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The effective area for a receiving antenna in a lossy medium is derived by solving a receiving problem of an insulated Hertzian dipole with its gain obtained beforehand. As a result, the effective area in a general medium is found to be the product of the gain and pi/Re[omegaradic{epsivmu*}]2. The latter term becomes same as the previous formula, pi/Re[omegaradic{epsivmu}]2=4pi/lambda2when the medium is only electrically or magnetically lossy. A simulation result of power transmission between two insulated small dipoles validates the theory.
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Lee et al. (2009) studied this question.
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