Skip to content

Commit cf49590

Browse files
steven-jasteven-ja
committed
finished maxwell equations notes
1 parent 8aa41fb commit cf49590

File tree

8 files changed

+196
-38
lines changed

8 files changed

+196
-38
lines changed

‎content/notes/physics/electromagnetism/index.md

+28-5
Original file line numberDiff line numberDiff line change
@@ -10,13 +10,36 @@ menu:
1010
---
1111
<!-- A Sample Program -->
1212
{{< note title="Maxwell Equation (Integral)">}}
13-
* **Gauss' Law**:
13+
1. **Gauss' Law**:
1414

15-
$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
15+
$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
1616

17-
* **Gauss' Law for Magnetism**
18-
$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
17+
2. **Gauss' Law for Magnetism**:
18+
$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
1919

20-
20+
3. **Maxwell-Faraday Equation**:
21+
22+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \\int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
23+
24+
4. **Ampère's circuital law**:
25+
26+
$$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$
27+
{{< /note >}}
28+
29+
{{< note title="Maxwell Equation (Differential)">}}
30+
1. **Gauss' Law**:
31+
32+
$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$
33+
34+
2. **Gauss' Law for Magnetism**:
35+
$$ \nabla \cdot \mathbf{B} = 0 $$
36+
37+
3. **Maxwell-Faraday Equation**:
38+
39+
$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$
40+
41+
4. **Ampère's circuital law**:
42+
43+
$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$
2144
{{< /note >}}
2245

‎public/index.json

+1-1
Large diffs are not rendered by default.

‎public/index.xml

+5-2
Original file line numberDiff line numberDiff line change
@@ -128,8 +128,11 @@ To achieve this, we will utilize the yfinance library to fetch stock information
128128
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
129129

130130
<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
131-
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
132-
Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
131+
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
132+
Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
133+
Maxwell-Faraday Equation:
134+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
135+
Ampère&amp;rsquo;s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</description>
133136
</item>
134137

135138
<item>

‎public/notes/index.html

+47-7
Original file line numberDiff line numberDiff line change
@@ -323,14 +323,54 @@
323323
<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
324324

325325
<div class="card">
326-
<div class="card-body"><ul>
326+
<div class="card-body"><ol>
327327
<li><strong>Gauss&rsquo; Law</strong>:</li>
328-
</ul>
329-
<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
330-
<ul>
331-
<li><strong>Gauss&rsquo; Law for Magnetism</strong>
332-
$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
333-
</ul></div>
328+
</ol>
329+
<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
330+
<ol start="2">
331+
<li>
332+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
333+
$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
334+
</li>
335+
<li>
336+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
337+
</li>
338+
</ol>
339+
<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
340+
<ol start="4">
341+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
342+
</ol>
343+
<p>$$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</p>
344+
</div>
345+
</div>
346+
347+
</div>
348+
</div>
349+
350+
<div class="note-card ">
351+
<div class="item">
352+
<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
353+
354+
<div class="card">
355+
<div class="card-body"><ol>
356+
<li><strong>Gauss&rsquo; Law</strong>:</li>
357+
</ol>
358+
<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
359+
<ol start="2">
360+
<li>
361+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
362+
$$ \nabla \cdot \mathbf{B} = 0 $$</p>
363+
</li>
364+
<li>
365+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
366+
</li>
367+
</ol>
368+
<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
369+
<ol start="4">
370+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
371+
</ol>
372+
<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
373+
</div>
334374
</div>
335375

336376
</div>

‎public/notes/index.xml

+5-2
Original file line numberDiff line numberDiff line change
@@ -24,8 +24,11 @@
2424
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
2525

2626
<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
27-
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
28-
Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
27+
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
28+
Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
29+
Maxwell-Faraday Equation:
30+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
31+
Ampère&amp;rsquo;s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</description>
2932
</item>
3033

3134
<item>

‎public/notes/physics/electromagnetism/index.html

+58-12
Original file line numberDiff line numberDiff line change
@@ -26,17 +26,23 @@
2626
<meta property="og:url" content="http://localhost:1313/notes/physics/electromagnetism/">
2727
<meta property="og:site_name" content="Stefano Giannini">
2828
<meta property="og:title" content="Electromagnetism">
29-
<meta property="og:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
30-
Gauss’ Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ ">
29+
<meta property="og:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
30+
Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
31+
Maxwell-Faraday Equation:
32+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
33+
Ampère’s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} &#43; \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$">
3134
<meta property="og:locale" content="en">
3235
<meta property="og:type" content="article">
3336
<meta property="article:section" content="notes">
3437

3538

3639
<meta name="twitter:card" content="summary">
3740
<meta name="twitter:title" content="Electromagnetism">
38-
<meta name="twitter:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
39-
Gauss’ Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ ">
41+
<meta name="twitter:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
42+
Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
43+
Maxwell-Faraday Equation:
44+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
45+
Ampère’s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} &#43; \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$">
4046

4147

4248

@@ -325,20 +331,60 @@
325331
<section class="content-section" id="content-section">
326332
<div class="content container-fluid" id="content">
327333
<div class="container-fluid note-card-holder" id="note-card-holder">
328-
<!-- A Sample Program -->
334+
<!-- A Sample Program -->
329335
<div class="note-card ">
330336
<div class="item">
331337
<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
332338

333339
<div class="card">
334-
<div class="card-body"><ul>
340+
<div class="card-body"><ol>
335341
<li><strong>Gauss&rsquo; Law</strong>:</li>
336-
</ul>
337-
<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
338-
<ul>
339-
<li><strong>Gauss&rsquo; Law for Magnetism</strong>
340-
$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
341-
</ul></div>
342+
</ol>
343+
<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
344+
<ol start="2">
345+
<li>
346+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
347+
$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
348+
</li>
349+
<li>
350+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
351+
</li>
352+
</ol>
353+
<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
354+
<ol start="4">
355+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
356+
</ol>
357+
<p>$$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</p>
358+
</div>
359+
</div>
360+
361+
</div>
362+
</div>
363+
364+
<div class="note-card ">
365+
<div class="item">
366+
<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
367+
368+
<div class="card">
369+
<div class="card-body"><ol>
370+
<li><strong>Gauss&rsquo; Law</strong>:</li>
371+
</ol>
372+
<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
373+
<ol start="2">
374+
<li>
375+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
376+
$$ \nabla \cdot \mathbf{B} = 0 $$</p>
377+
</li>
378+
<li>
379+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
380+
</li>
381+
</ol>
382+
<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
383+
<ol start="4">
384+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
385+
</ol>
386+
<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
387+
</div>
342388
</div>
343389

344390
</div>

‎public/notes/physics/index.html

+47-7
Original file line numberDiff line numberDiff line change
@@ -328,14 +328,54 @@
328328
<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
329329

330330
<div class="card">
331-
<div class="card-body"><ul>
331+
<div class="card-body"><ol>
332332
<li><strong>Gauss&rsquo; Law</strong>:</li>
333-
</ul>
334-
<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
335-
<ul>
336-
<li><strong>Gauss&rsquo; Law for Magnetism</strong>
337-
$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
338-
</ul></div>
333+
</ol>
334+
<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
335+
<ol start="2">
336+
<li>
337+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
338+
$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
339+
</li>
340+
<li>
341+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
342+
</li>
343+
</ol>
344+
<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
345+
<ol start="4">
346+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
347+
</ol>
348+
<p>$$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</p>
349+
</div>
350+
</div>
351+
352+
</div>
353+
</div>
354+
355+
<div class="note-card ">
356+
<div class="item">
357+
<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
358+
359+
<div class="card">
360+
<div class="card-body"><ol>
361+
<li><strong>Gauss&rsquo; Law</strong>:</li>
362+
</ol>
363+
<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
364+
<ol start="2">
365+
<li>
366+
<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
367+
$$ \nabla \cdot \mathbf{B} = 0 $$</p>
368+
</li>
369+
<li>
370+
<p><strong>Maxwell-Faraday Equation</strong>:</p>
371+
</li>
372+
</ol>
373+
<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
374+
<ol start="4">
375+
<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
376+
</ol>
377+
<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
378+
</div>
339379
</div>
340380

341381
</div>

‎public/notes/physics/index.xml

+5-2
Original file line numberDiff line numberDiff line change
@@ -11,8 +11,11 @@
1111
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
1212

1313
<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
14-
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
15-
Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
14+
<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
15+
Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
16+
Maxwell-Faraday Equation:
17+
$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
18+
Ampère&amp;rsquo;s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$</description>
1619
</item>
1720

1821

0 commit comments

Comments
 (0)