 
Maxwell equationsLet us first recall the principal equations. We get from the Maxwell equations in the magnetostatic case the relationswith 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
is standard. Thus, we end up with the equations 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 We can formulate a linear problem by the equations (10) and (9), which is a good approximation for the nonlinear problem if we can neglect saturation effects in ferromagnetic materials.  
