A Parallel Derivation to the Maxwell-Garnett Formula for the Magnetic Permeability of Mixed Materials
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Abstract
Although mixing formulas for the effective-medium type of approximations for the dielectric permittivities in the in-fi-nite-wavelength (i.e., quasistatic) limit, such as the Maxwell Garnett formula, have been popularly applied in the whole spectral range of electromagnetic fields, their magnetic counterpart has seldom been addressed up to this day. An effort is thus devoted to the derivation of such an equation to predict the final permeability as the result of mixing together several materials. In a similar fashion to the approach leading to the Maxwell Garnett formula, a model is adopted wherein an originally isotropic host material is embedded with a cluster of spherical homogeneous magnetic particles. It is expected that such obtained formula should find wide applications, and particularly in the light frequency domain in this blossomful era of nanometer technology.
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