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.

Bounds for the electrical resistance for non-homogeneous conducting body

“…Two-side estimation will be proven for the electrical conductance of non-homogeneous isotropic hollow three-dimensional conductor. The mathematical formalism follows the methods, which were used in papers [3][4][5]. In paper [3] upper and lower bounds are proven for the electrical resistance of homogeneous isotropic ring like axisymmetric conductor.…”

“…In paper [3] upper and lower bounds are proven for the electrical resistance of homogeneous isotropic ring like axisymmetric conductor. In paper [4] the capacitance of two-dimensional cylindrical capacitor, which consists of non-homogeneous dielectric materials is studied. Examples illustrate the applications of the derived bounding formulae of capacitance [4].…”

“…In paper [4] the capacitance of two-dimensional cylindrical capacitor, which consists of non-homogeneous dielectric materials is studied. Examples illustrate the applications of the derived bounding formulae of capacitance [4]. A mathematical heat transfer model is developed for the steady-state heat transfer problem for homogeneous isotropic body of rotation in [5] and it is used to obtain estimations of thermal heat transfer conductance.…”

Bounds for the Electrical Resistance for Non-homogeneous Two-dimensional Conducting Body

“…Two-side estimation will be proven for the electrical conductance of non-homogeneous isotropic two-dimensional conductor. The mathematical formalism follows the methods which are used in papers [1], [2], [3], [4]. In the Study of [1] upper and lower bounds are proven for electrical resistance of homogeneous isotropic ring-like axisymmetric conductor.…”

“…In the Study of [1] upper and lower bounds are proven for electrical resistance of homogeneous isotropic ring-like axisymmetric conductor. The Study of [2] deals with the capacitance of two-dimensional cylindrical capacitor which consists of non-homogeneous dielectric materials. Examples illustrate the applications of the derived bounding formulae of capacitance, [2].…”