Current Flow in Cylinders

Abstract

The mixed boundary value problem arising from the flow of current into a right circular cylinder of radius a through a perfectly conducting coaxial disk electrode at one end is solved approximately. The boundary conditions are met rigorously except that the electrode is not quite plane. A solution valid for all values of the disk radius is given for which in the worst case the deviation from flatness is nearly 0.01a. More exact solutions are worked out for disk radii ¼a, ½a, and ¾a and the first forty coefficients in the Bessel function series for the potential in the cylinder are tabulated. A cylinder whose diameter is eight times its length is also treated for disk radii ¼a and ½a and the first forty coefficients in the potential series are tabulated. The probable errors in the resistance formulas derived from these solutions are given.