Electrostatic energy of a solid spherical sector with uniform volume charge density

Abstract

We describe a mathematical method that makes possible the calculation of the electrostatic energy of a completely arbitrary solid spherical sector with uniform volume charge density. The success of the approach hinges on a specific transformation formula for the Coulomb potential that is valid in spherical coordinates. The final result is general and applies to any arbitrary angle of the solid spherical sector. Simple analytic expressions that are valid for the special cases of a solid sphere and hemisphere are obtained.