Evaluation of the effective-medium theory in a static conduction field

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Abstract
The effective-medium theory has been formulated by many authors under various methods. In this paper we derive the theory for very conductive random media under a constant average current density, using a vector potential with respect to the current density. We then show that the theory is equivalently formulated by three requirements. The first two requirements, which have been used previously, are the requirements that the spatial averages of electric field and current density due to each sphere component embedded in the effective medium are equal to the effective or average field and current density. The third requirement is that the spatial average of electric power equals the effective or average power. As a result it is recognized that the effective-medium theory has wide applicability and that it satisfies many requirements.