.curl]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_div" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>The Divergence</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_del.html">The \({\boldsymbol \nabla}\) Operator&emsp;<small>[c.m.dc.del]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_curl.html">The Curl&emsp;<small>[c.m.dc.curl]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_div" class="outline-5">
<h5 id="c_m_dc_div">The Divergence<a class="headline-permalink" href="./c_m_dc_div.html#c_m_dc_div"><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"/>
@ -1634,10 +1634,21 @@ Table of contents
<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>

21
build/c_m_dc_g.html
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="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_del.html">The \({\boldsymbol \nabla}\) Operator&emsp;<small>[c.m.dc.del]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_g" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Gradient</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_del.html">The \({\boldsymbol \nabla}\) Operator&emsp;<small>[c.m.dc.del]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_g" class="outline-5">
<h5 id="c_m_dc_g">Gradient<a class="headline-permalink" href="./c_m_dc_g.html#c_m_dc_g"><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"/>
@ -1658,10 +1658,21 @@ is a vector called the <b>gradient</b> of \(T\).
<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>

21
build/c_m_dc_pr.html
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="c_m_dc_curl.html">The Curl&emsp;<small>[c.m.dc.curl]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_d2.html">Second Derivatives&emsp;<small>[c.m.dc.d2]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_pr" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Product Rules</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_curl.html">The Curl&emsp;<small>[c.m.dc.curl]</small></a></li><li>Next:&nbsp;<a href="c_m_dc_d2.html">Second Derivatives&emsp;<small>[c.m.dc.d2]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_pr" class="outline-5">
<h5 id="c_m_dc_pr">Product Rules<a class="headline-permalink" href="./c_m_dc_pr.html#c_m_dc_pr"><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"/>
@ -1631,10 +1631,21 @@ Six product rules (on inside front cover of Gr).
<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>

21
build/c_m_dd.html
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="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_div.html">The Divergence of \(\hat{\bf r}/r^2\)&emsp;<small>[c.m.dd.div]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Dirac delta Distribution</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_div.html">The Divergence of \(\hat{\bf r}/r^2\)&emsp;<small>[c.m.dd.div]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_dd">Dirac delta Distribution<a class="headline-permalink" href="./c_m_dd.html#c_m_dd"><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"/>
@ -1633,10 +1633,21 @@ Table of contents
<li><a href="c_m_dd_3d.html">The Three-Dimensional Delta Function</a><span class="headline-id">c.m.dd.3d</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>

21
build/c_m_dd_1d.html
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="c_m_dd_div.html">The Divergence of \(\hat{\bf r}/r^2\)&emsp;<small>[c.m.dd.div]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_3d.html">The Three-Dimensional Delta Function&emsp;<small>[c.m.dd.3d]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_1d" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dd.html">Dirac delta Distribution</a></li><li>The One-Dimensional Dirac Delta Function</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dd_div.html">The Divergence of \(\hat{\bf r}/r^2\)&emsp;<small>[c.m.dd.div]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_3d.html">The Three-Dimensional Delta Function&emsp;<small>[c.m.dd.3d]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_1d" class="outline-5">
<h5 id="c_m_dd_1d">The One-Dimensional Dirac Delta Function<a class="headline-permalink" href="./c_m_dd_1d.html#c_m_dd_1d"><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"/>
@ -1645,10 +1645,21 @@ Consequences: for any smooth differentiable function \(f(x)\),
<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>

25
build/c_m_dd_3d.html
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="c_m_dd_1d.html">The One-Dimensional Dirac Delta Function&emsp;<small>[c.m.dd.1d]</small></a></li><li>Next:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_3d" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dd.html">Dirac delta Distribution</a></li><li>The Three-Dimensional Delta Function</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dd_1d.html">The One-Dimensional Dirac Delta Function&emsp;<small>[c.m.dd.1d]</small></a></li><li>Next:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_3d" class="outline-5">
<h5 id="c_m_dd_3d">The Three-Dimensional Delta Function<a class="headline-permalink" href="./c_m_dd_3d.html#c_m_dd_3d"><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"/>
@ -1645,14 +1645,14 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
More generally,
</p>
<div class="eqlabel" id="org276d185">
<div class="eqlabel" id="org63ae2fc">
<p>
<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><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"/>
</svg></a>
</p>
<div class="alteqlabels" id="org676b181">
<div class="alteqlabels" id="org4992249">
<ul class="org-ul">
<li>Gr (1.100)</li>
</ul>
@ -1688,10 +1688,21 @@ we have that
</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>

21
build/c_m_dd_div.html
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="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_1d.html">The One-Dimensional Dirac Delta Function&emsp;<small>[c.m.dd.1d]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_div" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dd.html">Dirac delta Distribution</a></li><li>The Divergence of \(\hat{\bf r}/r^2\)</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Next:&nbsp;<a href="c_m_dd_1d.html">The One-Dimensional Dirac Delta Function&emsp;<small>[c.m.dd.1d]</small></a></li><li>Up:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li></ul><div id="outline-container-c_m_dd_div" class="outline-5">
<h5 id="c_m_dd_div">The Divergence of \(\hat{\bf r}/r^2\)<a class="headline-permalink" href="./c_m_dd_div.html#c_m_dd_div"><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"/>
@ -1651,10 +1651,21 @@ Problem: in Gr(1.84), we've divided by zero when \(r = 0\).
<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>

21
build/c_m_ic.html
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="c_m_dc_d2.html">Second Derivatives&emsp;<small>[c.m.dc.d2]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Integral Calculus</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_d2.html">Second Derivatives&emsp;<small>[c.m.dc.d2]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_ic">Integral Calculus<a class="headline-permalink" href="./c_m_ic.html#c_m_ic"><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"/>
@ -1636,10 +1636,21 @@ Table of contents
<li><a href="c_m_ic_ip.html">Integration by Parts</a><span class="headline-id">c.m.ic.ip</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>

21
build/c_m_ic_ftc.html
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="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>The Fundamental Theorem of Calculus</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5">
<h5 id="c_m_ic_ftc">The Fundamental Theorem of Calculus<a class="headline-permalink" href="./c_m_ic_ftc.html#c_m_ic_ftc"><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"/>
@ -1634,10 +1634,21 @@ Table of contents
<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>

21
build/c_m_ic_ftg.html
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="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_gauss.html">Gauss' Theorem&emsp;<small>[c.m.ic.gauss]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftg" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>The Fundamental Theorem for Gradients</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_gauss.html">Gauss' Theorem&emsp;<small>[c.m.ic.gauss]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftg" class="outline-5">
<h5 id="c_m_ic_ftg">The Fundamental Theorem for Gradients<a class="headline-permalink" href="./c_m_ic_ftg.html#c_m_ic_ftg"><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"/>
@ -1643,10 +1643,21 @@ Table of contents
<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>

21
build/c_m_ic_gauss.html
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="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_stokes.html">Stokes' Theorem&emsp;<small>[c.m.ic.stokes]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_gauss" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>Gauss' Theorem</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_stokes.html">Stokes' Theorem&emsp;<small>[c.m.ic.stokes]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_gauss" class="outline-5">
<h5 id="c_m_ic_gauss">Gauss' Theorem<a class="headline-permalink" href="./c_m_ic_gauss.html#c_m_ic_gauss"><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"/>
@ -1637,10 +1637,21 @@ This is know either as <b>Gauss' theorem</b>, <b>Green's theorem</b> or the <b>d
<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>

21
build/c_m_ic_ip.html
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="c_m_ic_stokes.html">Stokes' Theorem&emsp;<small>[c.m.ic.stokes]</small></a></li><li>Next:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ip" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>Integration by Parts</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_stokes.html">Stokes' Theorem&emsp;<small>[c.m.ic.stokes]</small></a></li><li>Next:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ip" class="outline-5">
<h5 id="c_m_ic_ip">Integration by Parts<a class="headline-permalink" href="./c_m_ic_ip.html#c_m_ic_ip"><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"/>
@ -1644,10 +1644,21 @@ or in other words
</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>

39
build/c_m_ic_lsv.html
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="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>Line, Surface and Volume Integrals</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5">
<h5 id="c_m_ic_lsv">Line, Surface and Volume Integrals<a class="headline-permalink" href="./c_m_ic_lsv.html#c_m_ic_lsv"><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"/>
@ -1624,9 +1624,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_ic_lsv">
</div>
<div id="outline-container-org609a3df" class="outline-6">
<h6 id="org609a3df"><a href="#org609a3df">Line Integrals</a></h6>
<div class="outline-text-6" id="text-org609a3df">
<div id="outline-container-org552d286" class="outline-6">
<h6 id="org552d286"><a href="#org552d286">Line Integrals</a></h6>
<div class="outline-text-6" id="text-org552d286">
<p>
\[
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
@ -1655,9 +1655,9 @@ Integral over a closed loop:
</div>
</div>
<div id="outline-container-org8f657b7" class="outline-6">
<h6 id="org8f657b7"><a href="#org8f657b7">Surface Integrals</a></h6>
<div class="outline-text-6" id="text-org8f657b7">
<div id="outline-container-org8d260ce" class="outline-6">
<h6 id="org8d260ce"><a href="#org8d260ce">Surface Integrals</a></h6>
<div class="outline-text-6" id="text-org8d260ce">
<p>
\[
\int_{\cal S} {\bf v} \cdot d{\bf a}
@ -1677,9 +1677,9 @@ Over a closed surface:
</div>
</div>
<div id="outline-container-org2ec267e" class="outline-6">
<h6 id="org2ec267e"><a href="#org2ec267e">Volume Integrals</a></h6>
<div class="outline-text-6" id="text-org2ec267e">
<div id="outline-container-org57765dc" class="outline-6">
<h6 id="org57765dc"><a href="#org57765dc">Volume Integrals</a></h6>
<div class="outline-text-6" id="text-org57765dc">
<p>
\[
\int_{\cal V} T d\tau
@ -1705,10 +1705,21 @@ d\tau = dx dy dz
<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>

25
build/c_m_ic_stokes.html
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>
@ -1616,20 +1616,20 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_gauss.html">Gauss' Theorem&emsp;<small>[c.m.ic.gauss]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ip.html">Integration by Parts&emsp;<small>[c.m.ic.ip]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_stokes" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_ic.html">Integral Calculus</a></li><li>Stokes' Theorem</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_gauss.html">Gauss' Theorem&emsp;<small>[c.m.ic.gauss]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ip.html">Integration by Parts&emsp;<small>[c.m.ic.ip]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_stokes" class="outline-5">
<h5 id="c_m_ic_stokes">Stokes' Theorem<a class="headline-permalink" href="./c_m_ic_stokes.html#c_m_ic_stokes"><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"/>
</svg></a><span class="headline-id">c.m.ic.stokes</span></h5>
<div class="outline-text-5" id="text-c_m_ic_stokes">
<div class="eqlabel" id="org4321094">
<div class="eqlabel" id="org5b773ee">
<p>
<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><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"/>
</svg></a>
</p>
<div class="alteqlabels" id="org03c3b7b">
<div class="alteqlabels" id="org815e278">
<ul class="org-ul">
<li>Gr (1.57)</li>
</ul>
@ -1659,10 +1659,21 @@ the boundary shrinks to a point.
<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>

