Update 2022-02-09 22:41
This commit is contained in:
Jean-Sébastien
parent
3c40f5bfe8
commit
f3c2446d19
31
build/a.html
31
build/a.html
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1644,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1727,7 +1702,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
31
build/c.html
31
build/c.html
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1644,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1650,7 +1625,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1646,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1668,14 +1643,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
|||
<div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
|
||||
<h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
|
||||
<div class="eqlabel" id="org397e9ce">
|
||||
<div class="eqlabel" id="org5eb0619">
|
||||
<p>
|
||||
<a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org3648e8a">
|
||||
<div class="alteqlabels" id="orgfcf9b20">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(1.79)</li>
|
||||
</ul>
|
||||
|
|
@ -1696,14 +1671,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
|||
<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
|
||||
<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
|
||||
<div class="outline-text-6" id="text-c_m_cs_cyl_div">
|
||||
<div class="eqlabel" id="orgb76ebc0">
|
||||
<div class="eqlabel" id="org0f08fb2">
|
||||
<p>
|
||||
<a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgc052c68">
|
||||
<div class="alteqlabels" id="org483e629">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(2.21)</li>
|
||||
</ul>
|
||||
|
|
@ -1724,14 +1699,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
|||
<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
|
||||
<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
|
||||
<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
|
||||
<div class="eqlabel" id="orgaaf2c4a">
|
||||
<div class="eqlabel" id="org805726b">
|
||||
<p>
|
||||
<a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgcf0b798">
|
||||
<div class="alteqlabels" id="orgd6e48a1">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(2.21)</li>
|
||||
</ul>
|
||||
|
|
@ -1778,7 +1753,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1639,7 +1614,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1752,7 +1727,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1649,7 +1624,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1651,7 +1626,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1624,9 +1599,9 @@ Table of contents
|
|||
<div class="outline-text-5" id="text-c_m_dc_d2">
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga13f3ad" class="outline-6">
|
||||
<h6 id="orga13f3ad"><a href="#orga13f3ad">Divergence of gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-orga13f3ad">
|
||||
<div id="outline-container-orgddf1a80" class="outline-6">
|
||||
<h6 id="orgddf1a80"><a href="#orgddf1a80">Divergence of gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-orgddf1a80">
|
||||
<p>
|
||||
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
|
||||
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
|
||||
|
|
@ -1635,36 +1610,36 @@ given by the Laplacian of the corresponding vector elements.
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf350618" class="outline-6">
|
||||
<h6 id="orgf350618"><a href="#orgf350618">Curl of a gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-orgf350618">
|
||||
<div id="outline-container-org1c6301d" class="outline-6">
|
||||
<h6 id="org1c6301d"><a href="#org1c6301d">Curl of a gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-org1c6301d">
|
||||
<p>
|
||||
This always vanishes.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb23671d" class="outline-6">
|
||||
<h6 id="orgb23671d"><a href="#orgb23671d">Gradient of the divergence</a></h6>
|
||||
<div class="outline-text-6" id="text-orgb23671d">
|
||||
<div id="outline-container-orgce82ec3" class="outline-6">
|
||||
<h6 id="orgce82ec3"><a href="#orgce82ec3">Gradient of the divergence</a></h6>
|
||||
<div class="outline-text-6" id="text-orgce82ec3">
|
||||
<p>
|
||||
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0373292" class="outline-6">
|
||||
<h6 id="org0373292"><a href="#org0373292">Divergence of a curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org0373292">
|
||||
<div id="outline-container-org820bb5e" class="outline-6">
|
||||
<h6 id="org820bb5e"><a href="#org820bb5e">Divergence of a curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org820bb5e">
|
||||
<p>
|
||||
This always vanishes.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org21d697e" class="outline-6">
|
||||
<h6 id="org21d697e"><a href="#org21d697e">Curl of curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org21d697e">
|
||||
<div id="outline-container-org75d969a" class="outline-6">
|
||||
<h6 id="org75d969a"><a href="#org75d969a">Curl of curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org75d969a">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
|
||||
|
|
