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> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="a_l.html">Literature</a><span class="headline-id">a.l</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/a_l.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m.html">Mathematics</a><span class="headline-id">c.m</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_uf.html">Useful Formulas</a><span class="headline-id">c.m.uf</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_cs.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_cs_hyp.html">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

33
build/c_m_cs_cyl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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"> <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> <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="outline-text-6" id="text-c_m_cs_cyl_grad">
<div class="eqlabel" id="orgc4b6bac"> <div class="eqlabel" id="org397e9ce">
<p> <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"> <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="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"/> <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> </svg></a>
</p> </p>
<div class="alteqlabels" id="orgdcdbcb4"> <div class="alteqlabels" id="org3648e8a">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(1.79)</li> <li>Gr4(1.79)</li>
</ul> </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"> <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> <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="outline-text-6" id="text-c_m_cs_cyl_div">
<div class="eqlabel" id="orgf9d0262"> <div class="eqlabel" id="orgb76ebc0">
<p> <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"> <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="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"/> <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> </svg></a>
</p> </p>
<div class="alteqlabels" id="orgd456be1"> <div class="alteqlabels" id="orgc052c68">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(2.21)</li> <li>Gr4(2.21)</li>
</ul> </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"> <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> <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="outline-text-6" id="text-c_m_cs_cyl_curl">
<div class="eqlabel" id="orgeb922d3"> <div class="eqlabel" id="orgaaf2c4a">
<p> <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"> <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="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"/> <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> </svg></a>
</p> </p>
<div class="alteqlabels" id="org66ae846"> <div class="alteqlabels" id="orgcf0b798">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(2.21)</li> <li>Gr4(2.21)</li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_cs_hyp.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_cs_sph.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_dc_d2.html">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc_curl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

51
build/c_m_dc_d2.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 class="outline-text-5" id="text-c_m_dc_d2">
</div> </div>
<div id="outline-container-org5fd48d1" class="outline-6"> <div id="outline-container-orga13f3ad" class="outline-6">
<h6 id="org5fd48d1"><a href="#org5fd48d1">Divergence of gradient</a></h6> <h6 id="orga13f3ad"><a href="#orga13f3ad">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-org5fd48d1"> <div class="outline-text-6" id="text-orga13f3ad">
<p> <p>
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\). \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) 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 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> </div>
<div id="outline-container-org41a3448" class="outline-6"> <div id="outline-container-orgf350618" class="outline-6">
<h6 id="org41a3448"><a href="#org41a3448">Curl of a gradient</a></h6> <h6 id="orgf350618"><a href="#orgf350618">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org41a3448"> <div class="outline-text-6" id="text-orgf350618">
<p> <p>
This always vanishes. This always vanishes.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org6c4b5a7" class="outline-6"> <div id="outline-container-orgb23671d" class="outline-6">
<h6 id="org6c4b5a7"><a href="#org6c4b5a7">Gradient of the divergence</a></h6> <h6 id="orgb23671d"><a href="#orgb23671d">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org6c4b5a7"> <div class="outline-text-6" id="text-orgb23671d">
<p> <p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name. \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org68b62ab" class="outline-6"> <div id="outline-container-org0373292" class="outline-6">
<h6 id="org68b62ab"><a href="#org68b62ab">Divergence of a curl</a></h6> <h6 id="org0373292"><a href="#org0373292">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org68b62ab"> <div class="outline-text-6" id="text-org0373292">
<p> <p>
This always vanishes. This always vanishes.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org62690be" class="outline-6"> <div id="outline-container-org21d697e" class="outline-6">
<h6 id="org62690be"><a href="#org62690be">Curl of curl</a></h6> <h6 id="org21d697e"><a href="#org21d697e">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org62690be"> <div class="outline-text-6" id="text-org21d697e">
<p> <p>
\[ \[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v} {\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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc_del.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc_div.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc_g.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dc_pr.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dd.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dd_1d.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/c_m_dd_3d.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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, More generally,
</p> </p>
<div class="eqlabel" id="org276d185"> <div class="eqlabel" id="org63ae2fc">
<p> <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"> <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="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"/> <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> </svg></a>
</p> </p>
<div class="alteqlabels" id="org676b181"> <div class="alteqlabels" id="org4992249">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr (1.100)</li> <li>Gr (1.100)</li>
</ul> </ul>
@ -1688,10 +1688,21 @@ we have that
</div> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_dd_div.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_ic.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_ic_ip.html">Integration by Parts</a><span class="headline-id">c.m.ic.ip</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_ic_ftc.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_ic_ftg.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_ic_gauss.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_ic_ip.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