21
build/c_m_uf.html
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="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Useful Formulas</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_uf">Useful Formulas<a class="headline-permalink" href="./c_m_uf.html#c_m_uf"><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"/>
@ -1633,10 +1633,21 @@ Table of contents
<li><a href="c_m_uf_vi.html">Vector identities</a><span class="headline-id">c.m.uf.vi</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>

21
build/c_m_uf_cyl.html
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="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_sph.html">Spherical coordinates&emsp;<small>[c.m.uf.sph]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_cyl" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_uf.html">Useful Formulas</a></li><li>Cylindrical coordinates</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_sph.html">Spherical coordinates&emsp;<small>[c.m.uf.sph]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_cyl" class="outline-5">
<h5 id="c_m_uf_cyl">Cylindrical coordinates<a class="headline-permalink" href="./c_m_uf_cyl.html#c_m_uf_cyl"><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"/>
@ -1646,10 +1646,21 @@ Table of contents
<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>

21
build/c_m_uf_sph.html
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="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_vi.html">Vector identities&emsp;<small>[c.m.uf.vi]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_sph" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_uf.html">Useful Formulas</a></li><li>Spherical coordinates</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_vi.html">Vector identities&emsp;<small>[c.m.uf.vi]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_sph" class="outline-5">
<h5 id="c_m_uf_sph">Spherical coordinates<a class="headline-permalink" href="./c_m_uf_sph.html#c_m_uf_sph"><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"/>
@ -1646,10 +1646,21 @@ Table of contents
<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>

21
build/c_m_uf_vi.html
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="c_m_uf_sph.html">Spherical coordinates&emsp;<small>[c.m.uf.sph]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_vi" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_uf.html">Useful Formulas</a></li><li>Vector identities</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_uf_sph.html">Spherical coordinates&emsp;<small>[c.m.uf.sph]</small></a></li><li>Up:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li></ul><div id="outline-container-c_m_uf_vi" class="outline-5">
<h5 id="c_m_uf_vi">Vector identities<a class="headline-permalink" href="./c_m_uf_vi.html#c_m_uf_vi"><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"/>
@ -1649,10 +1649,21 @@ Table of contents
</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>

21
build/c_m_va.html
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="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li><li>Next:&nbsp;<a href="c_m_va_n.html">Notation and algebraic properties&emsp;<small>[c.m.va.n]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Vector Analysis</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li><li>Next:&nbsp;<a href="c_m_va_n.html">Notation and algebraic properties&emsp;<small>[c.m.va.n]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_va">Vector Analysis<a class="headline-permalink" href="./c_m_va.html#c_m_va"><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"/>
@ -1635,10 +1635,21 @@ Table of contents
<li><a href="c_m_va_pds.html">Position, Displacement and Separation Vectors</a><span class="headline-id">c.m.va.pds</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>

21
build/c_m_va_cp.html
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="c_m_va_sp.html">Scalar product&emsp;<small>[c.m.va.sp]</small></a></li><li>Next:&nbsp;<a href="c_m_va_tp.html">Triple Products&emsp;<small>[c.m.va.tp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_cp" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_va.html">Vector Analysis</a></li><li>Cross product</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va_sp.html">Scalar product&emsp;<small>[c.m.va.sp]</small></a></li><li>Next:&nbsp;<a href="c_m_va_tp.html">Triple Products&emsp;<small>[c.m.va.tp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_cp" class="outline-5">
<h5 id="c_m_va_cp">Cross product<a class="headline-permalink" href="./c_m_va_cp.html#c_m_va_cp"><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"/>
@ -1664,10 +1664,21 @@ this relation making plain that
<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>

21
build/c_m_va_n.html
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="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li><li>Next:&nbsp;<a href="c_m_va_sp.html">Scalar product&emsp;<small>[c.m.va.sp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_n" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_va.html">Vector Analysis</a></li><li>Notation and algebraic properties</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li><li>Next:&nbsp;<a href="c_m_va_sp.html">Scalar product&emsp;<small>[c.m.va.sp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_n" class="outline-5">
<h5 id="c_m_va_n">Notation and algebraic properties<a class="headline-permalink" href="./c_m_va_n.html#c_m_va_n"><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"/>
@ -1659,10 +1659,21 @@ Component notation (in \({\mathbb R}^3\) with cartesian coordinates):
<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>

21
build/c_m_va_pds.html
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="c_m_va_tp.html">Triple Products&emsp;<small>[c.m.va.tp]</small></a></li><li>Next:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_pds" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_va.html">Vector Analysis</a></li><li>Position, Displacement and Separation Vectors</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va_tp.html">Triple Products&emsp;<small>[c.m.va.tp]</small></a></li><li>Next:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_pds" class="outline-5">
<h5 id="c_m_va_pds">Position, Displacement and Separation Vectors<a class="headline-permalink" href="./c_m_va_pds.html#c_m_va_pds"><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"/>
@ -1693,10 +1693,21 @@ Separation vector: for two position vectors \({\bf r}_a, {\bf r}_b\),
</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>

21
build/c_m_va_sp.html
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="c_m_va_n.html">Notation and algebraic properties&emsp;<small>[c.m.va.n]</small></a></li><li>Next:&nbsp;<a href="c_m_va_cp.html">Cross product&emsp;<small>[c.m.va.cp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_sp" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_va.html">Vector Analysis</a></li><li>Scalar product</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va_n.html">Notation and algebraic properties&emsp;<small>[c.m.va.n]</small></a></li><li>Next:&nbsp;<a href="c_m_va_cp.html">Cross product&emsp;<small>[c.m.va.cp]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_sp" class="outline-5">
<h5 id="c_m_va_sp">Scalar product<a class="headline-permalink" href="./c_m_va_sp.html#c_m_va_sp"><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"/>
@ -1659,10 +1659,21 @@ In a general coordinate system with metric \(g\),
<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>

21
build/c_m_va_tp.html
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="c_m_va_cp.html">Cross product&emsp;<small>[c.m.va.cp]</small></a></li><li>Next:&nbsp;<a href="c_m_va_pds.html">Position, Displacement and Separation Vectors&emsp;<small>[c.m.va.pds]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_tp" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_va.html">Vector Analysis</a></li><li>Triple Products</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_va_cp.html">Cross product&emsp;<small>[c.m.va.cp]</small></a></li><li>Next:&nbsp;<a href="c_m_va_pds.html">Position, Displacement and Separation Vectors&emsp;<small>[c.m.va.pds]</small></a></li><li>Up:&nbsp;<a href="c_m_va.html">Vector Analysis&emsp;<small>[c.m.va]</small></a></li></ul><div id="outline-container-c_m_va_tp" class="outline-5">
<h5 id="c_m_va_tp">Triple Products<a class="headline-permalink" href="./c_m_va_tp.html#c_m_va_tp"><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"/>
@ -1706,10 +1706,21 @@ All higher vector products can be reduced to combinations of single vector produ
<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>

21
build/c_m_vf.html
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="c_m_dd_3d.html">The Three-Dimensional Delta Function&emsp;<small>[c.m.dd.3d]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li>Vector Fields</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dd_3d.html">The Three-Dimensional Delta Function&emsp;<small>[c.m.dd.3d]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_vf">Vector Fields<a class="headline-permalink" href="./c_m_vf.html#c_m_vf"><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"/>
@ -1632,10 +1632,21 @@ Table of contents
<li><a href="c_m_vf_pot.html">Potentials</a><span class="headline-id">c.m.vf.pot</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>

21
build/c_m_vf_helm.html
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="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_helm" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_vf.html">Vector Fields</a></li><li>The Helmholtz Theorem</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_helm" class="outline-5">
<h5 id="c_m_vf_helm">The Helmholtz Theorem<a class="headline-permalink" href="./c_m_vf_helm.html#c_m_vf_helm"><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"/>
@ -1651,10 +1651,21 @@ where
<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>

21
build/c_m_vf_pot.html
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="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_vf.html">Vector Fields</a></li><li>Potentials</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5">
<h5 id="c_m_vf_pot">Potentials<a class="headline-permalink" href="./c_m_vf_pot.html#c_m_vf_pot"><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"/>
@ -1678,10 +1678,21 @@ The following conditions are equivalent:
</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>

25
build/d.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Next:&nbsp;<a href="d_m.html">Diagnostics: Mathematical Preliminaries&emsp;<small>[d.m]</small></a></li></ul>
<ul class="breadcrumbs"><li>Diagnostics</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="d_m.html">Diagnostics: Mathematical Preliminaries&emsp;<small>[d.m]</small></a></li></ul>
<h2 id="d">Diagnostics<a class="headline-permalink" href="./d.html#d"><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"/>
</svg></a><span class="headline-id">d</span></h2>
<div class="outline-text-2" id="text-d">
<details class="objectives" id="orgdc678ad">
<summary id="org6e8a387">
<details class="objectives" id="org9cfb206">
<summary id="org87be4b2">
Objectives
</summary>
@ -1673,10 +1673,21 @@ I have little doubt you'll pass the course.
<li><a href="d_red.html">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</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>

