Point charge in the interior of an elastic dielectric half space

Abstract

The axisymmetric boundary value problem of an elastic dielectric half space, having a point charge “4πϵ” at a distance “ h” beneath its free surface, is solved by the methods of images and Hankel transforms. Expressions for the components of the displacement and polarization vectors, the stress and electric tensors throughout the (interior of the) half space are obtained and the surface energy density of deformation and polarization is determined. For the particular case of an elastic dielectric half space with a free surface and in the absence of charge, the results derived agree with those presented in [1]. Numerical results are presented on graphs depicting spatial and surface variations of various physical quantities indicating the effects of polarization.