39
build/c_m_ic_lsv.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 class="outline-text-5" id="text-c_m_ic_lsv">
</div> </div>
<div id="outline-container-org609a3df" class="outline-6"> <div id="outline-container-org552d286" class="outline-6">
<h6 id="org609a3df"><a href="#org609a3df">Line Integrals</a></h6> <h6 id="org552d286"><a href="#org552d286">Line Integrals</a></h6>
<div class="outline-text-6" id="text-org609a3df"> <div class="outline-text-6" id="text-org552d286">
<p> <p>
\[ \[
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l} {\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> </div>
<div id="outline-container-org8f657b7" class="outline-6"> <div id="outline-container-org8d260ce" class="outline-6">
<h6 id="org8f657b7"><a href="#org8f657b7">Surface Integrals</a></h6> <h6 id="org8d260ce"><a href="#org8d260ce">Surface Integrals</a></h6>
<div class="outline-text-6" id="text-org8f657b7"> <div class="outline-text-6" id="text-org8d260ce">
<p> <p>
\[ \[
\int_{\cal S} {\bf v} \cdot d{\bf a} \int_{\cal S} {\bf v} \cdot d{\bf a}
@ -1677,9 +1677,9 @@ Over a closed surface:
</div> </div>
</div> </div>
<div id="outline-container-org2ec267e" class="outline-6"> <div id="outline-container-org57765dc" class="outline-6">
<h6 id="org2ec267e"><a href="#org2ec267e">Volume Integrals</a></h6> <h6 id="org57765dc"><a href="#org57765dc">Volume Integrals</a></h6>
<div class="outline-text-6" id="text-org2ec267e"> <div class="outline-text-6" id="text-org57765dc">
<p> <p>
\[ \[
\int_{\cal V} T d\tau \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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/c_m_ic_stokes.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,20 +1616,20 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="outline-text-5" id="text-c_m_ic_stokes">
<div class="eqlabel" id="org4321094"> <div class="eqlabel" id="org5b773ee">
<p> <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"> <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="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"/> <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> </svg></a>
</p> </p>
<div class="alteqlabels" id="org03c3b7b"> <div class="alteqlabels" id="org815e278">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr (1.57)</li> <li>Gr (1.57)</li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_uf.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_uf_vi.html">Vector identities</a><span class="headline-id">c.m.uf.vi</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_uf_cyl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_uf_sph.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_uf_vi.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va_cp.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va_n.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va_pds.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va_sp.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_va_tp.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_vf.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="c_m_vf_pot.html">Potentials</a><span class="headline-id">c.m.vf.pot</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_vf_helm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/c_m_vf_pot.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/d.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">d</span></h2>
<div class="outline-text-2" id="text-d"> <div class="outline-text-2" id="text-d">
<details class="objectives" id="orgdc678ad"> <details class="objectives" id="org9cfb206">
<summary id="org6e8a387"> <summary id="org87be4b2">
Objectives Objectives
</summary> </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> <li><a href="d_red.html">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emd.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emd_ce.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emd_emw.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emf.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_ems.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_ems_ca.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_ems_ms.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emsm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_emsm_msm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_m.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/d_red.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emd.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">emd</span></h2>
<div class="outline-text-2" id="text-emd"> <div class="outline-text-2" id="text-emd">
<details class="prereq" id="org91070ea"> <details class="prereq" id="org94bea47">
<summary id="orgec443fc"> <summary id="orgb7d0bc3">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1633,8 +1633,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org7a852ae"> <details class="objectives" id="org0cdfa86">
<summary id="org301eba1"> <summary id="org2927d33">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <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> <li><a href="emd_emw.html">Electromagnetic waves in vacuum</a><span class="headline-id">emd.emw</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emd_Fl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emd_Fl_e.html">Energy in Magnetic Fields</a><span class="headline-id">emd.Fl.e</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

