Low-frequency interaction of magnetic dipoles and perfectly conducting spheroidal bodies in a conductive medium

Abstract : 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. 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 ) to 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 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 given in compact fashion, as infinite series expansions for n = 0, 2 or finite forms for n = 3.
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Panayiotis Vafeas, Gaële Perrusson, Dominique Lesselier. Low-frequency interaction of magnetic dipoles and perfectly conducting spheroidal bodies in a conductive medium. A. Charalambopoulos and D. I. Fotiadis and D. Polyzos. Advanced Topics in Scattering and Biomedical Engineering, Proc. 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, World Scientific Publishing Company, pp.107-114, 2008, 978-981-281-484-5;(e-book) 978-981-281-485-2. ⟨10.1142/9789812814852_0012⟩. ⟨hal-00637749⟩



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