A point charge is held fixed a distance above a large earthed conducting plane
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics
The Boundary-Value Problem, Ch Uniqueness, images and the Green function of a region
Problem
A point charge q=4.0nC is held fixed a distance d=3.0cm above a large earthed conducting plane. Someone argues: "The plane is earthed, but only q is stated as fixed; by the second uniqueness theorem, since no potential is stated on the boundary, V is undetermined up to a constant, so the induced charge and the force cannot be found." A second argument then adds: "And since V=0 on the plane, the energy stored in the field must be zero."
((a)) Say which uniqueness theorem actually governs this problem, and why the first argument misapplies the wrong one.
((b)) Find the work needed to bring q in from far away to its height d, and use it, with the energy density of the field, to show that the second argument is wrong.