21
build/d_emd.html
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="d_emsm_msm.html">Diagnostics: Magnetostatics in Matter&emsp;<small>[d.emsm.msm]</small></a></li><li>Next:&nbsp;<a href="d_emd_ce.html">Diagnostics: Conservation Laws&emsp;<small>[d.emd.ce]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emd" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Electromagnetodynamics</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emsm_msm.html">Diagnostics: Magnetostatics in Matter&emsp;<small>[d.emsm.msm]</small></a></li><li>Next:&nbsp;<a href="d_emd_ce.html">Diagnostics: Conservation Laws&emsp;<small>[d.emd.ce]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emd" class="outline-3">
<h3 id="d_emd">Diagnostics: Electromagnetodynamics<a class="headline-permalink" href="./d_emd.html#d_emd"><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"/>
@ -1653,10 +1653,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_emd_ce.html
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="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li><li>Next:&nbsp;<a href="d_emd_emw.html">Diagnostics: Electromagnetic Waves&emsp;<small>[d.emd.emw]</small></a></li><li>Up:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li></ul><div id="outline-container-d_emd_ce" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li><a class="breadcrumb-link"href="d_emd.html">Diagnostics: Electromagnetodynamics</a></li><li>Diagnostics: Conservation Laws</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li><li>Next:&nbsp;<a href="d_emd_emw.html">Diagnostics: Electromagnetic Waves&emsp;<small>[d.emd.emw]</small></a></li><li>Up:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li></ul><div id="outline-container-d_emd_ce" class="outline-3">
<h3 id="d_emd_ce">Diagnostics: Conservation Laws<a class="headline-permalink" href="./d_emd_ce.html#d_emd_ce"><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"/>
@ -1648,10 +1648,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_emd_emw.html
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="d_emd_ce.html">Diagnostics: Conservation Laws&emsp;<small>[d.emd.ce]</small></a></li><li>Next:&nbsp;<a href="d_emf.html">Diagnostics: Potentials, Gauges and Fields&emsp;<small>[d.emf]</small></a></li><li>Up:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li></ul><div id="outline-container-d_emd_emw" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li><a class="breadcrumb-link"href="d_emd.html">Diagnostics: Electromagnetodynamics</a></li><li>Diagnostics: Electromagnetic Waves</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emd_ce.html">Diagnostics: Conservation Laws&emsp;<small>[d.emd.ce]</small></a></li><li>Next:&nbsp;<a href="d_emf.html">Diagnostics: Potentials, Gauges and Fields&emsp;<small>[d.emf]</small></a></li><li>Up:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li></ul><div id="outline-container-d_emd_emw" class="outline-3">
<h3 id="d_emd_emw">Diagnostics: Electromagnetic Waves<a class="headline-permalink" href="./d_emd_emw.html#d_emd_emw"><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"/>
@ -1651,10 +1651,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_emf.html
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="d_emd_emw.html">Diagnostics: Electromagnetic Waves&emsp;<small>[d.emd.emw]</small></a></li><li>Next:&nbsp;<a href="d_red.html">Diagnostics: Relativistic Electrodynamics&emsp;<small>[d.red]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emf" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Potentials, Gauges and Fields</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emd_emw.html">Diagnostics: Electromagnetic Waves&emsp;<small>[d.emd.emw]</small></a></li><li>Next:&nbsp;<a href="d_red.html">Diagnostics: Relativistic Electrodynamics&emsp;<small>[d.red]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emf" class="outline-3">
<h3 id="d_emf">Diagnostics: Potentials, Gauges and Fields<a class="headline-permalink" href="./d_emf.html#d_emf"><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"/>
@ -1648,10 +1648,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_ems.html
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="d_m.html">Diagnostics: Mathematical Preliminaries&emsp;<small>[d.m]</small></a></li><li>Next:&nbsp;<a href="d_ems_ca.html">Diagnostics: Calculating or Approximating the Electostatic Potential&emsp;<small>[d.ems.ca]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_ems" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Electromagnetostatics</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_m.html">Diagnostics: Mathematical Preliminaries&emsp;<small>[d.m]</small></a></li><li>Next:&nbsp;<a href="d_ems_ca.html">Diagnostics: Calculating or Approximating the Electostatic Potential&emsp;<small>[d.ems.ca]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_ems" class="outline-3">
<h3 id="d_ems">Diagnostics: Electromagnetostatics<a class="headline-permalink" href="./d_ems.html#d_ems"><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"/>
@ -1670,10 +1670,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_ems_ca.html
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="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li><li>Next:&nbsp;<a href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li><li>Up:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li></ul><div id="outline-container-d_ems_ca" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li><a class="breadcrumb-link"href="d_ems.html">Diagnostics: Electromagnetostatics</a></li><li>Diagnostics: Calculating or Approximating the Electostatic Potential</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li><li>Next:&nbsp;<a href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li><li>Up:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li></ul><div id="outline-container-d_ems_ca" class="outline-3">
<h3 id="d_ems_ca">Diagnostics: Calculating or Approximating the Electostatic Potential<a class="headline-permalink" href="./d_ems_ca.html#d_ems_ca"><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"/>
@ -1653,10 +1653,21 @@ a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conductin
<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>

21
build/d_ems_ms.html
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="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li><li>Next:&nbsp;<a href="d_emsm_msm.html">Diagnostics: Magnetostatics in Matter&emsp;<small>[d.emsm.msm]</small></a></li><li>Up:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li></ul><div id="outline-container-d_ems_ms" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li><a class="breadcrumb-link"href="d_ems.html">Diagnostics: Electromagnetostatics</a></li><li>Diagnostics: Magnetostatics</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li><li>Next:&nbsp;<a href="d_emsm_msm.html">Diagnostics: Magnetostatics in Matter&emsp;<small>[d.emsm.msm]</small></a></li><li>Up:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li></ul><div id="outline-container-d_ems_ms" class="outline-3">
<h3 id="d_ems_ms">Diagnostics: Magnetostatics<a class="headline-permalink" href="./d_ems_ms.html#d_ems_ms"><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"/>
@ -1650,10 +1650,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_emsm.html
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="d_ems_ca.html">Diagnostics: Calculating or Approximating the Electostatic Potential&emsp;<small>[d.ems.ca]</small></a></li><li>Next:&nbsp;<a href="d_ems_ms.html">Diagnostics: Magnetostatics&emsp;<small>[d.ems.ms]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emsm" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Electromagnetostatics in Matter</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_ems_ca.html">Diagnostics: Calculating or Approximating the Electostatic Potential&emsp;<small>[d.ems.ca]</small></a></li><li>Next:&nbsp;<a href="d_ems_ms.html">Diagnostics: Magnetostatics&emsp;<small>[d.ems.ms]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_emsm" class="outline-3">
<h3 id="d_emsm">Diagnostics: Electromagnetostatics in Matter<a class="headline-permalink" href="./d_emsm.html#d_emsm"><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"/>
@ -1653,10 +1653,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_emsm_msm.html
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="d_ems_ms.html">Diagnostics: Magnetostatics&emsp;<small>[d.ems.ms]</small></a></li><li>Next:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li><li>Up:&nbsp;<a href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li></ul><div id="outline-container-d_emsm_msm" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li><a class="breadcrumb-link"href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter</a></li><li>Diagnostics: Magnetostatics in Matter</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_ems_ms.html">Diagnostics: Magnetostatics&emsp;<small>[d.ems.ms]</small></a></li><li>Next:&nbsp;<a href="d_emd.html">Diagnostics: Electromagnetodynamics&emsp;<small>[d.emd]</small></a></li><li>Up:&nbsp;<a href="d_emsm.html">Diagnostics: Electromagnetostatics in Matter&emsp;<small>[d.emsm]</small></a></li></ul><div id="outline-container-d_emsm_msm" class="outline-3">
<h3 id="d_emsm_msm">Diagnostics: Magnetostatics in Matter<a class="headline-permalink" href="./d_emsm_msm.html#d_emsm_msm"><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"/>
@ -1651,10 +1651,21 @@ As a strict minimum, you should be able to:
<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>

21
build/d_m.html
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="d.html">Diagnostics&emsp;<small>[d]</small></a></li><li>Next:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_m" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Mathematical Preliminaries</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li><li>Next:&nbsp;<a href="d_ems.html">Diagnostics: Electromagnetostatics&emsp;<small>[d.ems]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_m" class="outline-3">
<h3 id="d_m">Diagnostics: Mathematical Preliminaries<a class="headline-permalink" href="./d_m.html#d_m"><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"/>
@ -1661,10 +1661,21 @@ Things you should be able to do (ideally: from scratch, on a blank sheet of pape
<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>

21
build/d_red.html
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="d_emf.html">Diagnostics: Potentials, Gauges and Fields&emsp;<small>[d.emf]</small></a></li><li>Next:&nbsp;<a href="a.html">Appendices&emsp;<small>[a]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_red" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="d.html">Diagnostics</a></li><li>Diagnostics: Relativistic Electrodynamics</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="d_emf.html">Diagnostics: Potentials, Gauges and Fields&emsp;<small>[d.emf]</small></a></li><li>Next:&nbsp;<a href="a.html">Appendices&emsp;<small>[a]</small></a></li><li>Up:&nbsp;<a href="d.html">Diagnostics&emsp;<small>[d]</small></a></li></ul><div id="outline-container-d_red" class="outline-3">
<h3 id="d_red">Diagnostics: Relativistic Electrodynamics<a class="headline-permalink" href="./d_red.html#d_red"><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"/>
@ -1655,10 +1655,21 @@ As a strict minimum, you should be able to:
</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>

29
build/emd.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Next:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul>
<ul class="breadcrumbs"><li>Electromagnetodynamics</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul>
<h2 id="emd">Electromagnetodynamics<a class="headline-permalink" href="./emd.html#emd"><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"/>
</svg></a><span class="headline-id">emd</span></h2>
<div class="outline-text-2" id="text-emd">
<details class="prereq" id="org91070ea">
<summary id="orgec443fc">
<details class="prereq" id="org94bea47">
<summary id="orgb7d0bc3">
Prerequisites
</summary>
<ul class="org-ul">
@ -1633,8 +1633,8 @@ Prerequisites
</ul>
</details>
<details class="objectives" id="org7a852ae">
<summary id="org301eba1">
<details class="objectives" id="org0cdfa86">
<summary id="org2927d33">
Objectives
</summary>
<ul class="org-ul">
@ -1660,10 +1660,21 @@ Objectives
<li><a href="emd_emw.html">Electromagnetic waves in vacuum</a><span class="headline-id">emd.emw</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>

21
build/emd_Fl.html
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="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_Fl.html">Faraday's Law&emsp;<small>[emd.Fl.Fl]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li>Induction: Faraday's Law</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_Fl.html">Faraday's Law&emsp;<small>[emd.Fl.Fl]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<h3 id="emd_Fl">Induction: Faraday's Law<a class="headline-permalink" href="./emd_Fl.html#emd_Fl"><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"/>
@ -1634,10 +1634,21 @@ Table of contents
<li><a href="emd_Fl_e.html">Energy in Magnetic Fields</a><span class="headline-id">emd.Fl.e</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>

27
build/emd_Fl_Fl.html
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="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_ief.html">The Induced Electric Field&emsp;<small>[emd.Fl.ief]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_Fl" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Fl.html">Induction: Faraday's Law</a></li><li>Faraday's Law</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_ief.html">The Induced Electric Field&emsp;<small>[emd.Fl.ief]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_Fl" class="outline-4">
<h4 id="emd_Fl_Fl">Faraday's Law<a class="headline-permalink" href="./emd_Fl_Fl.html#emd_Fl_Fl"><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"/>
@ -1663,7 +1663,7 @@ Empirically: the changing magnetic field induces an electric current around
the circuit. This current is really driven by an electric field having a component
along the wire. The line integral of this field is called the
</p>
<div class="core div" id="orgcb2b8bd">
<div class="core div" id="org8786846">
<p>
<b>Electromotive force (or electromotance)</b>,
\[
@ -1685,7 +1685,7 @@ to the rate of change of the magnetic flux,
\]
so we obtain
</p>
<div class="core div" id="org826bbb5">
<div class="core div" id="org278fea1">
<p>
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
\[
@ -1703,7 +1703,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
\]
we obtain
</p>
<div class="core div" id="org4f576bd">
<div class="core div" id="org63211df">
<p>
<b>Faraday's law</b> (differential form)
\[
@ -1725,10 +1725,21 @@ to an opposing counter-reaction.
<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>

