[[Electrodynamics MOC]]
# Magnetic field

The **magnetic field** $\vab B$ is an abstract [[pseudovector]] which describes how magnetic forces will act upon a moving test charge
$$
\begin{align*}
\frac{\vab F}{Q} = \vab v \times \vab B
\end{align*}
$$
as described by the [[Lorentz force law]].
The magnetic field follows the [[Principle of Superposition]],
so the effects of different sources may be combined easily.

## Calculation

It follows from [[Maxwell's equations]] that
$$
\begin{align*}
\vab B(\vab r) = \frac{\mu_{0}}{4\pi} \iiint_{\mathbb{R}^3} \frac{\vab J(\vab r') \times \unitv \Sr}{\Sr^2} d\tau'
\end{align*}
$$
although historically this result is derived from consideration of the [[Biot-Savart Law]].

## Properties

- See [[Gauß's law for magnetic flux]]
- See [[Magnetostatics MOC]]

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