27
build/emd_Fl_Fl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 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 along the wire. The line integral of this field is called the
</p> </p>
<div class="core div" id="orgcb2b8bd"> <div class="core div" id="org8786846">
<p> <p>
<b>Electromotive force (or electromotance)</b>, <b>Electromotive force (or electromotance)</b>,
\[ \[
@ -1685,7 +1685,7 @@ to the rate of change of the magnetic flux,
\] \]
so we obtain so we obtain
</p> </p>
<div class="core div" id="org826bbb5"> <div class="core div" id="org278fea1">
<p> <p>
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>) <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 we obtain
</p> </p>
<div class="core div" id="org4f576bd"> <div class="core div" id="org63211df">
<p> <p>
<b>Faraday's law</b> (differential form) <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/emd_Fl_e.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
</p> </p>
<div class="core div" id="org612a7d5"> <div class="core div" id="orge86302b">
<p> <p>
\[ \[
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2 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)} \hspace{2cm} \mbox{(7.31 and 7.34)}
\end{align} \end{align}
<div class="example div" id="org8806452"> <div class="example div" id="org0c0ebda">
<p> <p>
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\). \paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
Find energy stored in section of length \(l\). 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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

27
build/emd_Fl_i.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </p>
<div class="example div" id="org105c83a"> <div class="example div" id="org6c1a2e4">
<p> <p>
\paragraph{Example 7.10:} \paragraph{Example 7.10:}
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside 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> </p>
<div class="example div" id="orgfde0fbc"> <div class="example div" id="org96ae3fa">
<p> <p>
\paragraph{Example 7.11:} find self-inductance of toroidal coil with \paragraph{Example 7.11:} find self-inductance of toroidal coil with
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\)) 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}. Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
</p> </p>
<div class="example div" id="org88909b4"> <div class="example div" id="orgde2bf6d">
<p> <p>
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\). \paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
What is the current ? 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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

27
build/emd_Fl_ief.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
{\bf Example 7.7:} {\bf Example 7.7:}
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ? \({\bf B}(t)\) 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>
<div class="example div" id="org5fbf230"> <div class="example div" id="org3040ba3">
<p> <p>
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim. {\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 \(a &lt; b\), 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. 'slow enough' phenomena.
</p> </p>
<div class="example div" id="org4c83960"> <div class="example div" id="org805b5d5">
<p> <p>
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find {\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
induced \({\bf E}\) field as a function of distance \(s\) from wire. 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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emd_Me.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emd_Me_mc.html">Magnetic Charge</a><span class="headline-id">emd.Me.mc</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

