Inverse Problem of Magnetostatics in Saturation Fields

Abstract

We have derived integro-differential equations whose solutions determine the shape of an arbitrary ferromagnetic saturation-magnetized body, or a cavity in it, without an a priori assumption that domains they occupy belong to any particular geometric class. The uniqueness of such determination is proved for a wide class of cases encountered in practice. As an important illustrative example, analytical formulas are derived for determining the resulting field of a spherical ferromagnetic body. These formulas uniquely determine the position and dimensions of the body.