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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 49 > pp. 87-111
## LOW-FREQUENCY SOLUTION FOR A PERFECTLY CONDUCTING SPHERE IN A CONDUCTIVE MEDIUM WITH DIPOLAR EXCITATIONBy P. Vafeas, G. Perrusson, and D. Lesselier
Abstract:
This contribution concerns the interaction of an arbitrarily orientated, time-harmonic, magnetic dipole with a perfectly conducting sphere embedded in a homogeneous conductive medium. A rigorous low-frequency expansion of the electromagnetic field in positive integral powers (jk) complex wavenumber of the exterior medium, is constructed. The first ^{n}, kn = 0 vector coefficient (static or Rayleigh) of the magnetic field is already available, so emphasis is on the calculation of the next two nontrivial vector coefficients (at n = 2 and at n = 3) of the magnetic field. 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) vector Laplace equations. They are given in compact fashion, as infinite series expansions of vector spherical harmonics with scalar coefficients (for n = 2). The good accuracy of both in-phase (the real part) and quadrature (the imaginary part) vector components of the diffusive magnetic field are illustrated by numerical computations in a realistic case of mineral exploration of the Earth by inductive means. This canonical representation, not available yet in the literature to this time (beyond the static term), may apply to other practical cases than this one in geoelectromagnetics, whilst it adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.
2. Oristaglio, M. L. and B. R. Spies (eds.), 3. Kaufman, A. A. and G. V. Keller, 4. Bourgeois, B., K. Suignard, and G. Perrusson, "Electric and magnetic dipoles for geometric interpretation of three-component electromagnetic data in geophysics," 5. Dassios G. and R. E. Kleinman, Low Frequency Scattering, 6. Perrusson, G., D. Lesselier, M. Lambert, B. Bourgeois, A. Charalambopoulos, and G. Dassios, "Conductive masses in a half-space Earth in the diffusive regime: Fast hybrid modeling of a low-contrast ellipsoid," 7. Habashy, T. M., R. W. Groom, and B. R. Spies, "Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering," 8. Charalambopoulos, A., G. Dassios, G. Perrusson, and D. Lesselier, "The localized nonlinear approximation in ellipsoidal geometry: a novel approach to the low frequency problem," 9. Hobson, E. W., 10. Perrusson, G., D. Lesselier, P. Vafeas, G. Kamvyssas, and G. Dassios, "Low-frequency electromagnetic modeling and retrieval of simple orebodies in a conductive Earth," 11. Ao, O. C., H. Braunisch, K. O'Neill, and J. A. Kong, "Quasimagnetostatic solution for a conducting and permeable spheroid with arbitrary excitation," 12. Bowman, J. J., P. L. Uslenghi, and T. B. Senior (eds.), 13. Varadan, V. K. and V. V. Varadan (eds.), 14. Perrusson, G., P. Vafeas, and D. Lesselier, 15. Morse, P. M. and H. Feshbach, 16. Tortel, H., "Electromagnetic imaging of a three-dimensional perfectly conducting object using a boundary integral formulation," 17. Dassios, G. and P. Vafeas, "Comparison of differential representations for radially symmetric Stokes flow," |

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