Charged Sphere in Cylinder

Abstract

The method first used to solve the problem of a freely charged right circular cylinder in J. Appl. Phys. 27, 917 (1956), is applied to the case of a charged conducting sphere enclosed by a coaxial circular conducting cylinder. The charge density on the sphere, the potential between it and the cylinder and the capacitance are given for sphere to cylinder radius ratios of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.95. All results are accurate to one part in 10⁷ or better. An approximate formula for the capacitance of a sphere in a cylindrical box is given.