27
build/emd_Me_Me.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
Full set of equations for the electromagnetic field: Full set of equations for the electromagnetic field:
</p> </p>
<div class="core div" id="org61cd67c"> <div class="core div" id="org501476d">
<p> <p>
{\bf Maxwell's equations} {\it (in vacuum)} {\bf Maxwell's equations} {\it (in vacuum)}
</p> </p>
@ -1641,7 +1641,7 @@ Full set of equations for the electromagnetic field:
<p> <p>
Complement: Complement:
</p> </p>
<div class="core div" id="org2b8e704"> <div class="core div" id="orgb357d3d">
<p> <p>
{\bf Force law} {\bf Force law}
\[ \[
@ -1665,7 +1665,7 @@ take divergence of \((iv)\).
<p> <p>
Better way of writing: all fields on left, all sources on right, Better way of writing: all fields on left, all sources on right,
</p> </p>
<div class="core div" id="orgac16379"> <div class="core div" id="org0a81935">
\begin{align} \begin{align}
(i) &amp;{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0}, (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, \\ &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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/emd_Me_dc.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 The extra term would thus be eliminated if we were to put
</p> </p>
<div class="core div" id="orgc09ac90"> <div class="core div" id="orgd8174ee">
<p> <p>
\[ \[
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t} {\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> <p>
Maxwell baptized this term the Maxwell baptized this term the
</p> </p>
<div class="core div" id="orgd2c9b8e"> <div class="core div" id="orgb36d854">
<p> <p>
{\bf Displacement current} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emd_Me_ebM.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emd_Me_mc.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emd_ce.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">emd.ce</span></h3>
<div class="outline-text-3" id="text-emd_ce"> <div class="outline-text-3" id="text-emd_ce">
<details class="prereq" id="orgcfe0487"> <details class="prereq" id="org26df1fb">
<summary id="orge8a2c1d"> <summary id="org34d471f">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org87970ae"> <details class="objectives" id="orgaff4273">
<summary id="org29e69c3"> <summary id="orge67f1e6">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <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> <li><a href="emd_ce_amom.html">Angular Momentum</a><span class="headline-id">emd.ce.amom</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emd_ce_amom.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
The angular momentum of EM fields is directly given by The angular momentum of EM fields is directly given by
</p> </p>
<div class="main div" id="org15be82e"> <div class="main div" id="org8fc773b">
<p> <p>
{\bf Angular momentum of EM fields} {\bf Angular momentum of EM fields}
\[ \[
@ -1640,10 +1640,21 @@ The angular momentum of EM fields is directly given by
</div> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emd_ce_ce.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 Since this is true for any volume, we have (re)derived the
</p> </p>
<div class="core div" id="orgf7fdcf4"> <div class="core div" id="org068de4a">
<p> <p>
{\bf Continuity equation} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/emd_ce_mom.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
This is thus simply a conservation law for momentum, with This is thus simply a conservation law for momentum, with
</p> </p>
<div class="main div" id="orgeb408ef"> <div class="main div" id="orgb401242">
<p> <p>
{\bf Momentum density in the EM fields} {\bf Momentum density in the EM fields}
\[ \[
@ -1649,7 +1649,7 @@ This is thus simply a conservation law for momentum, with
<p> <p>
In a region in which the mechanical momentum is not changing due to external influences, we then have the In a region in which the mechanical momentum is not changing due to external influences, we then have the
</p> </p>
<div class="main div" id="org94bfc0c"> <div class="main div" id="orgd377c8a">
<p> <p>
{\bf Continuity equation for EM momentum} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

27
build/emd_ce_mst.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
This expression can be greatly simplified by introducing the This expression can be greatly simplified by introducing the
</p> </p>
<div class="main div" id="org516af43"> <div class="main div" id="orgf0f558d">
<p> <p>
{\bf Maxwell stress tensor} {\bf Maxwell stress tensor}
\[ \[
@ -1702,7 +1702,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
<p> <p>
We then obtain We then obtain
</p> </p>
<div class="main div" id="org38f0a89"> <div class="main div" id="orgcd1da6b">
<p> <p>
{\bf EM force per unit volume} {\bf EM force per unit volume}
\[ \[
@ -1714,7 +1714,7 @@ We then obtain
<p> <p>
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
</p> </p>
<div class="main div" id="orgf9a42ff"> <div class="main div" id="orgf2db445">
<p> <p>
{\bf Total force on charges in volume} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

