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+++ title = "Electromagnetism" author = ["Dehaeze Thomas"] draft = false category = "Mechanics and Physics" +++
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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.