Under certain circumstances, it can be helpful to formulate the problems in terms of the electric scalar potential V and the magnetic vector potential A. They are given by the equalities:

The defining equation for the magnetic vector potential is a direct consequence of the magnetic Gauss’ law. The electric potential results from Faraday’s law. In the magnetostatic case where there are no currents present, Maxwell-Ampère’s law reduces to ∇ × H = 0. When this holds, it is also possible to define a magnetic scalar potential by the relation H = −∇Vm.