Ampere's Circuital Law

Ampere's law states: the line integral of the magnetic field around any closed loop equals $\mu_0$ times the net current enclosed by that loop:

Crucially, this line integral does not depend on the exact shape of the closed path, nor on exactly where inside it the enclosing conductor(s) sit -- only on the total current threading through the loop. ("Line integral" means an integral taken along a curve; a small circle on the integral sign, $\oint$, denotes that the curve is closed.) This single relation is what makes the f …