Update Content - 2023-01-10

content/zettels/electromagnetism.md

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+title = "Electromagnetism"
+draft = false
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+
+Tags
+:
+
+
+## Maxwell equations for magnetics {#maxwell-equations-for-magnetics}
+
+
+### Gauss law {#gauss-law}
+
+"Magnetic fieldlines are closed loop."
+
+\begin{equation}
+\oiint\_S (\bm{B} \cdot \hat{\bm{n}}) dS = 0
+\end{equation}
+
+
+### Faraday's law {#faraday-s-law}
+
+A changing magnetic field causes an electric field over a wire
+
+\begin{equation}
+\oint\_L \bm{E} \cdot d\bm{l} = -\frac{d}{dt} \iint\_S(\bm{B} \cdot \bm{n}) dS
+\end{equation}
+
+The line-integral of the electrical field over a closed loop L equals the change of the field through the open surface S bounded by the loop L.
+This is a voltage source (EMF), where the current is driven in the direction of the electric field.
+
+
+### Ampère's law {#ampère-s-law}
+
+"Current through a wire gives a magnetic field".
+
+\begin{equation}
+\oint\_L \bm{B} \cdot dl = \mu\_0 I
+\end{equation}
+
+The line integral of the magnetic field over a closed loop L is proportional to the current through the surface S enclosed by the loop L.
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+</div>