On the solution of the magnetostatic field problem in the case of magnetic permeability that is dependent on coordinates

A method for solving magnetostatic field problems is proposed for the case of magnetic permeability that is dependent on coordinates. The problem reduces to finding two scalar functions from a system of equations with the corresponding boundary conditions that are obtained for these functions. As an important example of the application of the described methods, an analytical expression has been derived for the strength of the resultant magnetic field inside and outside of a spherical magnetic body with the model magnetic permeability being dependent on the coordinates that are placed in an external magnetostatic field. The proposed approach allows an analytical solution of the magnetostatic equation for a sphere with the model permeability in an external magnetostatic field. The results provide the basis for discussion of the uniqueness of the solution of the inverse magnetostatic field problem.