Analysis of a circular earthing plate

A Fredholm integral equation of the first kind is developed for finding the charge distribution on a circular conducting plate buried in a homogeneous earth. The method of moments is used to solve the functional equations. Techniques are developed to evaluate and differentiate a singular integral by numerical means. An extremely fast rate of convergence is gained by expanding the charge distribution in functions with an appropriate singularity. It is observed that currents are dispersed into the earth in a small region near the edge of the disc. Contrary to popular perceptions, the earthing resistance of a disc is not inversely proportional to its area. A simple empirical formula for enumerating the earthing resistance of a disc in terms of its radius, its depth of burial, and the conductivity of the earth is derived