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Electromagnetic low-frequency dipolar excitation of two metal spheres in a conductive medium

Abstract : This work concerns the low-frequency interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spheres embedded within a homogeneous conductive medium. In several applications, where two bodies are placed near one another, the 3-D bispherical geometry provides a good approximation. The particular physical problem is modeled by considering two solid impenetrable (metallic) obstacles, excited by a magnetic dipole, where the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers (ik) to the power n, where n ≥ 0 , k being the complex wave number of the exterior medium, for the incident, scattered and total electric and magnetic fields. We deal with the most important terms of the low-frequency expansions of the non-axisymmetric scattered electromagnetic fields, that is the static (for n=0) and the dynamic (n=1,2,3) terms, while for n≥4 the contribution of the additional terms is of minor significance. The calculation of the exact solutions, satisfying Laplace's and Poisson's differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. Thus, we obtain the electromagnetic fields in an analytically compact fashion as infinite series expansions of bispherical eigenfunctions. This particular electromagnetic scattering problem is then simulated in order to investigate the effect of the radii ratio, the relative position of the spheres and the position of the dipole on the real and imaginary parts of the calculated scattered magnetic field.
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Contributor : Dominique Lesselier <>
Submitted on : Wednesday, December 14, 2011 - 10:10:06 PM
Last modification on : Thursday, June 17, 2021 - 3:49:28 AM

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Panayiotis Vafeas, Polykarpos Papadopoulos, Dominique Lesselier. Electromagnetic low-frequency dipolar excitation of two metal spheres in a conductive medium. Journal of Applied Mathematics, Hindawi Publishing Corporation, 2012, 2012, 628261 (37pp). ⟨10.1155/2012/628261⟩. ⟨hal-00652109⟩



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