25
build/emd_Fl_e.html
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="emd_Fl_i.html">Inductance&emsp;<small>[emd.Fl.i]</small></a></li><li>Next:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_e" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Fl.html">Induction: Faraday's Law</a></li><li>Energy in Magnetic Fields</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Fl_i.html">Inductance&emsp;<small>[emd.Fl.i]</small></a></li><li>Next:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_e" class="outline-4">
<h4 id="emd_Fl_e">Energy in Magnetic Fields<a class="headline-permalink" href="./emd_Fl_e.html#emd_Fl_e"><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"/>
@ -1682,7 +1682,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
\]
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
</p>
<div class="core div" id="org612a7d5">
<div class="core div" id="orge86302b">
<p>
\[
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
@ -1703,7 +1703,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
\hspace{2cm} \mbox{(7.31 and 7.34)}
\end{align}
<div class="example div" id="org8806452">
<div class="example div" id="org0c0ebda">
<p>
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
Find energy stored in section of length \(l\).
@ -1727,10 +1727,21 @@ Note: gives easy way to find inductance, since \(W = \frac{1}{2} L I^2\).
</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>

27
build/emd_Fl_i.html
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="emd_Fl_ief.html">The Induced Electric Field&emsp;<small>[emd.Fl.ief]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_e.html">Energy in Magnetic Fields&emsp;<small>[emd.Fl.e]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_i" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Fl.html">Induction: Faraday's Law</a></li><li>Inductance</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Fl_ief.html">The Induced Electric Field&emsp;<small>[emd.Fl.ief]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_e.html">Energy in Magnetic Fields&emsp;<small>[emd.Fl.e]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_i" class="outline-4">
<h4 id="emd_Fl_i">Inductance<a class="headline-permalink" href="./emd_Fl_i.html#emd_Fl_i"><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"/>
@ -1662,7 +1662,7 @@ M_{12} = M_{21}
\]
</p>
<div class="example div" id="org105c83a">
<div class="example div" id="org6c1a2e4">
<p>
\paragraph{Example 7.10:}
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
@ -1712,7 +1712,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
</p>
<div class="example div" id="orgfde0fbc">
<div class="example div" id="org96ae3fa">
<p>
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
@ -1739,7 +1739,7 @@ Total flux: \(N\) times this, so self-inductance is
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
</p>
<div class="example div" id="org88909b4">
<div class="example div" id="orgde2bf6d">
<p>
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
What is the current ?
@ -1763,10 +1763,21 @@ where \(\tau \equiv L/R\) is the {\bf time constant} of the circuit.
<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>

27
build/emd_Fl_ief.html
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="emd_Fl_Fl.html">Faraday's Law&emsp;<small>[emd.Fl.Fl]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_i.html">Inductance&emsp;<small>[emd.Fl.i]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_ief" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Fl.html">Induction: Faraday's Law</a></li><li>The Induced Electric Field</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Fl_Fl.html">Faraday's Law&emsp;<small>[emd.Fl.Fl]</small></a></li><li>Next:&nbsp;<a href="emd_Fl_i.html">Inductance&emsp;<small>[emd.Fl.i]</small></a></li><li>Up:&nbsp;<a href="emd_Fl.html">Induction: Faraday's Law&emsp;<small>[emd.Fl]</small></a></li></ul><div id="outline-container-emd_Fl_ief" class="outline-4">
<h4 id="emd_Fl_ief">The Induced Electric Field<a class="headline-permalink" href="./emd_Fl_ief.html#emd_Fl_ief"><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"/>
@ -1646,7 +1646,7 @@ law in integral form:
<div class="example div" id="org6f81c6a">
<div class="example div" id="org547c6ca">
<p>
{\bf Example 7.7:}
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
@ -1662,7 +1662,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
</div>
<div class="example div" id="org5fbf230">
<div class="example div" id="org3040ba3">
<p>
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
Uniform magnetic field \({\bf B}_0\) in central region up to \(a &lt; b\),
@ -1696,7 +1696,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
'slow enough' phenomena.
</p>
<div class="example div" id="org4c83960">
<div class="example div" id="org805b5d5">
<p>
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
induced \({\bf E}\) field as a function of distance \(s\) from wire.
@ -1729,10 +1729,21 @@ Reason: in this case, we've overstepped the quasistatic limit. We need
<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>

21
build/emd_Me.html
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="emd_Fl_e.html">Energy in Magnetic Fields&emsp;<small>[emd.Fl.e]</small></a></li><li>Next:&nbsp;<a href="emd_Me_ebM.html">Electrodynamics Before Maxwell&emsp;<small>[emd.Me.ebM]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li>Maxwell's Equations</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Fl_e.html">Energy in Magnetic Fields&emsp;<small>[emd.Fl.e]</small></a></li><li>Next:&nbsp;<a href="emd_Me_ebM.html">Electrodynamics Before Maxwell&emsp;<small>[emd.Me.ebM]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<h3 id="emd_Me">Maxwell's Equations<a class="headline-permalink" href="./emd_Me.html#emd_Me"><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"/>
@ -1634,10 +1634,21 @@ Table of contents
<li><a href="emd_Me_mc.html">Magnetic Charge</a><span class="headline-id">emd.Me.mc</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>

27
build/emd_Me_Me.html
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="emd_Me_dc.html">Maxwell's Correction to Ampère's Law; the Displacement Current&emsp;<small>[emd.Me.dc]</small></a></li><li>Next:&nbsp;<a href="emd_Me_mc.html">Magnetic Charge&emsp;<small>[emd.Me.mc]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_Me" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Me.html">Maxwell's Equations</a></li><li>Maxwell's Equations</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me_dc.html">Maxwell's Correction to Ampère's Law; the Displacement Current&emsp;<small>[emd.Me.dc]</small></a></li><li>Next:&nbsp;<a href="emd_Me_mc.html">Magnetic Charge&emsp;<small>[emd.Me.mc]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_Me" class="outline-4">
<h4 id="emd_Me_Me">Maxwell's Equations<a class="headline-permalink" href="./emd_Me_Me.html#emd_Me_Me"><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"/>
@ -1625,7 +1625,7 @@ Table of contents
<p>
Full set of equations for the electromagnetic field:
</p>
<div class="core div" id="org61cd67c">
<div class="core div" id="org501476d">
<p>
{\bf Maxwell's equations} {\it (in vacuum)}
</p>
@ -1641,7 +1641,7 @@ Full set of equations for the electromagnetic field:
<p>
Complement:
</p>
<div class="core div" id="org2b8e704">
<div class="core div" id="orgb357d3d">
<p>
{\bf Force law}
\[
@ -1665,7 +1665,7 @@ take divergence of \((iv)\).
<p>
Better way of writing: all fields on left, all sources on right,
</p>
<div class="core div" id="orgac16379">
<div class="core div" id="org0a81935">
\begin{align}
(i) &amp;{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
&amp;(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
@ -1680,10 +1680,21 @@ Better way of writing: all fields on left, all sources on right,
<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>

25
build/emd_Me_dc.html
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="emd_Me_ebM.html">Electrodynamics Before Maxwell&emsp;<small>[emd.Me.ebM]</small></a></li><li>Next:&nbsp;<a href="emd_Me_Me.html">Maxwell's Equations&emsp;<small>[emd.Me.Me]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_dc" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Me.html">Maxwell's Equations</a></li><li>Maxwell's Correction to Ampère's Law; the Displacement Current</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me_ebM.html">Electrodynamics Before Maxwell&emsp;<small>[emd.Me.ebM]</small></a></li><li>Next:&nbsp;<a href="emd_Me_Me.html">Maxwell's Equations&emsp;<small>[emd.Me.Me]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_dc" class="outline-4">
<h4 id="emd_Me_dc">Maxwell's Correction to Ampère's Law; the Displacement Current<a class="headline-permalink" href="./emd_Me_dc.html#emd_Me_dc"><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"/>
@ -1632,7 +1632,7 @@ the continuity equation as
\]
The extra term would thus be eliminated if we were to put
</p>
<div class="core div" id="orgc09ac90">
<div class="core div" id="orgd8174ee">
<p>
\[
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
@ -1656,7 +1656,7 @@ Real confirmation of Maxwell's theory: 1888, Hertz's experiments on propagation
<p>
Maxwell baptized this term the
</p>
<div class="core div" id="orgd2c9b8e">
<div class="core div" id="orgb36d854">
<p>
{\bf Displacement current}
\[
@ -1689,10 +1689,21 @@ Flat surface: OK, \(E = 0\) and \(I_{\mbox{enc}} = I\). Balloon surface: \(I
<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>

21
build/emd_Me_ebM.html
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="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li><li>Next:&nbsp;<a href="emd_Me_dc.html">Maxwell's Correction to Ampère's Law; the Displacement Current&emsp;<small>[emd.Me.dc]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_ebM" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Me.html">Maxwell's Equations</a></li><li>Electrodynamics Before Maxwell</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li><li>Next:&nbsp;<a href="emd_Me_dc.html">Maxwell's Correction to Ampère's Law; the Displacement Current&emsp;<small>[emd.Me.dc]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_ebM" class="outline-4">
<h4 id="emd_Me_ebM">Electrodynamics Before Maxwell<a class="headline-permalink" href="./emd_Me_ebM.html#emd_Me_ebM"><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"/>
@ -1659,10 +1659,21 @@ So for non-steady currents, the 'current enclosed by a loop' is ill-defined.
<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>

21
build/emd_Me_mc.html
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="emd_Me_Me.html">Maxwell's Equations&emsp;<small>[emd.Me.Me]</small></a></li><li>Next:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_mc" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_Me.html">Maxwell's Equations</a></li><li>Magnetic Charge</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me_Me.html">Maxwell's Equations&emsp;<small>[emd.Me.Me]</small></a></li><li>Next:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li><li>Up:&nbsp;<a href="emd_Me.html">Maxwell's Equations&emsp;<small>[emd.Me]</small></a></li></ul><div id="outline-container-emd_Me_mc" class="outline-4">
<h4 id="emd_Me_mc">Magnetic Charge<a class="headline-permalink" href="./emd_Me_mc.html#emd_Me_mc"><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"/>
@ -1657,10 +1657,21 @@ Maxwell's equations {\bf beg} for magnetic charges. But we've never found any!
</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>

