Low-frequency modeling of the interaction of a magnetic dipole and two perfectly conducting spheres in a conductive medium

Abstract : This work concerns the interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spherical bodies embedded in a homogeneous conductive medium. For many practical applications involving two buried obstacles nearly located such as Earth's subsurface electromagnetic probing or other physical cases (e.g. geo-electromagnetics), the bispherical geometry might provide a very good approximation. The particular physics here concerns two solid impenetrable bodies under a magnetic dipole excitation, where the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers (ik)* at power 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 and thus no scattered ones, while for n = 0 the Rayleigh electromagnetic term is obtained in terms of infinite series. Emphasis is given on the calculation of the next two nontrivial terms (at n = 2 and at n = 3) of the aforementioned fields. Consequently, 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 . Let us notice that the difficulty of the Poisson's that has to be solved for n = 2 is not minor and for this case we present only the methodology to obtain the solution. Finally, our analytical approach calls for the use of the well-known cut-off method in order to obtain properly closed solutions.
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Contributor : Dominique Lesselier <>
Submitted on : Tuesday, December 8, 2009 - 4:48:17 PM
Last modification on : Friday, September 28, 2018 - 1:16:41 AM


  • HAL Id : hal-00439858, version 1



Panayiotis Vafeas, Dominique Lesselier. Low-frequency modeling of the interaction of a magnetic dipole and two perfectly conducting spheres in a conductive medium. 9th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, Oct 2009, Patras, Greece. ⟨hal-00439858⟩



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