Bounding Formulae for Capacitance of Cylindrical Capacitor with Nonhomogeneous Dielectric Material

Abstract

The paper deals with the capacitance of cylindrical capacitor which consists of nonhomogeneous dielectric materials. The infinite long cylindrical surfaces of capacitor have uniform distributed electric charges in axial direction, so that electrostatic boundary value problem which determines the electric field in the nonhomogeneous dielectric material is a twodimensional boundaryvalue problem. The derivation of the bounding formulae is based on the CauchySchwarz inequality. Examples illustrate the applications of the derived upper and lower bound formulae.