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Electromagnetic scattering due to a spherical conductor in presence of a slightly conducting dielectric cover has been studied. Numerical results have been presented for a three-layer model, excited by a uniform time harmonic magnetic field, where the intermediate layer accounts for the spacing between the core and the shield. Scattering coefficients for the covered and uncovered situations are compared in terms of an insertion loss parameter. The resulting curves provide information about the interesting frequency bands of supertransmission of energy between the source and the core-conductor. The results may find application in electromagnetic probing of some terrestrial and lunar situations.