# Changes

'''Ampere's Law''' , named for [[Andre-Marie Ampere]], relates electric [[current]] to [[magnetic field]]s, and is ~~a law that simplifies ~~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 ~~has many similarities ~~is the magnetic analogue to [[Gauss's Law]], and can be stated in integral form as~~:~~

: <math>\~~oint_S ~~oint_C \vec{B} \cdot \mathrm{d}\vec{s}

= \mu_0 I_{\mathrm{enc}}</math>

where <math>\vec{B}</math> is magnetic field, ''C'' is a closed curve, <math>I_{\mathrm{enc}}</math> is current enclosed by ''C'', and <math>\mu_0</math> is the permeability of free space.

In differential form, Ampere's Law is written

:<math> \vec{\nabla}\times\vec{B}=\mu_0\vec{J}</math>

where <math>\vec{J}</math> is current density.

[[category:Physics]]

[[category:Electricity]]