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Ampere's law

505 bytes added, 03:14, 24 September 2008
'''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.