Bounding Formulae for the Capacitance of a Cylindrical Two-dimensional Capacitor with Cartesian Orthotropic Dielectric Material

Abstract

This paper addresses the evaluation of a two-dimensional cylindrical capacitor featuring homogeneous Cartesian anisotropic dielectric material. The development of a bounding formula forms the crux of the investigation and is grounded in the principles of the Cauchy-Schwarz inequality, a mathematical concept widely acknowledged for establishing relationships between different mathematical entities. In the course of this study, a dual-sided bound is systematically derived for the circular cylindrical two-dimensional capacitor through the application of well-established inequality relations. These bounds play a pivotal role in setting limits on the capacitance of the system, providing valuable insights into its electrical behavior.