digital-brain/content/zettels/electromagnetism.md

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+++ title = "Electromagnetism" draft = false +++

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Maxwell equations for magnetics

Gauss law

"Magnetic fieldlines are closed loop."

\begin{equation} \oiint_S (\bm{B} \cdot \hat{\bm{n}}) dS = 0 \end{equation}

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

"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