Abstract
There are many problems where a detailed understanding of the interaction energy of systems of dipoles is needed, including electrorheological and magnetorheological fluids, ferrofluids, magnetic composites, and dielectrics. We have constructed soluble microscopic problems involving electric and magnetic dipoles to investigate energy balance, and have come to some understanding of the proper form of the dipolar free energy in aggregations of induced or permanent dipoles and mixtures thereof. The resulting equations clarify misconceptions sometimes found in the literature, and lead to greater intuition about the subtle aspects of the dipolar interactions. We discuss the application of these equations to dipole simulations to extract the dipole energy and material dielectric constant.
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