The potential distribution in a constricted cylinder

Abstract

An approximate solution of Laplace's equation is used to determine the potential distribution in a current-carrying cylinder containing a circular constriction along its axis. Although the expression for the potential was derived for the case when the radius b of the constriction is small in comparison with the radius a of the cylinder, the results have been found to represent a good approximation to the exact solution for values of b/a approaching 0.5.