Quasi-magneto static solution for a conducting and permeable spheroid with arbitrary excitation

Broad-band electromagnetic induction (EMI) methods are promising in the detection and discrimination of subsurface metallic targets. In this paper, the quasi-magneto-static solution for a conducting and permeable prolate spheroid under arbitrary excitation by a time-harmonic primary field is obtained by using the separation of variables method with vector spheroidal wave functions. Numerical results for the induced dipole moments are presented for uniform axial and transverse excitations, where the primary field is oriented along the major and minor axis of the prolate spheroid, respectively. We show that the EMI frequency responses are sensitive to the orientation and permeability of the spheroid. An approximation is also developed that aims to extend the exact solution to higher frequencies by assuming slight penetration of the primary field into the spheroid. Under this approximation, a system of equations that refers only to the external field expansions is derived. It is shown that, for spheroids with high relative permeability, this approximation is in fact capable of yielding an accurate broad-band response even for highly elongated spheroids.