Self-consistency conditions for the effective-medium approximation in composite materials

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Abstract
Two different self-consistency conditions are used in the literature to derive the effective-medium-approximation equations. They are (a) that the net polarization of the medium should be zero, and (b) that the effective electric field should be the same as the average of the electric field in every grain. These two approaches lead to different predictions, as we show, for conducting spheroidal particles in an insulating background. It is found that the self-consistency condition of the zero net polarization field should be used to explain the transport properties of randomly inhomogeneous media.