The time periodic equation this physics interface solves is Ampère’s law, illustrated here in the 2D case with in-plane fields and assuming materials with a relative permeability μr.

The dependent variable AZ is a function of the phase. The same may be true for the other variables, for example μr and the current density JZ. This phase dependence may be intrinsic, or it may be coming from a definition containing other phase dependent variables. As an example, if the magnetic flux density B(ϕ) =∇ × (AZ(ϕ)eZ) and its norm B(ϕ) = |B(ϕ)| are introduced, it is possible to express the relative permeability as

in order to model a region where a B-H relation is used as input. Here, H(B) is the B-H function, which relates the magnetic field to the magnetic flux density.