This work concerns the interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with a perfectly conducting prolate or oblate spheroidal body embedded in a homogeneous conductive medium. For many practical applications involving buried obstacles such as Earth's subsurface electromagnetic probing or other physical cases (e.g. geoelectromagnetics), spheroidal geometry provides a very good approximation. Consequently, our analytical contribution deals with prolate spheroids, since the corresponding results for the oblate spheroidal geometry can be readily obtained through a simple transformation. The particular physics concerns a solid impenetrable body under a magnetic dipole excitation, where the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers (ik)~n, n >= 0 , k being the complex wavenumber of the exterior medium, for the incident, scattered and total electric and magnetic fields. Our goal is to obtain the most important terms of the low-frequency expansions of the electromagnetic fields, that is the static (for n = 0) and the dynamic (n-1,2,3 ) terms. In particular, for n = 1 there are no incident fields, while for n = 0 the Rayleigh electromagnetic term is easily obtained. Emphasis is given on the calculation of the next two nontrivial terms (at n = 2 and at n = 3 ) of the magnetic and the electric fields. Those are found in closed form from exact solutions of coupled (at n - 2 , to the one at n = 0) or uncoupled (at n = 3 ) Laplace equations and they are given in compact fashion, as infinite series expansions for n = 0,2 or finite forms for n = 3 . This research adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.
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