The electric potential and field of a finite conducting rod, and a conducting disk

Abstract

The electric potential and field of a finite conducting rod are calculated. This is done by two methods. In the first, ellipsoidal coordinates are used to solve the Laplace equation outside the rod. In the second, asymptotic behavior of the electric field is used to find the position-dependence of the change density on the rod, which is then used to calculate the potential and field. An analytic continuation is performed to relate this problem to that of a conducting disk. Using this, the electric potential and field of a disk are determined. The charge densities are also calculated.