29
build/emd_ce.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me_mc.html">Magnetic Charge&emsp;<small>[emd.Me.mc]</small></a></li><li>Next:&nbsp;<a href="emd_ce_ce.html">The Continuity Equation&emsp;<small>[emd.ce.ce]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li>Charge and Energy Flows</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_Me_mc.html">Magnetic Charge&emsp;<small>[emd.Me.mc]</small></a></li><li>Next:&nbsp;<a href="emd_ce_ce.html">The Continuity Equation&emsp;<small>[emd.ce.ce]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<h3 id="emd_ce">Charge and Energy Flows<a class="headline-permalink" href="./emd_ce.html#emd_ce"><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"/>
</svg></a><span class="headline-id">emd.ce</span></h3>
<div class="outline-text-3" id="text-emd_ce">
<details class="prereq" id="orgcfe0487">
<summary id="orge8a2c1d">
<details class="prereq" id="org26df1fb">
<summary id="org34d471f">
Prerequisites
</summary>
<ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul>
</details>
<details class="objectives" id="org87970ae">
<summary id="org29e69c3">
<details class="objectives" id="orgaff4273">
<summary id="orge67f1e6">
Objectives
</summary>
<ul class="org-ul">
@ -1656,10 +1656,21 @@ Objectives
<li><a href="emd_ce_amom.html">Angular Momentum</a><span class="headline-id">emd.ce.amom</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>

23
build/emd_ce_amom.html
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="emd_ce_mom.html">Momentum&emsp;<small>[emd.ce.mom]</small></a></li><li>Next:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_amom" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_ce.html">Charge and Energy Flows</a></li><li>Angular Momentum</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_mom.html">Momentum&emsp;<small>[emd.ce.mom]</small></a></li><li>Next:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_amom" class="outline-4">
<h4 id="emd_ce_amom">Angular Momentum<a class="headline-permalink" href="./emd_ce_amom.html#emd_ce_amom"><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"/>
@ -1625,7 +1625,7 @@ Table of contents
<p>
The angular momentum of EM fields is directly given by
</p>
<div class="main div" id="org15be82e">
<div class="main div" id="org8fc773b">
<p>
{\bf Angular momentum of EM fields}
\[
@ -1640,10 +1640,21 @@ The angular momentum of EM fields is directly given by
</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>

23
build/emd_ce_ce.html
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="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li><li>Next:&nbsp;<a href="emd_ce_poy.html">Poynting's Theorem; the Poynting Vector&emsp;<small>[emd.ce.poy]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_ce" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_ce.html">Charge and Energy Flows</a></li><li>The Continuity Equation</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li><li>Next:&nbsp;<a href="emd_ce_poy.html">Poynting's Theorem; the Poynting Vector&emsp;<small>[emd.ce.poy]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_ce" class="outline-4">
<h4 id="emd_ce_ce">The Continuity Equation<a class="headline-permalink" href="./emd_ce_ce.html#emd_ce_ce"><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"/>
@ -1644,7 +1644,7 @@ This means that
\]
Since this is true for any volume, we have (re)derived the
</p>
<div class="core div" id="orgf7fdcf4">
<div class="core div" id="org068de4a">
<p>
{\bf Continuity equation}
\[
@ -1670,10 +1670,21 @@ imposes a functional constraint on these sources: not {\it any} \(\rho\) and
<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>

25
build/emd_ce_mom.html
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="emd_ce_mst.html">Maxwell's Stress Tensor&emsp;<small>[emd.ce.mst]</small></a></li><li>Next:&nbsp;<a href="emd_ce_amom.html">Angular Momentum&emsp;<small>[emd.ce.amom]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_mom" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_ce.html">Charge and Energy Flows</a></li><li>Momentum</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_mst.html">Maxwell's Stress Tensor&emsp;<small>[emd.ce.mst]</small></a></li><li>Next:&nbsp;<a href="emd_ce_amom.html">Angular Momentum&emsp;<small>[emd.ce.amom]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_mom" class="outline-4">
<h4 id="emd_ce_mom">Momentum<a class="headline-permalink" href="./emd_ce_mom.html#emd_ce_mom"><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"/>
@ -1637,7 +1637,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
<p>
This is thus simply a conservation law for momentum, with
</p>
<div class="main div" id="orgeb408ef">
<div class="main div" id="orgb401242">
<p>
{\bf Momentum density in the EM fields}
\[
@ -1649,7 +1649,7 @@ This is thus simply a conservation law for momentum, with
<p>
In a region in which the mechanical momentum is not changing due to external influences, we then have the
</p>
<div class="main div" id="org94bfc0c">
<div class="main div" id="orgd377c8a">
<p>
{\bf Continuity equation for EM momentum}
\[
@ -1663,10 +1663,21 @@ In a region in which the mechanical momentum is not changing due to external inf
<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>

27
build/emd_ce_mst.html
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="emd_ce_poy.html">Poynting's Theorem; the Poynting Vector&emsp;<small>[emd.ce.poy]</small></a></li><li>Next:&nbsp;<a href="emd_ce_mom.html">Momentum&emsp;<small>[emd.ce.mom]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_mst" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_ce.html">Charge and Energy Flows</a></li><li>Maxwell's Stress Tensor</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_poy.html">Poynting's Theorem; the Poynting Vector&emsp;<small>[emd.ce.poy]</small></a></li><li>Next:&nbsp;<a href="emd_ce_mom.html">Momentum&emsp;<small>[emd.ce.mom]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_mst" class="outline-4">
<h4 id="emd_ce_mst">Maxwell's Stress Tensor<a class="headline-permalink" href="./emd_ce_mst.html#emd_ce_mst"><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"/>
@ -1679,7 +1679,7 @@ and similarly for \({\boldsymbol B}\). We thus get
<p>
This expression can be greatly simplified by introducing the
</p>
<div class="main div" id="org516af43">
<div class="main div" id="orgf0f558d">
<p>
{\bf Maxwell stress tensor}
\[
@ -1702,7 +1702,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
<p>
We then obtain
</p>
<div class="main div" id="org38f0a89">
<div class="main div" id="orgcd1da6b">
<p>
{\bf EM force per unit volume}
\[
@ -1714,7 +1714,7 @@ We then obtain
<p>
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
</p>
<div class="main div" id="orgf9a42ff">
<div class="main div" id="orgf2db445">
<p>
{\bf Total force on charges in volume}
\[
@ -1728,10 +1728,21 @@ where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
<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>

33
build/emd_ce_poy.html
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="emd_ce_ce.html">The Continuity Equation&emsp;<small>[emd.ce.ce]</small></a></li><li>Next:&nbsp;<a href="emd_ce_mst.html">Maxwell's Stress Tensor&emsp;<small>[emd.ce.mst]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_poy" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_ce.html">Charge and Energy Flows</a></li><li>Poynting's Theorem; the Poynting Vector</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_ce.html">The Continuity Equation&emsp;<small>[emd.ce.ce]</small></a></li><li>Next:&nbsp;<a href="emd_ce_mst.html">Maxwell's Stress Tensor&emsp;<small>[emd.ce.mst]</small></a></li><li>Up:&nbsp;<a href="emd_ce.html">Charge and Energy Flows&emsp;<small>[emd.ce]</small></a></li></ul><div id="outline-container-emd_ce_poy" class="outline-4">
<h4 id="emd_ce_poy">Poynting's Theorem; the Poynting Vector<a class="headline-permalink" href="./emd_ce_poy.html#emd_ce_poy"><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"/>
@ -1691,7 +1691,7 @@ so we get
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
we obtain
</p>
<div class="main div" id="org33b0d12">
<div class="main div" id="org75886ff">
<p>
{\bf Poynting's theorem}
\[
@ -1716,7 +1716,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
<p>
Energy per unit time, per unit area carried by EM fields:
</p>
<div class="core div" id="orgb00d4be">
<div class="core div" id="orgb6d912b">
<p>
{\bf Poynting vector}
\[
@ -1729,7 +1729,7 @@ Energy per unit time, per unit area carried by EM fields:
<p>
We can thus express Poynting's theorem more compactly:
</p>
<div class="core div" id="org618d06c">
<div class="core div" id="org7131f77">
<p>
{\bf Poynting's theorem}
\[
@ -1742,7 +1742,7 @@ We can thus express Poynting's theorem more compactly:
<p>
where we have defined the total
</p>
<div class="core div" id="orgb4f2685">
<div class="core div" id="org44b728f">
<p>
{\bf Energy in electromagnetic fields}
\[
@ -1765,7 +1765,7 @@ Then,
\]
so we get the
</p>
<div class="core div" id="org1eaf77c">
<div class="core div" id="org11d0bdb">
<p>
{\bf Poynting theorem (differential form)}
\[
@ -1782,7 +1782,7 @@ and has a similar for to the continuity equation
<div class="example div" id="org545c704">
<div class="example div" id="orgd2f58ae">
<p>
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting.
Assuming that the field is uniform, the electric field parallel to the wire is
@ -1812,10 +1812,21 @@ and the value is as expected.
<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>

29
build/emd_emw.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_amom.html">Angular Momentum&emsp;<small>[emd.ce.amom]</small></a></li><li>Next:&nbsp;<a href="emd_emw_we.html">The Wave Equation&emsp;<small>[emd.emw.we]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li>Electromagnetic waves in vacuum</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_ce_amom.html">Angular Momentum&emsp;<small>[emd.ce.amom]</small></a></li><li>Next:&nbsp;<a href="emd_emw_we.html">The Wave Equation&emsp;<small>[emd.emw.we]</small></a></li><li>Up:&nbsp;<a href="emd.html">Electromagnetodynamics&emsp;<small>[emd]</small></a></li></ul>
<h3 id="emd_emw">Electromagnetic waves in vacuum<a class="headline-permalink" href="./emd_emw.html#emd_emw"><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"/>
</svg></a><span class="headline-id">emd.emw</span></h3>
<div class="outline-text-3" id="text-emd_emw">
<details class="prereq" id="org5bcd123">
<summary id="org41526cb">
<details class="prereq" id="orgdec6d72">
<summary id="orge09a2b2">
Prerequisites
</summary>
<ul class="org-ul">
@ -1633,8 +1633,8 @@ Prerequisites
</ul>
</details>
<details class="objectives" id="org81e7bec">
<summary id="org62ac99a">
<details class="objectives" id="org9488daa">
<summary id="orgd8d77da">
Objectives
</summary>
<ul class="org-ul">
@ -1660,10 +1660,21 @@ Objectives
<li><a href="emd_emw_ep.html">Energy and Momentum</a><span class="headline-id">emd.emw.ep</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>