33
build/emd_ce_poy.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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, Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
we obtain we obtain
</p> </p>
<div class="main div" id="org33b0d12"> <div class="main div" id="org75886ff">
<p> <p>
{\bf Poynting's theorem} {\bf Poynting's theorem}
\[ \[
@ -1716,7 +1716,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
<p> <p>
Energy per unit time, per unit area carried by EM fields: Energy per unit time, per unit area carried by EM fields:
</p> </p>
<div class="core div" id="orgb00d4be"> <div class="core div" id="orgb6d912b">
<p> <p>
{\bf Poynting vector} {\bf Poynting vector}
\[ \[
@ -1729,7 +1729,7 @@ Energy per unit time, per unit area carried by EM fields:
<p> <p>
We can thus express Poynting's theorem more compactly: We can thus express Poynting's theorem more compactly:
</p> </p>
<div class="core div" id="org618d06c"> <div class="core div" id="org7131f77">
<p> <p>
{\bf Poynting's theorem} {\bf Poynting's theorem}
\[ \[
@ -1742,7 +1742,7 @@ We can thus express Poynting's theorem more compactly:
<p> <p>
where we have defined the total where we have defined the total
</p> </p>
<div class="core div" id="orgb4f2685"> <div class="core div" id="org44b728f">
<p> <p>
{\bf Energy in electromagnetic fields} {\bf Energy in electromagnetic fields}
\[ \[
@ -1765,7 +1765,7 @@ Then,
\] \]
so we get the so we get the
</p> </p>
<div class="core div" id="org1eaf77c"> <div class="core div" id="org11d0bdb">
<p> <p>
{\bf Poynting theorem (differential form)} {\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> <p>
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting. \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 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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emd_emw.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">emd.emw</span></h3>
<div class="outline-text-3" id="text-emd_emw"> <div class="outline-text-3" id="text-emd_emw">
<details class="prereq" id="org5bcd123"> <details class="prereq" id="orgdec6d72">
<summary id="org41526cb"> <summary id="orge09a2b2">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1633,8 +1633,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org81e7bec"> <details class="objectives" id="org9488daa">
<summary id="org62ac99a"> <summary id="orgd8d77da">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <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> <li><a href="emd_emw_ep.html">Energy and Momentum</a><span class="headline-id">emd.emw.ep</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/emd_emw_ep.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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: or more succinctly:
</p> </p>
<div class="main div" id="orgeb0be24"> <div class="main div" id="org1741f9a">
<p> <p>
{\bf Poynting vector of a monochromatic EM wave} {\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> <p>
Similary, we get the Similary, we get the
</p> </p>
<div class="main div" id="org372457d"> <div class="main div" id="orgf6ab132">
<p> <p>
{\bf Momentum density of a monochromatic EM wave} {\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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emd_emw_mpw.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 Generalizing to propagation in the direction of an arbitrary wavevector
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
</p> </p>
<div class="core div" id="org22a7fdd"> <div class="core div" id="org9f5b19f">
<p> <p>
{\bf E and B fields for a monochromatic EM plane wave} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emd_emw_we.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 \({\boldsymbol \nabla} \cdot {\bf B} = 0\), Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
we get the we get the
</p> </p>
<div class="core div" id="org1160663"> <div class="core div" id="orgfcad186">
<p> <p>
{\bf Wave equations for electric and magnetic fields in vacuum} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_emwm.html">Electromagnetic Waves in Matter</a><span class="headline-id">emdm.emwm</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_Me.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_Me_bc.html">Boundary Conditions</a><span class="headline-id">emdm.Me.bc</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

