HEJ, HU ISSN 1418-7108Manuscript no.: ANM-981030-A

## Maxwell equations

Let us first recall the principal equations. We get from the Maxwell equations in the magnetostatic case the relations

 (1) (2) (3)

with in the nonlinear model, cf. [8]. Here, the magnetic field strength is denoted by , the magnetic induction by , and is the current density. Since (3) holds, we can introduce the magnetic vector potential by
 (4)

In magnetostatics, the Coulomb gauge
 (5)

is standard. Thus, we end up with the equations

 (6) (7)

for the unknown vector potential . If permanent magnets are involved, must be replaced by . According to material properties, the coefficient depends on the position . With the unknown , equations (6) and (7) can be rewritten as

 (8) (9)

We can formulate a linear problem by the equations (10) and (9),
 (10)

which is a good approximation for the nonlinear problem if we can neglect saturation effects in ferromagnetic materials.
 HEJ, HU ISSN 1418-7108Manuscript no.: ANM-981030-A