Stored electrostatic energy of a uniformly charged annulus

Abstract

We show that a method that makes clever use of the axial symmetry of the model considerably simplifies the calculation of the electrostatic Coulomb self-energy of an annulus with uniform surface charge density. Differently from a disk, the case of an annulus represents a rather challenging geometry with no obvious solution for the calculation. The final result obtained for the electrostatic Coulomb self-energy of a uniformly charged annulus is expressed in compact form as a function of the ratio of the inner radius relative to the outer radius and involves special standard functions such as the complete elliptic integrals of the first and second kind.