@ -1689,7 +1664,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1650,7 +1625,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1647,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1671,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1644,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1646,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1658,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1645,14 +1620,14 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
|
|||
More generally,
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org63ae2fc">
|
||||
<div class="eqlabel" id="orga2fc830">
|
||||
<p>
|
||||
<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org4992249">
|
||||
<div class="alteqlabels" id="org6add17c">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.100)</li>
|
||||
</ul>
|
||||
|
|
@ -1671,9 +1646,24 @@ More generally,
|
|||
Since
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org321d3a4">
|
||||
<p>
|
||||
<a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgb03949d">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.101)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
\begin{equation}
|
||||
{\boldsymbol \nabla}_1 \left(\frac{1}{r_{12}}\right) = -\frac{\hat{\bf r}_{12}}{r_{12}^2}
|
||||
\label{Gr(1.101)}
|
||||
\tag{div1or}\label{div1or}
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
|
|
@ -1701,7 +1691,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1664,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1649,7 +1624,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1647,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1656,7 +1631,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1650,7 +1625,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1657,7 +1632,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1624,9 +1599,9 @@ Table of contents
|
|||
<div class="outline-text-5" id="text-c_m_ic_lsv">
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org552d286" class="outline-6">
|
||||
<h6 id="org552d286"><a href="#org552d286">Line Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org552d286">
|
||||
<div id="outline-container-org4fa4b6a" class="outline-6">
|
||||
<h6 id="org4fa4b6a"><a href="#org4fa4b6a">Line Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org4fa4b6a">
|
||||
<p>
|
||||
\[
|
||||
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
|
||||
|
|
@ -1655,9 +1630,9 @@ Integral over a closed loop:
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8d260ce" class="outline-6">
|
||||
<h6 id="org8d260ce"><a href="#org8d260ce">Surface Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org8d260ce">
|
||||
<div id="outline-container-org3cf12c2" class="outline-6">
|
||||
<h6 id="org3cf12c2"><a href="#org3cf12c2">Surface Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org3cf12c2">
|
||||
<p>
|
||||
\[
|
||||
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
||||
|
|
@ -1677,9 +1652,9 @@ Over a closed surface:
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org57765dc" class="outline-6">
|
||||
<h6 id="org57765dc"><a href="#org57765dc">Volume Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org57765dc">
|
||||
<div id="outline-container-orgd48f6eb" class="outline-6">
|
||||
<h6 id="orgd48f6eb"><a href="#orgd48f6eb">Volume Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-orgd48f6eb">
|
||||
<p>
|
||||
\[
|
||||
\int_{\cal V} T d\tau
|
||||
|
|
@ -1718,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1622,14 +1597,14 @@ Table of contents
|
|||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a><span class="headline-id">c.m.ic.stokes</span></h5>
|
||||
<div class="outline-text-5" id="text-c_m_ic_stokes">
|
||||
<div class="eqlabel" id="org5b773ee">
|
||||
<div class="eqlabel" id="org54da3f4">
|
||||
<p>
|
||||
<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org815e278">
|
||||
<div class="alteqlabels" id="org3a4e967">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.57)</li>
|
||||
</ul>
|
||||
|
|
@ -1672,7 +1647,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1646,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1659,7 +1634,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1659,7 +1634,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1662,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1648,7 +1623,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1677,7 +1652,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1672,7 +1647,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1706,7 +1681,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1672,7 +1647,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1719,7 +1694,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1645,7 +1620,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1664,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1691,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
35
build/d.html
35
build/d.html
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">d</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-d">
|
||||
<details class="objectives" id="org9cfb206">
|
||||
<summary id="org87be4b2">
|
||||
<details class="objectives" id="org40c4648">
|
||||
<summary id="orgce477d7">
|
||||
Objectives
|
||||
