Analytic solutions for capacitance of cylinders near a dielectric interface

Though there is no exact analytic solution for the capacitance between two cylinders near a dielectric interface, the method of images is used to derive analytic expressions that are accurate for widely separated cylinders, cylinders in close proximity, and widely separated cylinders near a dielectric interface. These solutions are compared with numerical simulations to verify the utility of the derived expressions. The necessity for numerical simulation in the general case is demonstrated. These analytic solutions can be incorporated into self-capacitance terms for solenoids and transmission lines.