25
build/emd_emw_ep.html
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="emd_emw_mpw.html">Monochromatic Plane Waves&emsp;<small>[emd.emw.mpw]</small></a></li><li>Next:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_ep" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_emw.html">Electromagnetic waves in vacuum</a></li><li>Energy and Momentum</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_emw_mpw.html">Monochromatic Plane Waves&emsp;<small>[emd.emw.mpw]</small></a></li><li>Next:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_ep" class="outline-4">
<h4 id="emd_emw_ep">Energy and Momentum<a class="headline-permalink" href="./emd_emw_ep.html#emd_emw_ep"><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"/>
@ -1653,7 +1653,7 @@ so for a monochromatic EM plan wave,
\]
or more succinctly:
</p>
<div class="main div" id="orgeb0be24">
<div class="main div" id="org1741f9a">
<p>
{\bf Poynting vector of a monochromatic EM wave}
\[
@ -1669,7 +1669,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
<p>
Similary, we get the
</p>
<div class="main div" id="org372457d">
<div class="main div" id="orgf6ab132">
<p>
{\bf Momentum density of a monochromatic EM wave}
\[
@ -1705,10 +1705,21 @@ The {\it radiation pressure} is the momentum transfer per unit area per unit of
</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>

23
build/emd_emw_mpw.html
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="emd_emw_we.html">The Wave Equation&emsp;<small>[emd.emw.we]</small></a></li><li>Next:&nbsp;<a href="emd_emw_ep.html">Energy and Momentum&emsp;<small>[emd.emw.ep]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_mpw" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_emw.html">Electromagnetic waves in vacuum</a></li><li>Monochromatic Plane Waves</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_emw_we.html">The Wave Equation&emsp;<small>[emd.emw.we]</small></a></li><li>Next:&nbsp;<a href="emd_emw_ep.html">Energy and Momentum&emsp;<small>[emd.emw.ep]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_mpw" class="outline-4">
<h4 id="emd_emw_mpw">Monochromatic Plane Waves<a class="headline-permalink" href="./emd_emw_mpw.html#emd_emw_mpw"><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"/>
@ -1654,7 +1654,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
Generalizing to propagation in the direction of an arbitrary wavevector
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
</p>
<div class="core div" id="org22a7fdd">
<div class="core div" id="org9f5b19f">
<p>
{\bf E and B fields for a monochromatic EM plane wave}
\[
@ -1683,10 +1683,21 @@ or if you prefer explicit real parts (adding a possible phase shift \(\delta\)):
<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>

23
build/emd_emw_we.html
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="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li><li>Next:&nbsp;<a href="emd_emw_mpw.html">Monochromatic Plane Waves&emsp;<small>[emd.emw.mpw]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_we" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emd.html">Electromagnetodynamics</a></li><li><a class="breadcrumb-link"href="emd_emw.html">Electromagnetic waves in vacuum</a></li><li>The Wave Equation</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li><li>Next:&nbsp;<a href="emd_emw_mpw.html">Monochromatic Plane Waves&emsp;<small>[emd.emw.mpw]</small></a></li><li>Up:&nbsp;<a href="emd_emw.html">Electromagnetic waves in vacuum&emsp;<small>[emd.emw]</small></a></li></ul><div id="outline-container-emd_emw_we" class="outline-4">
<h4 id="emd_emw_we">The Wave Equation<a class="headline-permalink" href="./emd_emw_we.html#emd_emw_we"><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"/>
@ -1651,7 +1651,7 @@ These take the form of coupled first-order partial differential equations for \(
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
we get the
</p>
<div class="core div" id="org1160663">
<div class="core div" id="orgfcad186">
<p>
{\bf Wave equations for electric and magnetic fields in vacuum}
\[
@ -1692,10 +1692,21 @@ the actual electric and magnetic fields are given by the real part.
<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>

21
build/emdm.html
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>Next:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul>
<ul class="breadcrumbs"><li>Electromagnetodynamics in Matter</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul>
<h2 id="emdm">Electromagnetodynamics in Matter<a class="headline-permalink" href="./emdm.html#emdm"><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"/>
@ -1632,10 +1632,21 @@ Table of contents
<li><a href="emdm_emwm.html">Electromagnetic Waves in Matter</a><span class="headline-id">emdm.emwm</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>

21
build/emdm_Me.html
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="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li><li>Next:&nbsp;<a href="emdm_Me_Mem.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me.Mem]</small></a></li><li>Up:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li>Maxwell's Equations in Matter</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li><li>Next:&nbsp;<a href="emdm_Me_Mem.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me.Mem]</small></a></li><li>Up:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li></ul>
<h3 id="emdm_Me">Maxwell's Equations in Matter<a class="headline-permalink" href="./emdm_Me.html#emdm_Me"><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"/>
@ -1632,10 +1632,21 @@ Table of contents
<li><a href="emdm_Me_bc.html">Boundary Conditions</a><span class="headline-id">emdm.Me.bc</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>

37
build/emdm_Me_Mem.html
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="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li><li>Next:&nbsp;<a href="emdm_Me_bc.html">Boundary Conditions&emsp;<small>[emdm.Me.bc]</small></a></li><li>Up:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul><div id="outline-container-emdm_Me_Mem" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_Me.html">Maxwell's Equations in Matter</a></li><li>Maxwell's Equations in Matter</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li><li>Next:&nbsp;<a href="emdm_Me_bc.html">Boundary Conditions&emsp;<small>[emdm.Me.bc]</small></a></li><li>Up:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul><div id="outline-container-emdm_Me_Mem" class="outline-4">
<h4 id="emdm_Me_Mem">Maxwell's Equations in Matter<a class="headline-permalink" href="./emdm_Me_Mem.html#emdm_Me_Mem"><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"/>
@ -1658,7 +1658,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\]
We therefore have the
</p>
<div class="core div" id="orgff46cb4">
<div class="core div" id="org15d7510">
<p>
{\bf Polarization current density}
\[
@ -1676,7 +1676,7 @@ the polarization current is the result of linear motion of charge when
polarization changes). We can check consistency with the continuity equation
associated to the conservation of bound charges:
</p>
<aside id="orgbce7d73">
<aside id="org9c1ef52">
<p>
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
\({\boldsymbol J}_b\) but this is not the convention used here.
@ -1699,7 +1699,7 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
In view of this: total charge density can be separated into 2 parts,
{\it free} and {\it bound}:
</p>
<div class="main div" id="org4df7865">
<div class="main div" id="org2c2e80a">
<p>
\[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
@ -1712,7 +1712,7 @@ In view of this: total charge density can be separated into 2 parts,
and current can be separated into three parts, {\it free}, {\it bound} and
{\it polarization}:
</p>
<div class="main div" id="orgcc32502">
<div class="main div" id="orgafd7f00">
<p>
\[
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
@ -1736,7 +1736,7 @@ Gauss's law: can be rewritten
\]
where (as in static case)
</p>
<div class="core div" id="org7600f00">
<div class="core div" id="orgbd7306c">
<p>
\[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@ -1762,7 +1762,7 @@ or
\]
where as before
</p>
<div class="core div" id="orgb942ad8">
<div class="core div" id="orgde049dc">
<p>
\[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@ -1780,7 +1780,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
<p>
In terms of free charges and currents, we thus get
</p>
<div class="core div" id="orgd9d30d5">
<div class="core div" id="orgf901bae">
<p>
{\bf Maxwell's equations {\it (in matter)}}
</p>
@ -1806,7 +1806,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
in terms of \({\bf E}\) and \({\bf B}\).
For the restricted case of linear media:
</p>
<div class="main div" id="orge1df28e">
<div class="main div" id="org5288a81">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
@ -1828,10 +1828,21 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
<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>

23
build/emdm_Me_bc.html
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="emdm_Me_Mem.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me.Mem]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li><li>Up:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul><div id="outline-container-emdm_Me_bc" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_Me.html">Maxwell's Equations in Matter</a></li><li>Boundary Conditions</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_Me_Mem.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me.Mem]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li><li>Up:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul><div id="outline-container-emdm_Me_bc" class="outline-4">
<h4 id="emdm_Me_bc">Boundary Conditions<a class="headline-permalink" href="./emdm_Me_bc.html#emdm_Me_bc"><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"/>
@ -1625,7 +1625,7 @@ Table of contents
<p>
Discontinuities between different media, deduced from
</p>
<div class="core div" id="orgbbf71a6">
<div class="core div" id="org77f30b2">
<p>
{\bf Maxwell's equations {\it (in matter)}, integral form}
</p>
@ -1701,10 +1701,21 @@ These are basis of theory of reflection and refraction.
</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>

21
build/emdm_emwm.html
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="emdm_Me_bc.html">Boundary Conditions&emsp;<small>[emdm.Me.bc]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_plm.html">Propagation in Linear Media&emsp;<small>[emdm.emwm.plm]</small></a></li><li>Up:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li>Electromagnetic Waves in Matter</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_Me_bc.html">Boundary Conditions&emsp;<small>[emdm.Me.bc]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_plm.html">Propagation in Linear Media&emsp;<small>[emdm.emwm.plm]</small></a></li><li>Up:&nbsp;<a href="emdm.html">Electromagnetodynamics in Matter&emsp;<small>[emdm]</small></a></li></ul>
<h3 id="emdm_emwm">Electromagnetic Waves in Matter<a class="headline-permalink" href="./emdm_emwm.html#emdm_emwm"><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"/>
@ -1635,10 +1635,21 @@ Table of contents
<li><a href="emdm_emwm_wg.html">Waveguides</a><span class="headline-id">emdm.emwm.wg</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>

21
build/emdm_emwm_ad.html
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="emdm_emwm_refl_Ba.html">Brewster's Angle&emsp;<small>[emdm.emwm.refl.Ba]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_ad_c.html">EM Waves in Conductors&emsp;<small>[emdm.emwm.ad.c]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li>Absorption and Dispersion</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_Ba.html">Brewster's Angle&emsp;<small>[emdm.emwm.refl.Ba]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_ad_c.html">EM Waves in Conductors&emsp;<small>[emdm.emwm.ad.c]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<h4 id="emdm_emwm_ad">Absorption and Dispersion<a class="headline-permalink" href="./emdm_emwm_ad.html#emdm_emwm_ad"><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"/>
@ -1631,10 +1631,21 @@ Table of contents
<li><a href="emdm_emwm_ad_c.html">EM Waves in Conductors</a><span class="headline-id">emdm.emwm.ad.c</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>

21
build/emdm_emwm_ad_c.html
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="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li></ul><div id="outline-container-emdm_emwm_ad_c" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_ad.html">Absorption and Dispersion</a></li><li>EM Waves in Conductors</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li></ul><div id="outline-container-emdm_emwm_ad_c" class="outline-5">
<h5 id="emdm_emwm_ad_c">EM Waves in Conductors<a class="headline-permalink" href="./emdm_emwm_ad_c.html#emdm_emwm_ad_c"><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"/>
@ -1727,10 +1727,21 @@ so the final form of the fields is
</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>