</summary>
|
||||
|
||||
|
|
@ -1686,7 +1661,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1666,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1661,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1664,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1661,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1683,7 +1658,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1666,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1663,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1666,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1664,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1674,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1668,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-emd">
|
||||
<details class="prereq" id="org94bea47">
|
||||
<summary id="orgb7d0bc3">
|
||||
<details class="prereq" id="orgc5008fa">
|
||||
<summary id="org88d0f1c">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1633,8 +1608,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="org0cdfa86">
|
||||
<summary id="org2927d33">
|
||||
<details class="objectives" id="org036b173">
|
||||
<summary id="org9627cee">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1673,7 +1648,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1647,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1663,7 +1638,7 @@ Empirically: the changing magnetic field induces an electric current around
|
|||
the circuit. This current is really driven by an electric field having a component
|
||||
along the wire. The line integral of this field is called the
|
||||
</p>
|
||||
<div class="core div" id="org8786846">
|
||||
<div class="core div" id="orge05960f">
|
||||
<p>
|
||||
<b>Electromotive force (or electromotance)</b>,
|
||||
\[
|
||||
|
|
@ -1685,7 +1660,7 @@ to the rate of change of the magnetic flux,
|
|||
\]
|
||||
so we obtain
|
||||
</p>
|
||||
<div class="core div" id="org278fea1">
|
||||
<div class="core div" id="org726542f">
|
||||
<p>
|
||||
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
|
||||
\[
|
||||
|
|
@ -1703,7 +1678,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
|
|||
\]
|
||||
we obtain
|
||||
</p>
|
||||
<div class="core div" id="org63211df">
|
||||
<div class="core div" id="orge08eeaf">
|
||||
<p>
|
||||
<b>Faraday's law</b> (differential form)
|
||||
\[
|
||||
|
|
@ -1738,7 +1713,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1682,7 +1657,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
|
|||
\]
|
||||
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
|
||||
</p>
|
||||
<div class="core div" id="orge86302b">
|
||||
<div class="core div" id="org430dd21">
|
||||
<p>
|
||||
\[
|
||||
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
|
||||
|
|
@ -1703,7 +1678,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
|
|||
\hspace{2cm} \mbox{(7.31 and 7.34)}
|
||||
\end{align}
|
||||
|
||||
<div class="example div" id="org0c0ebda">
|
||||
<div class="example div" id="org2441b5d">
|
||||
<p>
|
||||
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
|
||||
Find energy stored in section of length \(l\).
|
||||
|
|
@ -1740,7 +1715,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1662,7 +1637,7 @@ M_{12} = M_{21}
|
|||
\]
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org6c1a2e4">
|
||||
<div class="example div" id="org1839798">
|
||||
<p>
|
||||
\paragraph{Example 7.10:}
|
||||
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
|
||||
|
|
@ -1712,7 +1687,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
|
|||
</p>
|
||||
|
||||
|
||||
<div class="example div" id="org96ae3fa">
|
||||
<div class="example div" id="org435f19e">
|
||||
<p>
|
||||
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
|
||||
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
|
||||
|
|
@ -1739,7 +1714,7 @@ Total flux: \(N\) times this, so self-inductance is
|
|||
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="orgde2bf6d">
|
||||
<div class="example div" id="orgadb84c5">
|
||||
<p>
|
||||
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
|
||||
What is the current ?
|
||||
|
|
@ -1776,7 +1751,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1646,7 +1621,7 @@ law in integral form:
|
|||
|
||||
|
||||
|
||||
<div class="example div" id="org547c6ca">
|
||||
<div class="example div" id="org0e50d64">
|
||||
<p>
|
||||
{\bf Example 7.7:}
|
||||
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
|
||||
|
|
@ -1662,7 +1637,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
|
|||
</div>
|
||||
|
||||
|
||||
<div class="example div" id="org3040ba3">
|
||||
<div class="example div" id="orgda9093e">
|
||||
<p>
|
||||
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
|
||||
Uniform magnetic field \({\bf B}_0\) in central region up to \(a < b\),
|
||||
|
|
@ -1696,7 +1671,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
|
|||
'slow enough' phenomena.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org805b5d5">
|
||||
<div class="example div" id="orgcb11b45">
|
||||
<p>
|
||||
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
|
||||
induced \({\bf E}\) field as a function of distance \(s\) from wire.
