On Potential Problems Involving Spheroids inside a Cylinder

Abstract

Abstract This paper gives a solution of Laplace's equation for prolate and oblate spheroids inside a coaxial cylinder on which the potential is either zero or such that its normal derivative is zero. The solution is given in the form of a series involving Legendre and Bessel functions whose coefficients are found as the solution of an infinite number of linear equations in an infinite number of unknowns. Examples are given to show that useful solutions may be obtained by this method provided that the radius of the cylinder is large enough. These examples give the potential due to a charged oblate spheroid inside an earthed cylinder and the flow past a prolate spheroid inside a cylindrical channel.