Boundary-Value Problems in Electrostatics: II — John David Jackson
Physics — E&M · method-of-images-infinite-plane
Problem
A point charge q is brought to a position a distance d away from an infinite plane conductor held at zero potential. Using the method of images, find:
(a) the surface-charge density induced on the plane, and plot it;
(b) the force between the plane and the charge by using Coulomb's law for the force between the charge and its image;
(c) the total force acting on the plane by integrating σ2/2ϵ0 over the whole plane;
(d) the work necessary to remove the charge q from its position to infinity;
(e) the potential energy between the charge q and its image [compare the answer to part d and discuss].
(f) Find the answer to part d in electron volts for an electron originally one angstrom from the surface.