23
build/emdm_emwm_plm.html
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="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refr.html">Refraction&emsp;<small>[emdm.emwm.refr]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul><div id="outline-container-emdm_emwm_plm" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li>Propagation in Linear Media</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refr.html">Refraction&emsp;<small>[emdm.emwm.refr]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul><div id="outline-container-emdm_emwm_plm" class="outline-4">
<h4 id="emdm_emwm_plm">Propagation in Linear Media<a class="headline-permalink" href="./emdm_emwm_plm.html#emdm_emwm_plm"><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"/>
@ -1660,7 +1660,7 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
\]
where the index of refraction of the material is defined as
</p>
<div class="main div" id="orgeaea7cb">
<div class="main div" id="org72bb44e">
<p>
{\bf Index of refraction}
\[
@ -1702,10 +1702,21 @@ I = \frac{1}{2} \varepsilon v E_0^2
<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>

21
build/emdm_emwm_refl.html
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="emdm_emwm_refr.html">Refraction&emsp;<small>[emdm.emwm.refr]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li>Reflection and Transmission</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refr.html">Refraction&emsp;<small>[emdm.emwm.refr]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<h4 id="emdm_emwm_refl">Reflection and Transmission<a class="headline-permalink" href="./emdm_emwm_refl.html#emdm_emwm_refl"><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"/>
@ -1646,10 +1646,21 @@ Detailed study: starts from boundary conditions \ref{Gr(7.64)},
<li><a href="emdm_emwm_refl_Ba.html">Brewster's Angle</a><span class="headline-id">emdm.emwm.refl.Ba</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>

21
build/emdm_emwm_refl_Ba.html
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="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_Ba" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_refl.html">Reflection and Transmission</a></li><li>Brewster's Angle</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_ad.html">Absorption and Dispersion&emsp;<small>[emdm.emwm.ad]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_Ba" class="outline-5">
<h5 id="emdm_emwm_refl_Ba">Brewster's Angle<a class="headline-permalink" href="./emdm_emwm_refl_Ba.html#emdm_emwm_refl_Ba"><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"/>
@ -1626,10 +1626,21 @@ Table of contents
</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>

21
build/emdm_emwm_refl_Fe.html
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="emdm_emwm_refl_oi.html">Oblique Incidence&emsp;<small>[emdm.emwm.refl.oi]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Ba.html">Brewster's Angle&emsp;<small>[emdm.emwm.refl.Ba]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_Fe" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_refl.html">Reflection and Transmission</a></li><li>Fresnel's Equations</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_oi.html">Oblique Incidence&emsp;<small>[emdm.emwm.refl.oi]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Ba.html">Brewster's Angle&emsp;<small>[emdm.emwm.refl.Ba]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_Fe" class="outline-5">
<h5 id="emdm_emwm_refl_Fe">Fresnel's Equations<a class="headline-permalink" href="./emdm_emwm_refl_Fe.html#emdm_emwm_refl_Fe"><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"/>
@ -1627,10 +1627,21 @@ Table of contents
<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>

21
build/emdm_emwm_refl_ni.html
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="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_oi.html">Oblique Incidence&emsp;<small>[emdm.emwm.refl.oi]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_ni" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_refl.html">Reflection and Transmission</a></li><li>Normal Incidence</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_oi.html">Oblique Incidence&emsp;<small>[emdm.emwm.refl.oi]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_ni" class="outline-5">
<h5 id="emdm_emwm_refl_ni">Normal Incidence<a class="headline-permalink" href="./emdm_emwm_refl_ni.html#emdm_emwm_refl_ni"><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"/>
@ -1718,10 +1718,21 @@ R + T = 1.
<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>

29
build/emdm_emwm_refl_oi.html
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="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_oi" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_refl.html">Reflection and Transmission</a></li><li>Oblique Incidence</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_oi" class="outline-5">
<h5 id="emdm_emwm_refl_oi">Oblique Incidence<a class="headline-permalink" href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi"><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"/>
@ -1660,7 +1660,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
<p>
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
</p>
<div class="core div" id="orga1858e0">
<div class="core div" id="org699621d">
<p>
{\bf First law of reflection:}
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
@ -1675,7 +1675,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
and the angle of refraction (\(\theta_T\)) obey the following laws:
</p>
<div class="core div" id="orgc1aaaad">
<div class="core div" id="orgb0b59f9">
<p>
{\bf Law of reflection}
\[
@ -1733,7 +1733,7 @@ while the third equation becomes
\]
Writing everything in terms of the incident amplitude, we get
</p>
<div class="main div" id="org4da7748">
<div class="main div" id="orgefa3e67">
<p>
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
\[
@ -1753,7 +1753,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
</p>
<div class="main div" id="orge2d9787">
<div class="main div" id="orgd248cb3">
<p>
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
\[
@ -1788,10 +1788,21 @@ Of course, we get \(R + T = 1\) as expected.
<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>

21
build/emdm_emwm_refr.html
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="emdm_emwm_plm.html">Propagation in Linear Media&emsp;<small>[emdm.emwm.plm]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul><div id="outline-container-emdm_emwm_refr" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li>Refraction</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_plm.html">Propagation in Linear Media&emsp;<small>[emdm.emwm.plm]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul><div id="outline-container-emdm_emwm_refr" class="outline-4">
<h4 id="emdm_emwm_refr">Refraction<a class="headline-permalink" href="./emdm_emwm_refr.html#emdm_emwm_refr"><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"/>
@ -1627,10 +1627,21 @@ Table of contents
<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>

21
build/emdm_emwm_wg.html
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="emdm_emwm_ad_c.html">EM Waves in Conductors&emsp;<small>[emdm.emwm.ad.c]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_gw.html">Guided waves&emsp;<small>[emdm.emwm.wg.gw]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li>Waveguides</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_ad_c.html">EM Waves in Conductors&emsp;<small>[emdm.emwm.ad.c]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_gw.html">Guided waves&emsp;<small>[emdm.emwm.wg.gw]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm.html">Electromagnetic Waves in Matter&emsp;<small>[emdm.emwm]</small></a></li></ul>
<h4 id="emdm_emwm_wg">Waveguides<a class="headline-permalink" href="./emdm_emwm_wg.html#emdm_emwm_wg"><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"/>
@ -1633,10 +1633,21 @@ Table of contents
<li><a href="emdm_emwm_wg_c.html">Coaxial Lines</a><span class="headline-id">emdm.emwm.wg.c</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>

21
build/emdm_emwm_wg_c.html
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="emdm_emwm_wg_r.html">Rectangular Waveguides&emsp;<small>[emdm.emwm.wg.r]</small></a></li><li>Next:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_c" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_wg.html">Waveguides</a></li><li>Coaxial Lines</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_wg_r.html">Rectangular Waveguides&emsp;<small>[emdm.emwm.wg.r]</small></a></li><li>Next:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_c" class="outline-5">
<h5 id="emdm_emwm_wg_c">Coaxial Lines<a class="headline-permalink" href="./emdm_emwm_wg_c.html#emdm_emwm_wg_c"><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"/>
@ -1653,10 +1653,21 @@ where \(A\) is a constant amplitude. Substituting and taking the real part,
</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>

21
build/emdm_emwm_wg_gw.html
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="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_r.html">Rectangular Waveguides&emsp;<small>[emdm.emwm.wg.r]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_gw" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_wg.html">Waveguides</a></li><li>Guided waves</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_r.html">Rectangular Waveguides&emsp;<small>[emdm.emwm.wg.r]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_gw" class="outline-5">
<h5 id="emdm_emwm_wg_gw">Guided waves<a class="headline-permalink" href="./emdm_emwm_wg_gw.html#emdm_emwm_wg_gw"><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"/>
@ -1677,10 +1677,21 @@ with an identical equation for \(B_z\). If \(E_z = 0\) the waves are called {\bf
<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>

21
build/emdm_emwm_wg_r.html
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="emdm_emwm_wg_gw.html">Guided waves&emsp;<small>[emdm.emwm.wg.gw]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_c.html">Coaxial Lines&emsp;<small>[emdm.emwm.wg.c]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_r" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_wg.html">Waveguides</a></li><li>Rectangular Waveguides</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_wg_gw.html">Guided waves&emsp;<small>[emdm.emwm.wg.gw]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_wg_c.html">Coaxial Lines&emsp;<small>[emdm.emwm.wg.c]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_wg.html">Waveguides&emsp;<small>[emdm.emwm.wg]</small></a></li></ul><div id="outline-container-emdm_emwm_wg_r" class="outline-5">
<h5 id="emdm_emwm_wg_r">Rectangular Waveguides<a class="headline-permalink" href="./emdm_emwm_wg_r.html#emdm_emwm_wg_r"><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"/>
@ -1686,10 +1686,21 @@ which is {\it greater} than \(c\). The energy of the wave however propagates at
<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>

29
build/emf.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Next:&nbsp;<a href="emf_svp.html">Scalar and Vector Potentials&emsp;<small>[emf.svp]</small></a></li></ul>
<ul class="breadcrumbs"><li>Electromagnetic Fields</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="emf_svp.html">Scalar and Vector Potentials&emsp;<small>[emf.svp]</small></a></li></ul>
<h2 id="emf">Electromagnetic Fields<a class="headline-permalink" href="./emf.html#emf"><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"/>
</svg></a><span class="headline-id">emf</span></h2>
<div class="outline-text-2" id="text-emf">
<details class="prereq" id="org86ffe7e">
<summary id="org72ae362">
<details class="prereq" id="org50b623e">
<summary id="org0ab4ba1">
Prerequisites
</summary>
<ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul>
</details>
<details class="objectives" id="org9d4a979">
<summary id="org984c0c5">
<details class="objectives" id="orgd15b77d">
<summary id="org61c366f">
Objectives
</summary>
<ul class="org-ul">
@ -1654,10 +1654,21 @@ Objectives
<li><a href="emf_g.html">Gauge Freedom and Choices</a><span class="headline-id">emf.g</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>

21
build/emf_g.html
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="emf_svp.html">Scalar and Vector Potentials&emsp;<small>[emf.svp]</small></a></li><li>Next:&nbsp;<a href="emf_g_Cg.html">Coulomb Gauge&emsp;<small>[emf.g.Cg]</small></a></li><li>Up:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emf.html">Electromagnetic Fields</a></li><li>Gauge Freedom and Choices</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emf_svp.html">Scalar and Vector Potentials&emsp;<small>[emf.svp]</small></a></li><li>Next:&nbsp;<a href="emf_g_Cg.html">Coulomb Gauge&emsp;<small>[emf.g.Cg]</small></a></li><li>Up:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li></ul>
<h3 id="emf_g">Gauge Freedom and Choices<a class="headline-permalink" href="./emf_g.html#emf_g"><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"/>
@ -1651,10 +1651,21 @@ implementing a <b>gauge transformation</b>.
<li><a href="emf_g_Lg.html">Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations</a><span class="headline-id">emf.g.Lg</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>

