Theory for the Magnetic Fields, No Currents Interface
In magnetostatic problems where no electric currents are present, it is possible to formulate and solve the problem using a scalar magnetic potential. In a current-free region you have ∇ × H = 0. This implies that the magnetic scalar potential Vm can be defined from the relation H = −∇ Vm, which is analogous to the definition of the electric potential for static electric fields.
Using the constitutive relation B = μ0(H + M), the equation ∇ ⋅ B = 0 becomes
(5-5)
The Magnetic Fields, No Currents Interface uses this equation for modeling of magnetostatics in the absence of electric currents.
In planar 2D the dynamic formulations also involves the thickness d in the z direction:
 
For a discussion about the boundary element method used with The Magnetic Fields, No Currents, Boundary Elements Interface, see Theory for the Boundary Elements PDE in the COMSOL Multiphysics Reference Manual.