On the application of 2D potential theory to electrostatic simulation

Abstract

Abstract Computing the charge density on the surfaces of conductors is fundamental to many electrostatic applications. Difficulties arise in two‐dimensional simulation due to the O(log|r|) potential. Fully understanding the 2D potential problem, and reasonably connecting the mathematical formulation with physical interpretation, are key to handling this difficulty properly. In the absence of these factors it is easy for one to propose an ill‐posed problem. In this paper, a complete investigation of potential theory, from 3D to 2D, is made for computing charge density on the surfaces of conductors. Various integral formulations are derived ‐ these are applicable in different situations. It is shown that, in general, the electrostatic potential need not be finite valued at infinity for 2D problems. Numerical examples for the 2D case are constructed to show that the formulations are consistent. Criteria for choosing the most appropriate formulation for a given problem are suggested.