# Ampere's law

Ampere's Law, named for Andre-Marie Ampere, relates electric current to magnetic fields, and is one of Maxwell's Equations. It is often used in the calculation of the magnetic field at a point due to one or many current-carrying wires. It is the magnetic analogue to Gauss's Law, and can be stated in integral form as

$\oint_C \vec{B} \cdot \mathrm{d}\vec{s} = \mu_0 I_{\mathrm{enc}}$

where $\vec{B}$ is magnetic field, C is a closed curve, Ienc is current enclosed by C, and μ0 is the permeability of free space.

In differential form, Ampere's Law is written

$\vec{\nabla}\times\vec{B}=\mu_0\vec{J}$

where $\vec{J}$ is current density.