|
||||
|
|
@ -1742,7 +1717,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1647,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1625,7 +1600,7 @@ Table of contents
|
|||
<p>
|
||||
Full set of equations for the electromagnetic field:
|
||||
</p>
|
||||
<div class="core div" id="org501476d">
|
||||
<div class="core div" id="orga5920b3">
|
||||
<p>
|
||||
{\bf Maxwell's equations} {\it (in vacuum)}
|
||||
</p>
|
||||
|
|
@ -1641,7 +1616,7 @@ Full set of equations for the electromagnetic field:
|
|||
<p>
|
||||
Complement:
|
||||
</p>
|
||||
<div class="core div" id="orgb357d3d">
|
||||
<div class="core div" id="org9ee0da3">
|
||||
<p>
|
||||
{\bf Force law}
|
||||
\[
|
||||
|
|
@ -1665,7 +1640,7 @@ take divergence of \((iv)\).
|
|||
<p>
|
||||
Better way of writing: all fields on left, all sources on right,
|
||||
</p>
|
||||
<div class="core div" id="org0a81935">
|
||||
<div class="core div" id="orgdda2f9a">
|
||||
\begin{align}
|
||||
(i) &{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
|
||||
&(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
|
||||
|
|
@ -1693,7 +1668,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1632,7 +1607,7 @@ the continuity equation as
|
|||
\]
|
||||
The extra term would thus be eliminated if we were to put
|
||||
</p>
|
||||
<div class="core div" id="orgd8174ee">
|
||||
<div class="core div" id="org45d3060">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
|
||||
|
|
@ -1656,7 +1631,7 @@ Real confirmation of Maxwell's theory: 1888, Hertz's experiments on propagation
|
|||
<p>
|
||||
Maxwell baptized this term the
|
||||
</p>
|
||||
<div class="core div" id="orgb36d854">
|
||||
<div class="core div" id="org90773a4">
|
||||
<p>
|
||||
{\bf Displacement current}
|
||||
\[
|
||||
|
|
@ -1702,7 +1677,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1672,7 +1647,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1670,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd.ce</span></h3>
|
||||
|
||||
<div class="outline-text-3" id="text-emd_ce">
|
||||
<details class="prereq" id="org26df1fb">
|
||||
<summary id="org34d471f">
|
||||
<details class="prereq" id="org9908421">
|
||||
<summary id="orgdbb6aa4">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1632,8 +1607,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgaff4273">
|
||||
<summary id="orge67f1e6">
|
||||
<details class="objectives" id="org1b20ea0">
|
||||
<summary id="orgc447c59">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1669,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1625,7 +1600,7 @@ Table of contents
|
|||
<p>
|
||||
The angular momentum of EM fields is directly given by
|
||||
</p>
|
||||
<div class="main div" id="org8fc773b">
|
||||
<div class="main div" id="orgd94c7c7">
|
||||
<p>
|
||||
{\bf Angular momentum of EM fields}
|
||||
\[
|
||||
|
|
@ -1653,7 +1628,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1644,7 +1619,7 @@ This means that
|
|||
\]
|
||||
Since this is true for any volume, we have (re)derived the
|
||||
</p>
|
||||
<div class="core div" id="org068de4a">
|
||||
<div class="core div" id="org17b3983">
|
||||
<p>
|
||||
{\bf Continuity equation}
|
||||
\[
|
||||
|
|
@ -1683,7 +1658,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1637,7 +1612,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
|
|||
<p>
|
||||
