Ampere’s Law#

Ampere’s Law is the curl of the magnetic field $\text{bvec}B$,

$$\mathrm{\nabla }\times \text{bvec}B={\mu }_0\text{bvec}J$$

Integral Form#

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

$$\oint \text{bvec}B\cdot \mathcal{d}\text{bvec}l={\mu }_0{I}_{\mathrm{enc}}$$

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.