Abstract
A formula is derived for the effective complex dielectric constant of a dielectric medium containing a cubical array of dielectric or metallic impurities. The formula is given to two levels of approximation; one based on the Clausius-Mosotti equation which assumes zero contribution to the polarization from dipoles within the Lorentz sphere. The second is a generalization of a more accurate calculation of Rayleigh. Specific expressions are given for the real dielectric constant and the effective conductivity (and loss tangent) both as a function of frequency and impurity content. Formulas are valid for wavelengths large compared with the dimensions of the impurities. Results are compared with experimental values of Kharadly and Jackson. The complex dielectric constant is also obtained from the more accurate dc formula for a uniform array of spheres embedded in a uniform dielectric as derived by Zuzovsky and Brenner and again from the dc formula of a random array as derived by Felderhof.
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