This is thus simply a conservation law for momentum, with
|
||||
</p>
|
||||
<div class="main div" id="orgb401242">
|
||||
<div class="main div" id="org37cec17">
|
||||
<p>
|
||||
{\bf Momentum density in the EM fields}
|
||||
\[
|
||||
|
|
@ -1649,7 +1624,7 @@ This is thus simply a conservation law for momentum, with
|
|||
<p>
|
||||
In a region in which the mechanical momentum is not changing due to external influences, we then have the
|
||||
</p>
|
||||
<div class="main div" id="orgd377c8a">
|
||||
<div class="main div" id="orgcd3036a">
|
||||
<p>
|
||||
{\bf Continuity equation for EM momentum}
|
||||
\[
|
||||
|
|
@ -1676,7 +1651,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1679,7 +1654,7 @@ and similarly for \({\boldsymbol B}\). We thus get
|
|||
<p>
|
||||
This expression can be greatly simplified by introducing the
|
||||
</p>
|
||||
<div class="main div" id="orgf0f558d">
|
||||
<div class="main div" id="orge78bc78">
|
||||
<p>
|
||||
{\bf Maxwell stress tensor}
|
||||
\[
|
||||
|
|
@ -1702,7 +1677,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
|
|||
<p>
|
||||
We then obtain
|
||||
</p>
|
||||
<div class="main div" id="orgcd1da6b">
|
||||
<div class="main div" id="org8f28e32">
|
||||
<p>
|
||||
{\bf EM force per unit volume}
|
||||
\[
|
||||
|
|
@ -1714,7 +1689,7 @@ We then obtain
|
|||
<p>
|
||||
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
|
||||
</p>
|
||||
<div class="main div" id="orgf2db445">
|
||||
<div class="main div" id="org942d34e">
|
||||
<p>
|
||||
{\bf Total force on charges in volume}
|
||||
\[
|
||||
|
|
@ -1741,7 +1716,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1691,7 +1666,7 @@ so we get
|
|||
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
|
||||
we obtain
|
||||
</p>
|
||||
<div class="main div" id="org75886ff">
|
||||
<div class="main div" id="orgc3e7fad">
|
||||
<p>
|
||||
{\bf Poynting's theorem}
|
||||
\[
|
||||
|
|
@ -1716,7 +1691,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
|
|||
<p>
|
||||
Energy per unit time, per unit area carried by EM fields:
|
||||
</p>
|
||||
<div class="core div" id="orgb6d912b">
|
||||
<div class="core div" id="orgf0750fa">
|
||||
<p>
|
||||
{\bf Poynting vector}
|
||||
\[
|
||||
|
|
@ -1729,7 +1704,7 @@ Energy per unit time, per unit area carried by EM fields:
|
|||
<p>
|
||||
We can thus express Poynting's theorem more compactly:
|
||||
</p>
|
||||
<div class="core div" id="org7131f77">
|
||||
<div class="core div" id="orged7fe8f">
|
||||
<p>
|
||||
{\bf Poynting's theorem}
|
||||
\[
|
||||
|
|
@ -1742,7 +1717,7 @@ We can thus express Poynting's theorem more compactly:
|
|||
<p>
|
||||
where we have defined the total
|
||||
</p>
|
||||
<div class="core div" id="org44b728f">
|
||||
<div class="core div" id="org27d8494">
|
||||
<p>
|
||||
{\bf Energy in electromagnetic fields}
|
||||
\[
|
||||
|
|
@ -1765,7 +1740,7 @@ Then,
|
|||
\]
|
||||
so we get the
|
||||
</p>
|
||||
<div class="core div" id="org11d0bdb">
|
||||
<div class="core div" id="org40d56f8">
|
||||
<p>
|
||||
{\bf Poynting theorem (differential form)}
|
||||
\[
|
||||
|
|
@ -1782,7 +1757,7 @@ and has a similar for to the continuity equation
|
|||
|
||||
|
||||
|
||||
<div class="example div" id="orgd2f58ae">
|
||||
<div class="example div" id="orge1eb64c">
|
||||
<p>
|
||||
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting.
