The magnetic vector potential may also be used in the time-harmonic case if the wave-length is significantly larger than largest time-scales in the system. Then the equation for vector potential may be solved with a time-harmonic trial function. The resulting equation for the vector potential is therefore imaginary.

The figures below present a simple induction heating geometry. The coil generates on alternating magnetic field that causes currents in the conducting materials. These currents face resistance and therefore Joule losses are generated in the crucible.

The pictures are as follows:
a) In-phase component of the vector potential
b) Out-of-phase component of the vector potential
c) Joule losses