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26 | 26 | <meta property="og:url" content="http://localhost:1313/notes/physics/electromagnetism/"> |
27 | 27 | <meta property="og:site_name" content="Stefano Giannini"> |
28 | 28 | <meta property="og:title" content="Electromagnetism"> |
29 | | - <meta property="og:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$ |
| 29 | + <meta property="og:description" content="Maxwell Equations (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$ |
30 | 30 | Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ |
31 | 31 | Maxwell-Faraday Equation: |
32 | 32 | $$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$ |
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38 | 38 |
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39 | 39 | <meta name="twitter:card" content="summary"> |
40 | 40 | <meta name="twitter:title" content="Electromagnetism"> |
41 | | - <meta name="twitter:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$ |
| 41 | + <meta name="twitter:description" content="Maxwell Equations (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$ |
42 | 42 | Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ |
43 | 43 | Maxwell-Faraday Equation: |
44 | 44 | $$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$ |
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307 | 307 | <!-- A Sample Program --> |
308 | 308 | <div class="note-card "> |
309 | 309 | <div class="item"> |
310 | | - <h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5> |
| 310 | + <h5 class="note-title"><span>Maxwell Equations (Integral)</span></h5> |
311 | 311 |
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312 | 312 | <div class="card"> |
313 | 313 | <div class="card-body"><ol> |
@@ -336,21 +336,19 @@ <h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5> |
336 | 336 |
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337 | 337 | <div class="note-card "> |
338 | 338 | <div class="item"> |
339 | | - <h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5> |
| 339 | + <h5 class="note-title"><span>Maxwell Equations (Differential)</span></h5> |
340 | 340 |
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341 | 341 | <div class="card"> |
342 | 342 | <div class="card-body"><ol> |
343 | 343 | <li><strong>Gauss’ Law</strong>:</li> |
344 | 344 | </ol> |
345 | 345 | <p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p> |
346 | 346 | <ol start="2"> |
347 | | -<li> |
348 | | -<p><strong>Gauss’ Law for Magnetism</strong>: |
349 | | -$$ \nabla \cdot \mathbf{B} = 0 $$</p> |
350 | | -</li> |
351 | | -<li> |
352 | | -<p><strong>Maxwell-Faraday Equation</strong>:</p> |
353 | | -</li> |
| 347 | +<li><strong>Gauss’ Law for Magnetism</strong>:</li> |
| 348 | +</ol> |
| 349 | +<p>$$ \nabla \cdot \mathbf{B} = 0 $$</p> |
| 350 | +<ol start="3"> |
| 351 | +<li><strong>Maxwell-Faraday Equation</strong>:</li> |
354 | 352 | </ol> |
355 | 353 | <p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p> |
356 | 354 | <ol start="4"> |
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