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.

Topics
Energy system, Free energy, Magnetic properties, Dielectric properties, Magnetic fluids
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For dipole sites within a few lattice constants of the sphere surface, the approximation that the surface cuts through a dielectric continuum begins to fail.
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It is of interest to note that because the free energy is not lowered when induced dipoles are arranged into a spherical aggregation, there is no tendency for that to happen spontaneously. The shape with lowest energy, regardless of lattice arrangement, is a long column aligned with the applied field. This shape eliminates the depolarizing field, which allows for maximal dipole polarization.
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Reference 4, pp. 2825–2826 reports similar computations for elongated rectangular solids.
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© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
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