Ampere's law

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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


where \vec{J} is current density.

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