A point charge is free to move along the -axis 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 is free to move along the z-axis above a large earthed conducting plane occupying z=0, released from rest at some height z=z0>0 under the electrostatic force alone (the plane remains earthed at all times).
((a)) Pose this as a boundary-value problem in the form used for posing problems: state the region, the equation V satisfies there, and the condition on each piece of the boundary, for a fixed instantaneous height z.
((b)) Using the image force on q, decide whether there is any height z>0 at which the electrostatic force on q alone can vanish.
((c)) The uniqueness theorems concern two candidate solutions of the same fixed problem (same sources, same boundary data). Explain why they do not, by themselves, settle whether an equilibrium height exists as q is allowed to move.