Digital computer calculation of the electric potential and field of a rod gap

The electric field and potential distribution in the gap between a cylindrical rod having a hemispherical tip and an infinite plane perpendicular to the cylinder axis was determined using a charge simulation technique. This method assumes a charge at the center of the hemisphere and a finite number of semi-infinite axial charges in the cylindrical portion of the rod electrode. Boundary conditions in the cylindrical and spherical portions enabled the formulation of simultaneous equations whose digital solution yielded the assumed lumped charges. The digital computer program provided values of the potential and both field components anywhere in the gap with an accuracy of about 2 percent.