where Je is an externally generated current density,
v is the relative velocity of the domain in the physics interface’s or node’s frame, and
Em(J) is a (possibly nonlinear) relation sometimes called
E-J characteristic, which describes the electric field in the local (material) frame as a function of the current density. The total current density J is finally obtained from Ampère’s Law:
The Em(
J) characteristic introduced in the previous section can be specified in different ways in the
Faraday’s Law node. The most common case is a linear relation between
Em and
J. In magnetostatics and in time-dependent studies (in the quasistatic approximation) this relation is specified by the resistivity or the electrical conductivity:
σ and
ρ can be tensor quantities, in which case the inverse is intended as the inverse of a tensor. In frequency-domain, the displacement current is included, giving the following relations: