Point Charge Dynamics Near a Grounded Conducting Plane

Abstract

The classic image problem in electromagnetism involves a grounded infinite conducting plane and a point charge. The force of attraction between the point charge and the plane is identified using an equivalent-field picture of an image charge with opposite sign equidistant behind the plane resulting in a 1/{\it r}${}^2$ force of attraction between the original charge and the plane. If the point charge is released from rest it will reach the plane in a time $\tau$. This time $\tau$ has not been calculated correctly up to now. Clarification of the inconsistency is presented along with a correct solution to the classic image problem. Other electromagnetism problems are mentioned with attractive 1/{\it r}${}^n$ forces (where {\it n} $\ge$ 1). Such situations arise between a point charge and a line charge (1/{\it r}), between a line charge and a point dipole (1/{\it r}${}^2$), between a point charge and a point dipole (1/{\it r}${}^3)$, and between a point dipole and a second point dipole (1/{\it r}${}^4$).

6 pages, 4 figures