37
build/emdm_Me_Mem.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 We therefore have the
</p> </p>
<div class="core div" id="orgff46cb4"> <div class="core div" id="org15d7510">
<p> <p>
{\bf Polarization current density} {\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 polarization changes). We can check consistency with the continuity equation
associated to the conservation of bound charges: associated to the conservation of bound charges:
</p> </p>
<aside id="orgbce7d73"> <aside id="org9c1ef52">
<p> <p>
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current 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. \({\boldsymbol J}_b\) 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, In view of this: total charge density can be separated into 2 parts,
{\it free} and {\it bound}: {\it free} and {\it bound}:
</p> </p>
<div class="main div" id="org4df7865"> <div class="main div" id="org2c2e80a">
<p> <p>
\[ \[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf 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 and current can be separated into three parts, {\it free}, {\it bound} and
{\it polarization}: {\it polarization}:
</p> </p>
<div class="main div" id="orgcc32502"> <div class="main div" id="orgafd7f00">
<p> <p>
\[ \[
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M} {\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
@ -1736,7 +1736,7 @@ Gauss's law: can be rewritten
\] \]
where (as in static case) where (as in static case)
</p> </p>
<div class="core div" id="org7600f00"> <div class="core div" id="orgbd7306c">
<p> <p>
\[ \[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P} {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@ -1762,7 +1762,7 @@ or
\] \]
where as before where as before
</p> </p>
<div class="core div" id="orgb942ad8"> <div class="core div" id="orgde049dc">
<p> <p>
\[ \[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M} {\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> <p>
In terms of free charges and currents, we thus get In terms of free charges and currents, we thus get
</p> </p>
<div class="core div" id="orgd9d30d5"> <div class="core div" id="orgf901bae">
<p> <p>
{\bf Maxwell's equations {\it (in matter)}} {\bf Maxwell's equations {\it (in matter)}}
</p> </p>
@ -1806,7 +1806,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
in terms of \({\bf E}\) and \({\bf B}\). in terms of \({\bf E}\) and \({\bf B}\).
For the restricted case of linear media: For the restricted case of linear media:
</p> </p>
<div class="main div" id="orge1df28e"> <div class="main div" id="org5288a81">
<p> <p>
\[ \[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emdm_Me_bc.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
Discontinuities between different media, deduced from Discontinuities between different media, deduced from
</p> </p>
<div class="core div" id="orgbbf71a6"> <div class="core div" id="org77f30b2">
<p> <p>
{\bf Maxwell's equations {\it (in matter)}, integral form} {\bf Maxwell's equations {\it (in matter)}, integral form}
</p> </p>
@ -1701,10 +1701,21 @@ These are basis of theory of reflection and refraction.
</div> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_emwm_wg.html">Waveguides</a><span class="headline-id">emdm.emwm.wg</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_ad.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_emwm_ad_c.html">EM Waves in Conductors</a><span class="headline-id">emdm.emwm.ad.c</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_ad_c.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/emdm_emwm_plm.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 where the index of refraction of the material is defined as
</p> </p>
<div class="main div" id="orgeaea7cb"> <div class="main div" id="org72bb44e">
<p> <p>
{\bf Index of refraction} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_refl.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_emwm_refl_Ba.html">Brewster's Angle</a><span class="headline-id">emdm.emwm.refl.Ba</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_refl_Ba.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_refl_Fe.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_refl_ni.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emdm_emwm_refl_oi.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <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 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> </p>
<div class="core div" id="orga1858e0"> <div class="core div" id="org699621d">
<p> <p>
{\bf First law of reflection:} {\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. 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 with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
and the angle of refraction (\(\theta_T\)) obey the following laws: and the angle of refraction (\(\theta_T\)) obey the following laws:
</p> </p>
<div class="core div" id="orgc1aaaad"> <div class="core div" id="orgb0b59f9">
<p> <p>
{\bf Law of reflection} {\bf Law of reflection}
\[ \[
@ -1733,7 +1733,7 @@ while the third equation becomes
\] \]
Writing everything in terms of the incident amplitude, we get Writing everything in terms of the incident amplitude, we get
</p> </p>
<div class="main div" id="org4da7748"> <div class="main div" id="orgefa3e67">
<p> <p>
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)} {\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)}). 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 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> </p>
<div class="main div" id="orge2d9787"> <div class="main div" id="orgd248cb3">
<p> <p>
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}} {\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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_refr.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_wg.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="emdm_emwm_wg_c.html">Coaxial Lines</a><span class="headline-id">emdm.emwm.wg.c</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_wg_c.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_wg_gw.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emdm_emwm_wg_r.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emf.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">emf</span></h2>
<div class="outline-text-2" id="text-emf"> <div class="outline-text-2" id="text-emf">
<details class="prereq" id="org86ffe7e"> <details class="prereq" id="org50b623e">
<summary id="org72ae362"> <summary id="org0ab4ba1">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org9d4a979"> <details class="objectives" id="orgd15b77d">
<summary id="org984c0c5"> <summary id="org61c366f">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <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> <li><a href="emf_g.html">Gauge Freedom and Choices</a><span class="headline-id">emf.g</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emf_g.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/emf_g_Cg.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/emf_g_Lg.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 These can be written compactly upon introducing a new operator: the
</p> </p>
<div class="core div" id="orgd4a4d0b"> <div class="core div" id="org9e9974a">
<p> <p>
{\bf d'Alembertian operator} {\bf d'Alembertian operator}
\[ \[
@ -1651,7 +1651,7 @@ These can be written compactly upon introducing a new operator: the
<p> <p>
so we get the so we get the
</p> </p>
<div class="core div" id="orgbeb1250"> <div class="core div" id="org521f6f7">
<p> <p>
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)} {\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
\[ \[
@ -1686,10 +1686,21 @@ we have by direct inspection
</div> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/emf_svp.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <p>
Easiest: Easiest:
</p> </p>
<div class="core div" id="org45e0ed0"> <div class="core div" id="org25c4e2b">
<p> <p>
\[ \[
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A} {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
@ -1655,7 +1655,7 @@ Putting this into Faraday's law gives
\] \]
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
</p> </p>
<div class="core div" id="orgb9810af"> <div class="core div" id="orgad63bf4">
<p> <p>
\[ \[
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t} {\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> <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 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> </p>
<div class="main div" id="org1c236f0"> <div class="main div" id="org64e1b1a">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0} {\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
@ -1684,7 +1684,7 @@ whereas Amp{\`ere}-Maxwell becomes
\] \]
which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\), 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> </p>
<div class="main div" id="orgf3f4dcd"> <div class="main div" id="org184a5ba">
<p> <p>
\[ \[
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right) \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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

