The steady-state integral form is more useful in situations with high degrees of symmetry than the equivalent Biot-Savart Law.
Taking the divergence of this relation leads to a statement which, according to Noether's theorem, is implied by gauge invariance. In its original form, it was inconsistent with the action of charging capacitors, so a term proportional to the time derivative of the electric field, known as the displacement current, was added. The steady-state integral form is more useful in situations with high degrees of symmetry than the equivalent Biot-Savart Law. For 10 points, name this member of the Maxwell equations that gives the magnetic field circulating around a current.
Taking the divergence of this relation leads to a statement which, according to Noether's theorem, is implied by gauge invariance.
{Ampere's} Law