On uniformity of the field inside small scatterers

摘要

The electrostatic problem for a homogeneous axisymmetric particle is considered. The approach applied is similar to the extended boundary condition method often used in the light scattering theory. The surface integrals forming the elements of an analog of the well known T-matrix are studied in detail. The inverse problem is solved under the condition that the internal field is uniform. It is proved that this condition is satisfied for axisymmetric particles only if they are spheroids. Approximate solutions to the electrostatic problem that are based on the assumption of the uniform internal field are discussed as well.