Potential and Capacity of Concentric Coaxial Capped Cylinders

Publisher Website
Google Scholar
Abstract
An exact solution is obtained for the potential in the space between two finite concentric coaxial right circular capped cylinders; and from the potentials an exact solution of the capacity is found. A set of infinite equations is involved but detailed numerical calculations, made for nine different geometries, show that if the ratio of height of the outer cylinder to diameter of the inner cylinder is less than about unity only the first eight equations and the first eight unknowns in them need be considered for obtaining three figure accuracy of the capacity. The theory is correct when the inner cylinder shrinks to a disk and also when the radius of the outer cylinder goes to infinity. Thus the theory yields the capacity for a horizontal disk midway between infinite conducting planes. When the planes become infinitesimally close to the disk the problem becomes two-dimensional, and the three-dimensional capacity expression goes over to an expression obtained by a conformal transformation. A table of coefficients for 1st, 2nd, 3rd, 4th, 6th, and 8th order approximations is given for computing quantities of interest and to show the rapidity of convergence of results for the nine geometries considered. For one of the cases the equipotentials and lines of force are computed and diagrammed.

This publication has 2 references indexed in Scilit: