Image force on a moving charge

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Abstract
We derive a general expression for the image force felt by a charged particle which moves at constant speed normal to the surface of an isotropic dielectric. The method includes retardation effects fully, and may be extended to apply to a more general particle trajectory if desired. In contrast to results reported by others, we find the image force always reduces at large distances to the expression provided by electrostatics when the particle velocity is nonrelativistic. We examine the form assumed by the image force in some special limits. In particular, we find a difference between the image force felt by a particle which approaches the surface, and one that recedes from it after crossing the surface.