A point charge finds itself at a height above an infinite half-space of dielectric material. The…
A point charge finds itself at a height above an infinite half-space of dielectric material. The charge has magnitude , the dielectric has a uniform permittivity , and there are no unpaired charges in the volume of the dielectric or on its surface. The Cartesian coordinates and are in the plane of the dielectric interface, while y is directed perpendicular to the interface and into the free space region. Thus, the charge is at . The field in the free space region can be taken as the superposition of a particular solution due to the point charge and a homogeneous solution due to a charge at below the interface. The field in the dielectric can be taken as that of a charge at .
(a) Show that the potential is given by
(b) Show that the charge is attracted to the dielectric with the force