|
||||
Assuming that the field is uniform, the electric field parallel to the wire is
|
||||
|
|
@ -1825,7 +1800,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd.emw</span></h3>
|
||||
|
||||
<div class="outline-text-3" id="text-emd_emw">
|
||||
<details class="prereq" id="orgdec6d72">
|
||||
<summary id="orge09a2b2">
|
||||
<details class="prereq" id="org2757254">
|
||||
<summary id="org0bb0a4d">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1633,8 +1608,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="org9488daa">
|
||||
<summary id="orgd8d77da">
|
||||
<details class="objectives" id="orga6e02f8">
|
||||
<summary id="org0f51f09">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1673,7 +1648,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1653,7 +1628,7 @@ so for a monochromatic EM plan wave,
|
|||
\]
|
||||
or more succinctly:
|
||||
</p>
|
||||
<div class="main div" id="org1741f9a">
|
||||
<div class="main div" id="org19f6b89">
|
||||
<p>
|
||||
{\bf Poynting vector of a monochromatic EM wave}
|
||||
\[
|
||||
|
|
@ -1669,7 +1644,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
|
|||
<p>
|
||||
Similary, we get the
|
||||
</p>
|
||||
<div class="main div" id="orgf6ab132">
|
||||
<div class="main div" id="org8e7b46e">
|
||||
<p>
|
||||
{\bf Momentum density of a monochromatic EM wave}
|
||||
\[
|
||||
|
|
@ -1718,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1654,7 +1629,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
|
|||
Generalizing to propagation in the direction of an arbitrary wavevector
|
||||
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
|
||||
</p>
|
||||
<div class="core div" id="org9f5b19f">
|
||||
<div class="core div" id="org7add9b6">
|
||||
<p>
|
||||
{\bf E and B fields for a monochromatic EM plane wave}
|
||||
\[
|
||||
|
|
@ -1696,7 +1671,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1651,7 +1626,7 @@ These take the form of coupled first-order partial differential equations for \(
|
|||
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
|
||||
we get the
|
||||
</p>
|
||||
<div class="core div" id="orgfcad186">
|
||||
<div class="core div" id="org2e89450">
|
||||
<p>
|
||||
{\bf Wave equations for electric and magnetic fields in vacuum}
|
||||
\[
|
||||
|
|
@ -1705,7 +1680,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1645,7 +1620,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1645,7 +1620,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1658,7 +1633,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
|
|||
\]
|
||||
We therefore have the
|
||||
</p>
|
||||
<div class="core div" id="org15d7510">
|
||||
<div class="core div" id="org643b4aa">
|
||||
<p>
|
||||
{\bf Polarization current density}
|
||||
\[
|
||||
|
|
@ -1676,7 +1651,7 @@ the polarization current is the result of linear motion of charge when
|
|||
polarization changes). We can check consistency with the continuity equation
|
||||
associated to the conservation of bound charges:
|
||||
</p>
|
||||
<aside id="org9c1ef52">
|
||||
<aside id="orgf5df19a">
|
||||
<p>
|
||||
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
|
||||
\({\boldsymbol J}_b\) but this is not the convention used here.
|
||||
|
|
@ -1699,7 +1674,7 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
|
|||
In view of this: total charge density can be separated into 2 parts,
|
||||
{\it free} and {\it bound}:
|
||||
</p>
|
||||
<div class="main div" id="org2c2e80a">
|
||||
<div class="main div" id="orgfd1ad39">
|
||||
<p>
|
||||
\[
|
||||
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
|
||||
|
|
@ -1712,7 +1687,7 @@ In view of this: total charge density can be separated into 2 parts,
|
|||
and current can be separated into three parts, {\it free}, {\it bound} and
|
||||
{\it polarization}:
|
||||
</p>
|
||||
<div class="main div" id="orgafd7f00">
|
||||
<div class="main div" id="org09b6579">
|
||||
<p>
|
||||
\[
|
||||
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
|
||||
|
|
@ -1736,7 +1711,7 @@ Gauss's law: can be rewritten
|
|||
\]
|
||||
where (as in static case)
|
||||
</p>
|
||||
<div class="core div" id="orgbd7306c">
|
||||
<div class="core div" id="orgcb69874">
|
||||
<p>
|
||||
\[
|
||||
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
||||
|
|
@ -1762,7 +1737,7 @@ or
|
|||
\]
|
||||
where as before
|
||||
</p>
|
||||
<div class="core div" id="orgde049dc">
|
||||
<div class="core div" id="orga76243f">
|
||||
<p>
|
||||
\[
|
||||
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
||||
|
|
@ -1780,7 +1755,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
|
|||
<p>
|
||||
In terms of free charges and currents, we thus get
|
||||
</p>
|
||||
<div class="core div" id="orgf901bae">
|
||||
<div class="core div" id="org5d9c2e0">
|
||||
<p>
|
||||
{\bf Maxwell's equations {\it (in matter)}}
|
||||
</p>
|
||||
|
|
@ -1806,7 +1781,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
|
|||
in terms of \({\bf E}\) and \({\bf B}\).
