The overall magnetic properties of magnetic particle-filled composites are studied with the consideration of direct magnetic interactions between randomly dispersed particles. The local magnetic field for two particles embedded in the infinite medium is solved and the pairwise magnetic particle interaction is defined. Integrating the pairwise interactions from all particles provides the homogenized magnetic fields, from which the effective magnetic permeability is derived. If the particle interaction is dropped, the result is reduced to Maxwell-Garnett's model.
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Yin et al. (2005) studied this question.
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