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.