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‎content/notes/physics/electromagnetism/index.md

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<!-- A Sample Program -->
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{{< note title="Maxwell Equation (Integral)">}}
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* **Gauss' Law**:
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1. **Gauss' Law**:
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$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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* **Gauss' Law for Magnetism**
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$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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2. **Gauss' Law for Magnetism**:
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$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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3. **Maxwell-Faraday Equation**:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \\int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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4. **Ampère's circuital law**:
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$$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$
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{{< /note >}}
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{{< note title="Maxwell Equation (Differential)">}}
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1. **Gauss' Law**:
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$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$
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2. **Gauss' Law for Magnetism**:
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$$ \nabla \cdot \mathbf{B} = 0 $$
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3. **Maxwell-Faraday Equation**:
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$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$
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4. **Ampère's circuital law**:
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$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$
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{{< /note >}}
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‎public/index.json

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‎public/index.xml

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<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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Maxwell-Faraday Equation:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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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>
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‎public/notes/index.html

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<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
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<div class="card">
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<div class="card-body"><ul>
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<div class="card-body"><ol>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ul>
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<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ul>
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<li><strong>Gauss&rsquo; Law for Magnetism</strong>
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$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
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</ul></div>
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</ol>
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<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<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>
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</div>
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</div>
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</div>
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<div class="note-card ">
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<div class="item">
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<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
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<div class="card">
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<div class="card-body"><ol>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ol>
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<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \nabla \cdot \mathbf{B} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
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</div>
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<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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Maxwell-Faraday Equation:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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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>
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‎public/notes/physics/electromagnetism/index.html

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<meta property="og:url" content="http://localhost:1313/notes/physics/electromagnetism/">
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<meta property="og:site_name" content="Stefano Giannini">
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<meta property="og:title" content="Electromagnetism">
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<meta property="og:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss’ Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ ">
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<meta property="og:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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Maxwell-Faraday Equation:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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Ampère’s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} &#43; \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$">
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<meta property="og:locale" content="en">
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<meta property="article:section" content="notes">
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<meta name="twitter:card" content="summary">
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<meta name="twitter:title" content="Electromagnetism">
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<meta name="twitter:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss’ Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ ">
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<meta name="twitter:description" content="Maxwell Equation (Integral) Gauss’ Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss’ Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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Maxwell-Faraday Equation:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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Ampère’s circuital law: $$ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{l} = \mu_0 \left(\iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} &#43; \epsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}\right) $$">
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<section class="content-section" id="content-section">
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<div class="content container-fluid" id="content">
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<div class="container-fluid note-card-holder" id="note-card-holder">
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<!-- A Sample Program -->
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<!-- A Sample Program -->
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<div class="note-card ">
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<div class="item">
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<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
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<div class="card">
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<div class="card-body"><ul>
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<div class="card-body"><ol>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ul>
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<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ul>
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<li><strong>Gauss&rsquo; Law for Magnetism</strong>
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$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
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</ul></div>
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</ol>
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<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<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>
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</div>
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</div>
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</div>
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</div>
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<div class="note-card ">
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<div class="item">
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<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
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<div class="card">
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<div class="card-body"><ol>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ol>
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<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \nabla \cdot \mathbf{B} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
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</div>
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‎public/notes/physics/index.html

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<h5 class="note-title"><span>Maxwell Equation (Integral)</span></h5>
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<div class="card">
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<div class="card-body"><ul>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ul>
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<p>$$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ul>
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<li><strong>Gauss&rsquo; Law for Magnetism</strong>
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$$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</li>
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</ul></div>
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</ol>
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<p>$$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<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>
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</div>
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</div>
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<div class="note-card ">
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<div class="item">
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<h5 class="note-title"><span>Maxwell Equation (Differential)</span></h5>
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<div class="card">
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<div class="card-body"><ol>
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<li><strong>Gauss&rsquo; Law</strong>:</li>
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</ol>
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<p>$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$</p>
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<ol start="2">
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<li>
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<p><strong>Gauss&rsquo; Law for Magnetism</strong>:
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$$ \nabla \cdot \mathbf{B} = 0 $$</p>
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</li>
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<li>
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<p><strong>Maxwell-Faraday Equation</strong>:</p>
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</li>
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</ol>
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<p>$$ \nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} $$</p>
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<ol start="4">
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<li><strong>Ampère&rsquo;s circuital law</strong>:</li>
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</ol>
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<p>$$ \nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) $$</p>
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</div>
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‎public/notes/physics/index.xml

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<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/notes/physics/electromagnetism/</guid>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \qquad \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism $$ \qquad \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$ </description>
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<description>Maxwell Equation (Integral) Gauss&amp;rsquo; Law: $$ \iint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = 4 \pi \iiint_{\Omega} \rho dV $$
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Gauss&amp;rsquo; Law for Magnetism: $$ \iint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 $$
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Maxwell-Faraday Equation:
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$$ \oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{l} = -\frac{d}{dt} \int_{\Sigma} \mathbf{B} \cdot d\mathbf{S} $$
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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>
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