ON THE APPLICATION OF 2D POTENTIAL-THEORY TO ELECTROSTATIC SIMULATION

Computing the charge density on the surfaces of conductors is fundamen tal to many electrostatic applications, Difficulties arise in two-dime nsional simulation due to the O(log\\r\\) potential. Fully understandi ng the 2D potential problem, and reasonably connecting the mathematica l formulation with physical interpretation, are key to handling this d ifficulty properly. In the absence of these factors it is easy for one to propose an ill-posed problem. In this paper, a complete investigat ion of potential theory, from 3D to 2D, is made for computing charge d ensity on the surfaces of conductors, Various integral formulations ar e derived - these are applicable in different situations. It is shown that, in general, the electrostatic potential need not be finite value d 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 sug gested.