The boundary value problem of two ferromagnetic spheres introduced in a uniform magnetic field is solved by using scalar potentials and bispherical coordinates. Under the approximation of an ideal ferromagnetic material, the potential of the outside field is constant over the sphere surfaces and the resultant field has the same structure as the electrostatic field of two uncharged conducting spheres in a uniform electric field. The magnetic flux density inside each sphere is derived from a Laplacian scalar potential by imposing the continuity of the normal component of flux density through the sphere surfaces. The constants of integration of this potential are determined from an infinite tridiagonal matrix equation which yields a computationally efficient solution, of controllable accuracy.

Keywords: Electromagnetics, Magnetic field modeling, Magnetic scalar potential