Direct and Inverse Problems of Magnetostatics for Uniformly Magnetized Bodies

Abstract

The paper describes the basic schemes for solving direct and inverse magnetostatic problems based on the fundamental integro-differential equation of magnetostatics, both for the general case of arbitrary magnetization of a magnet, arising when it is placed in the field of external sources, and for the case of its uniform magnetization. It is shown that the schemes presented in the paper for solving these problems for uniformly magnetized bodies, although requiring the creation of conditions to ensure such magnetization, nevertheless allow one to avoid many fundamental problems of general schemes, significantly simplify them, and propose a number of new effective algorithms. An algorithm is described and justified that reduces the solution of the direct problem for a magnet with a defect in the case of uniform magnetization to the solution of direct problems for “defect-freeˮ magnets. This algorithm significantly expands the database of various geometric shapes of magnets and defect shapes in them, for which, under their uniform magnetization, an algorithm for an analytical or numerical-analytical method for solving the direct problem of magnetostatics exists.