|
||||
For the restricted case of linear media:
|
||||
</p>
|
||||
<div class="main div" id="org5288a81">
|
||||
<div class="main div" id="orgca90a26">
|
||||
<p>
|
||||
\[
|
||||
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
|
||||
|
|
@ -1841,7 +1816,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1625,7 +1600,7 @@ Table of contents
|
|||
<p>
|
||||
Discontinuities between different media, deduced from
|
||||
</p>
|
||||
<div class="core div" id="org77f30b2">
|
||||
<div class="core div" id="org1ce4cee">
|
||||
<p>
|
||||
{\bf Maxwell's equations {\it (in matter)}, integral form}
|
||||
</p>
|
||||
|
|
@ -1714,7 +1689,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1648,7 +1623,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1644,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1740,7 +1715,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1660,7 +1635,7 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
|
|||
\]
|
||||
where the index of refraction of the material is defined as
|
||||
</p>
|
||||
<div class="main div" id="org72bb44e">
|
||||
<div class="main div" id="org4373079">
|
||||
<p>
|
||||
{\bf Index of refraction}
|
||||
\[
|
||||
|
|
@ -1715,7 +1690,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1659,7 +1634,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1639,7 +1614,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1640,7 +1615,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1731,7 +1706,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1660,7 +1635,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
|
|||
<p>
|
||||
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
|
||||
</p>
|
||||
<div class="core div" id="org699621d">
|
||||
<div class="core div" id="orga0e77f3">
|
||||
<p>
|
||||
{\bf First law of reflection:}
|
||||
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
|
||||
|
|
@ -1675,7 +1650,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
|
|||
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
|
||||
and the angle of refraction (\(\theta_T\)) obey the following laws:
|
||||
</p>
|
||||
<div class="core div" id="orgb0b59f9">
|
||||
<div class="core div" id="orgc1a2ec9">
|
||||
<p>
|
||||
{\bf Law of reflection}
|
||||
\[
|
||||
|
|
@ -1733,7 +1708,7 @@ while the third equation becomes
|
|||
\]
|
||||
Writing everything in terms of the incident amplitude, we get
|
||||
</p>
|
||||
<div class="main div" id="orgefa3e67">
|
||||
<div class="main div" id="org933ec71">
|
||||
<p>
|
||||
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
|
||||
\[
|
||||
|
|
@ -1753,7 +1728,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
|
|||
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
|
||||
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
|
||||
</p>
|
||||
<div class="main div" id="orgd248cb3">
|
||||
<div class="main div" id="orga399926">
|
||||
<p>
|
||||
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
|
||||
\[
|
||||
|
|
@ -1801,7 +1776,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1640,7 +1615,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1646,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1666,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1690,7 +1665,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1699,7 +1674,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emf</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-emf">
|
||||
<details class="prereq" id="org50b623e">
|
||||
<summary id="org0ab4ba1">
|
||||
<details class="prereq" id="orge054fff">
|
||||
<summary id="orgb667583">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1632,8 +1607,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgd15b77d">
|
||||
<summary id="org61c366f">
|
||||
<details class="objectives" id="org92751e6">
|
||||
<summary id="org8a7509c">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1667,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1664,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1663,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1638,7 +1613,7 @@ while the equation for \(V\) becomes
|
|||
\]
|
||||
These can be written compactly upon introducing a new operator: the
|
||||
</p>
|
||||
<div class="core div" id="org9e9974a">
|
||||
<div class="core div" id="org0a132cf">
|
||||
<p>
|
||||
{\bf d'Alembertian operator}
|
||||
\[
|
||||
|
|
@ -1651,7 +1626,7 @@ These can be written compactly upon introducing a new operator: the
|
|||
<p>
|
||||
so we get the
|
||||
</p>
|
||||
<div class="core div" id="org521f6f7">
|
||||
<div class="core div" id="org6df9df9">
|
||||
<p>
|
||||
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
|
||||
\[
|
||||
|
|
@ -1699,7 +1674,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1639,7 +1614,7 @@ Useful strategy: represent fields in terms of potentials.