21
build/emf_g_Cg.html
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="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li><li>Next:&nbsp;<a href="emf_g_Lg.html">Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations&emsp;<small>[emf.g.Lg]</small></a></li><li>Up:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li></ul><div id="outline-container-emf_g_Cg" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emf.html">Electromagnetic Fields</a></li><li><a class="breadcrumb-link"href="emf_g.html">Gauge Freedom and Choices</a></li><li>Coulomb Gauge</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li><li>Next:&nbsp;<a href="emf_g_Lg.html">Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations&emsp;<small>[emf.g.Lg]</small></a></li><li>Up:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li></ul><div id="outline-container-emf_g_Cg" class="outline-4">
<h4 id="emf_g_Cg">Coulomb Gauge<a class="headline-permalink" href="./emf_g_Cg.html#emf_g_Cg"><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"/>
@ -1650,10 +1650,21 @@ Although Gauss's law looks nice in the Coulomb gauge, Amp{\`e}re-Maxwell does no
<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>

25
build/emf_g_Lg.html
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="emf_g_Cg.html">Coulomb Gauge&emsp;<small>[emf.g.Cg]</small></a></li><li>Next:&nbsp;<a href="red.html">Relativistic Electrodynamics&emsp;<small>[red]</small></a></li><li>Up:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li></ul><div id="outline-container-emf_g_Lg" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emf.html">Electromagnetic Fields</a></li><li><a class="breadcrumb-link"href="emf_g.html">Gauge Freedom and Choices</a></li><li>Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emf_g_Cg.html">Coulomb Gauge&emsp;<small>[emf.g.Cg]</small></a></li><li>Next:&nbsp;<a href="red.html">Relativistic Electrodynamics&emsp;<small>[red]</small></a></li><li>Up:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li></ul><div id="outline-container-emf_g_Lg" class="outline-4">
<h4 id="emf_g_Lg">Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations<a class="headline-permalink" href="./emf_g_Lg.html#emf_g_Lg"><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"/>
@ -1638,7 +1638,7 @@ while the equation for \(V\) becomes
\]
These can be written compactly upon introducing a new operator: the
</p>
<div class="core div" id="orgd4a4d0b">
<div class="core div" id="org9e9974a">
<p>
{\bf d'Alembertian operator}
\[
@ -1651,7 +1651,7 @@ These can be written compactly upon introducing a new operator: the
<p>
so we get the
</p>
<div class="core div" id="orgbeb1250">
<div class="core div" id="org521f6f7">
<p>
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
\[
@ -1686,10 +1686,21 @@ we have by direct inspection
</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>

29
build/emf_svp.html
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="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li><li>Next:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li><li>Up:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li></ul><div id="outline-container-emf_svp" class="outline-3">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emf.html">Electromagnetic Fields</a></li><li>Scalar and Vector Potentials</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li><li>Next:&nbsp;<a href="emf_g.html">Gauge Freedom and Choices&emsp;<small>[emf.g]</small></a></li><li>Up:&nbsp;<a href="emf.html">Electromagnetic Fields&emsp;<small>[emf]</small></a></li></ul><div id="outline-container-emf_svp" class="outline-3">
<h3 id="emf_svp">Scalar and Vector Potentials<a class="headline-permalink" href="./emf_svp.html#emf_svp"><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"/>
@ -1639,7 +1639,7 @@ Useful strategy: represent fields in terms of potentials.
<p>
Easiest:
</p>
<div class="core div" id="org45e0ed0">
<div class="core div" id="org25c4e2b">
<p>
\[
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
@ -1655,7 +1655,7 @@ Putting this into Faraday's law gives
\]
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
</p>
<div class="core div" id="orgb9810af">
<div class="core div" id="orgad63bf4">
<p>
\[
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
@ -1668,7 +1668,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
<p>
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) into Gauss's law gives
</p>
<div class="main div" id="org1c236f0">
<div class="main div" id="org64e1b1a">
<p>
\[
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
@ -1684,7 +1684,7 @@ whereas Amp{\`ere}-Maxwell becomes
\]
which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
</p>
<div class="main div" id="orgf3f4dcd">
<div class="main div" id="org184a5ba">
<p>
\[
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
@ -1705,10 +1705,21 @@ which becomes after simple rearrangement and use of the identity \({\boldsymbol
<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>

21
build/ems.html
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>Next:&nbsp;<a href="ems_es.html">Electrostatics&emsp;<small>[ems.es]</small></a></li></ul>
<ul class="breadcrumbs"><li>Electromagnetostatics</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="ems_es.html">Electrostatics&emsp;<small>[ems.es]</small></a></li></ul>
<h2 id="ems">Electromagnetostatics<a class="headline-permalink" href="./ems.html#ems"><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"/>
@ -1634,10 +1634,21 @@ Table of contents
<li><a href="ems_ms.html">Magnetostatics</a><span class="headline-id">ems.ms</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>

29
build/ems_ca.html
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>
@ -1616,15 +1616,15 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_es_c_cap.html">Capacitors&emsp;<small>[ems.es.c.cap]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Up:&nbsp;<a href="ems.html">Electromagnetostatics&emsp;<small>[ems]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li>Calculating or Approximating the Electrostatic Potential</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_es_c_cap.html">Capacitors&emsp;<small>[ems.es.c.cap]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Up:&nbsp;<a href="ems.html">Electromagnetostatics&emsp;<small>[ems]</small></a></li></ul>
<h3 id="ems_ca">Calculating or Approximating the Electrostatic Potential<a class="headline-permalink" href="./ems_ca.html#ems_ca"><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"/>
</svg></a><span class="headline-id">ems.ca</span></h3>
<div class="outline-text-3" id="text-ems_ca">
<details class="prereq" id="orgbb80f83">
<summary id="org379b6a1">
<details class="prereq" id="org813707e">
<summary id="org67fafaf">
Prerequisites
</summary>
<ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul>
</details>
<details class="objectives" id="orgd1100e2">
<summary id="org27953b9">
<details class="objectives" id="orgd74f98a">
<summary id="orgcfc756e">
Objectives
</summary>
<ul class="org-ul">
@ -1656,10 +1656,21 @@ Objectives
<li><a href="ems_ca_me.html">The Multipole Expansion</a><span class="headline-id">ems.ca.me</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>

29
build/ems_ca_fe.html
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="ems_ca.html">Calculating or Approximating the Electrostatic Potential&emsp;<small>[ems.ca]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_L.html">The Laplace Equation&emsp;<small>[ems.ca.fe.L]</small></a></li><li>Up:&nbsp;<a href="ems_ca.html">Calculating or Approximating the Electrostatic Potential&emsp;<small>[ems.ca]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li><a class="breadcrumb-link"href="ems_ca.html">Calculating or Approximating the Electrostatic Potential</a></li><li>Fundamental Equations for the Electrostatic Potential</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca.html">Calculating or Approximating the Electrostatic Potential&emsp;<small>[ems.ca]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_L.html">The Laplace Equation&emsp;<small>[ems.ca.fe.L]</small></a></li><li>Up:&nbsp;<a href="ems_ca.html">Calculating or Approximating the Electrostatic Potential&emsp;<small>[ems.ca]</small></a></li></ul>
<h4 id="ems_ca_fe">Fundamental Equations for the Electrostatic Potential<a class="headline-permalink" href="./ems_ca_fe.html#ems_ca_fe"><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"/>
@ -1628,7 +1628,7 @@ A generic configuration of static charges coupled via the Coulomb interaction
defines an electrostatic problem, whose solution is in principle obtained
from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
</p>
<div class="main div" id="org14f8ad7">
<div class="main div" id="orgcced719">
\begin{equation*}
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
\end{equation*}
@ -1638,7 +1638,7 @@ from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_v
or (often simpler) by calculating the electrostatic potential, using either the
explicit construction (\ref{eq:V_from_rho})
</p>
<div class="main div" id="org83b53d5">
<div class="main div" id="org68ed8a6">
<p>
\[
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
@ -1654,7 +1654,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
</p>
<div class="core div" id="org52d8655">
<div class="core div" id="org828a92b">
<p>
\[
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
@ -1668,7 +1668,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
In the specific case where the charge density vanishes, we fall back onto the simpler
Laplace equation
</p>
<div class="core div" id="orgceb6a79">
<div class="core div" id="org6c130c8">
<p>
\[
{\boldsymbol \nabla}^2 V = 0
@ -1688,10 +1688,21 @@ Laplace equation
<li><a href="ems_ca_fe_uP.html">Uniqueness of Solution to Poisson's Equation</a><span class="headline-id">ems.ca.fe.uP</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>

23
build/ems_ca_fe_L.html
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="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_g.html">Green's Identities&emsp;<small>[ems.ca.fe.g]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_L" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li><a class="breadcrumb-link"href="ems_ca.html">Calculating or Approximating the Electrostatic Potential</a></li><li><a class="breadcrumb-link"href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential</a></li><li>The Laplace Equation</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_g.html">Green's Identities&emsp;<small>[ems.ca.fe.g]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_L" class="outline-5">
<h5 id="ems_ca_fe_L">The Laplace Equation<a class="headline-permalink" href="./ems_ca_fe_L.html#ems_ca_fe_L"><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"/>
@ -1702,7 +1702,7 @@ are necessarily positive, we thus require \(f_x &gt; 0\), \(f_y &gt; 0\) and \(f
of the \(f_x + f_y + f_z = 0\) condition above.
</p>
<div class="info div" id="org12caa26">
<div class="info div" id="org65435f8">
<p>
<b>Earnshaw's theorem</b> <br>
Since solutions to Laplace's equation have no local minimum,
@ -1790,10 +1790,21 @@ This all feels a bit amateurish and not very systematic. Can we be more precise
<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>

25
build/ems_ca_fe_g.html
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>
@ -1616,17 +1616,17 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe_L.html">The Laplace Equation&emsp;<small>[ems.ca.fe.L]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_uP.html">Uniqueness of Solution to Poisson's Equation&emsp;<small>[ems.ca.fe.uP]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_g" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="ems.html">Electromagnetostatics</a></li><li><a class="breadcrumb-link"href="ems_ca.html">Calculating or Approximating the Electrostatic Potential</a></li><li><a class="breadcrumb-link"href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential</a></li><li>Green's Identities</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe_L.html">The Laplace Equation&emsp;<small>[ems.ca.fe.L]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_uP.html">Uniqueness of Solution to Poisson's Equation&emsp;<small>[ems.ca.fe.uP]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_g" class="outline-5">
<h5 id="ems_ca_fe_g">Green's Identities<a class="headline-permalink" href="./ems_ca_fe_g.html#ems_ca_fe_g"><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"/>
</svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
<div class="outline-text-5" id="text-ems_ca_fe_g">
<div class="info div" id="org8d7045e">
<div class="info div" id="orgd896c19">
<p>
<b>George Green</b>
</p>
<aside id="org53725f0">
<aside id="org07b8bae">
<p>
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
</p>
@ -1678,10 +1678,21 @@ interchanged, and subtract the result, we obtain another useful result known as
<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>

Some files were not shown because too many files have changed in this diff Show More