Analysis of a rectangular earthing plate

A Fredholm integral equation of the first kind is developed for finding the charge distribution on the surface of a rectangular plate buried in a homogeneous earth. The method of moments is used to solve the functional equations. Charge accumulations at the edges and the corners are represented by expansion functions with an appropriate singularity. Owing to edge and corner effects, the surge current is dispersed into earth in a relatively small region near the edge, especially the corners. Thus, the capacitance of an earthing plate is not directly proportional to its area. Based on the charge distribution, other characteristics of the plate are derived. The earthing resistance of a rectangular earthing plate is lower than that of a square plate of the same size, the resistance of the latter is lower than that of a circular disk. The potential profile of a square plate on the earth surface is much smoother compared with that of a rectangular plate, and therefore it exhibits lower step and touch potentials