21
build/ems.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> <li><a href="ems_ms.html">Magnetostatics</a><span class="headline-id">ems.ms</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/ems_ca.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,15 +1616,15 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </svg></a><span class="headline-id">ems.ca</span></h3>
<div class="outline-text-3" id="text-ems_ca"> <div class="outline-text-3" id="text-ems_ca">
<details class="prereq" id="orgbb80f83"> <details class="prereq" id="org813707e">
<summary id="org379b6a1"> <summary id="org67fafaf">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1632,8 +1632,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="orgd1100e2"> <details class="objectives" id="orgd74f98a">
<summary id="org27953b9"> <summary id="orgcfc756e">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <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> <li><a href="ems_ca_me.html">The Multipole Expansion</a><span class="headline-id">ems.ca.me</span></li>
</ul> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

29
build/ems_ca_fe.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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 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> from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
</p> </p>
<div class="main div" id="org14f8ad7"> <div class="main div" id="orgcced719">
\begin{equation*} \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} {\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*} \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 or (often simpler) by calculating the electrostatic potential, using either the
explicit construction (\ref{eq:V_from_rho}) explicit construction (\ref{eq:V_from_rho})
</p> </p>
<div class="main div" id="org83b53d5"> <div class="main div" id="org68ed8a6">
<p> <p>
\[ \[
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}. 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}) 'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
</p> </p>
<div class="core div" id="org52d8655"> <div class="core div" id="org828a92b">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}. {\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 In the specific case where the charge density vanishes, we fall back onto the simpler
Laplace equation Laplace equation
</p> </p>
<div class="core div" id="orgceb6a79"> <div class="core div" id="org6c130c8">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V = 0 {\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> <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> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

23
build/ems_ca_fe_L.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,7 +1616,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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. of the \(f_x + f_y + f_z = 0\) condition above.
</p> </p>
<div class="info div" id="org12caa26"> <div class="info div" id="org65435f8">
<p> <p>
<b>Earnshaw's theorem</b> <br> <b>Earnshaw's theorem</b> <br>
Since solutions to Laplace's equation have no local minimum, 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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

25
build/ems_ca_fe_g.html
View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-08 Tue 17:21 --> <!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -1616,17 +1616,17 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </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"> <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="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"/> <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> </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="outline-text-5" id="text-ems_ca_fe_g">
<div class="info div" id="org8d7045e"> <div class="info div" id="orgd896c19">
<p> <p>
<b>George Green</b> <b>George Green</b>
</p> </p>
<aside id="org53725f0"> <aside id="org07b8bae">
<p> <p>
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}. See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
</p> </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="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p> <p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"></p>
</div> </div>

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