Ampere’s Law

Ampere’s Law is the curl of the magnetic field \(\bvec B\),

\[ \nabla \times \bvec B = \mu_0 \bvec J \]

Integral Form

More often used is the integral form of Ampere’s law

\[ \oint \bvec B \cdot \mathcal d \bvec l = \mu_0 I_\mathrm{enc} \]

Note that this looks very similar to Gauss’ law and it is used within the same geometric symmetry that Gauss’ law is so great at.