Magnetic Monopole Interaction with a Magnetic Sphere

Abstract

The two-phase problem of a magnetic sphere of radius a with permeability constant µ i (interior phase) interacting with a monopole/magnetic source located at (0, 0, c), c > a, in the host medium with permeability µ e (exterior phase) is addressed in this paper. By considering the Maxwell-Maxwell (MM) framework, exact results for the scalar magnetostatic potentials in the regions exterior and interior to the magnetic sphere are presented in various forms. The constructed potentials in infinite series and closed forms satisfy a set of mixed boundary conditions on the sphere and provide image system interpretations similar to those in electrostatics. An alternative form of the solution reveals a new interpretation that the image system can also be expressed as a distribution of magnetic dipoles between the sphere center and the Kelvin's inverse