The Ohmic heating of particulates in a lossless medium

This paper provides a general theory on the Ohmic dissipation of electromagnetic energy by a spherical particulate that is embedded in a lossless medium. The particulate may possess an arbitrary electrical conductivity, and both the medium and the particulate may assume general values of permittivity and permeability. Under the assumption that the wavelength of the electromagnetic field in the medium is large compared with the particulate size, we provide an accurate account of the degree of Ohmic heating by the radio frequency (rf) electric field and by the rf magnetic field of the electromagnetic field. It is found that, in general, heating by the rf magnetic field is dominant whenever $δ<a$⁠, where $δ$ is the resistive skin depth and $a$ is the radius of the particulate. Analytic scaling laws in the various regimes are derived, from the static case to very high frequency, and for ratios of $δ∕a$ ranging from zero to infinity. The calculation is extended to a transient electromagnetic pulse. Also constructed is the loss tangent of the medium, resulting from a distribution of particulates.