|
|||
<p>
|
||||
Easiest:
|
||||
</p>
|
||||
<div class="core div" id="org25c4e2b">
|
||||
<div class="core div" id="org043dbf2">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
||||
|
|
@ -1655,7 +1630,7 @@ Putting this into Faraday's law gives
|
|||
\]
|
||||
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
|
||||
</p>
|
||||
<div class="core div" id="orgad63bf4">
|
||||
<div class="core div" id="org8471d76">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
|
||||
|
|
@ -1668,7 +1643,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
|
|||
<p>
|
||||
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) into Gauss's law gives
|
||||
</p>
|
||||
<div class="main div" id="org64e1b1a">
|
||||
<div class="main div" id="orgb6c325d">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
|
||||
|
|
@ -1684,7 +1659,7 @@ whereas Amp{\`ere}-Maxwell becomes
|
|||
\]
|
||||
which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
|
||||
</p>
|
||||
<div class="main div" id="org184a5ba">
|
||||
<div class="main div" id="org4caa993">
|
||||
<p>
|
||||
\[
|
||||
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
|
||||
|
|
@ -1718,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1647,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1623,8 +1598,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">ems.ca</span></h3>
|
||||
|
||||
<div class="outline-text-3" id="text-ems_ca">
|
||||
<details class="prereq" id="org813707e">
|
||||
<summary id="org67fafaf">
|
||||
<details class="prereq" id="orgd1b9be9">
|
||||
<summary id="orgc5d1771">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1632,8 +1607,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgd74f98a">
|
||||
<summary id="orgcfc756e">
|
||||
<details class="objectives" id="org547b0d5">
|
||||
<summary id="org5765814">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1669,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1628,7 +1603,7 @@ A generic configuration of static charges coupled via the Coulomb interaction
|
|||
defines an electrostatic problem, whose solution is in principle obtained
|
||||
from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
|
||||
</p>
|
||||
<div class="main div" id="orgcced719">
|
||||
<div class="main div" id="org6cf413c">
|
||||
\begin{equation*}
|
||||
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
|
||||
\end{equation*}
|
||||
|
|
@ -1638,7 +1613,7 @@ from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_v
|
|||
or (often simpler) by calculating the electrostatic potential, using either the
|
||||
explicit construction (\ref{eq:V_from_rho})
|
||||
</p>
|
||||
<div class="main div" id="org68ed8a6">
|
||||
<div class="main div" id="orgde2ce45">
|
||||
<p>
|
||||
\[
|
||||
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
|
||||
|
|
@ -1654,7 +1629,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
|
|||
'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
|
||||
</p>
|
||||
|
||||
<div class="core div" id="org828a92b">
|
||||
<div class="core div" id="org10253c2">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
|
||||
|
|
@ -1668,7 +1643,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
|
|||
In the specific case where the charge density vanishes, we fall back onto the simpler
|
||||
Laplace equation
|
||||
</p>
|
||||
<div class="core div" id="org6c130c8">
|
||||
<div class="core div" id="orgd876622">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla}^2 V = 0
|
||||
|
|
@ -1701,7 +1676,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1702,7 +1677,7 @@ are necessarily positive, we thus require \(f_x > 0\), \(f_y > 0\) and \(f
|
|||
of the \(f_x + f_y + f_z = 0\) condition above.
|
||||
</p>
|
||||
|
||||
<div class="info div" id="org65435f8">
|
||||
<div class="info div" id="org5574d7b">
|
||||
<p>
|
||||
<b>Earnshaw's theorem</b> <br>
|
||||
Since solutions to Laplace's equation have no local minimum,
|
||||
|
|
@ -1803,7 +1778,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-09 Wed 07:31 -->
|
||||
<!-- 2022-02-09 Wed 22:40 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -408,17 +408,13 @@ Table of contents
|
|||
<li>
|
||||
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -430,29 +426,8 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -1622,11 +1597,11 @@ Table of contents
|
|||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
|
||||
<div class="outline-text-5" id="text-ems_ca_fe_g">
|
||||
<div class="info div" id="orgd896c19">
|
||||
<div class="info div" id="org487295f">
|
||||
<p>
|
||||
<b>George Green</b>
|
||||
</p>
|
||||
<aside id="org07b8bae">
|
||||
<aside id="orgf55ecae">
|
||||
<p>
|
||||
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
|
||||
</p>
|
||||
|
|
@ -1691,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 07:31</p>
|
||||
<p class="date">Created: 2022-02-09 Wed 22:40</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue