Modeling Magnetic Field of a Hollow Object by Distributing Magnetic Charges on Spheroidal Surfaces

Abstract

To estimate the magnetic field outside a ferromagnetic hollow object such as ship or wheeled vehicle from the inside field measurements, we have developed a method to represent the object by the distribution of virtual magnetic charges on two sheets of confocal spheroidal surfaces. In the method, the magnetic field both inside and outside the object is expanded in prolate spheroidal harmonic functions of the lowest degree, and the surfaces are determined such that the charges when distributed axially and radially on them produce the same amount of the corresponding harmonic both inside and outside the object as the actual one respectively. In an example of an oblong steel box of the length L magnetized by the earth's field, the estimated field on a line extending parallel to the major axis with a distance 0.25L and a coverage ±0.7L was equal to the measured one with a standard error amounting to 9% of the peak field.