Spherical and spheroidal shells as models in magnetic detection

Abstract

The expressions for the scalar potentials of prolate and oblate spheroidal shells immersed in a dc uniform magnetic field are obtained. The expressions for the induced dipole moment of the shells are also evaluated. The problem is solved by finding solutions for the Laplace equation that satisfy boundary conditions at the shell surfaces. The shell thickness effect on the induced dipole moment and on its orientation are evaluated, The results appear to be useful for the analysis and for the prediction of magnetic signatures of hidden ferromagnetic objects belonging to a relatively large family.