Multipole electrostatic system mathematical modeling

This paper presents an electrostatic multipole system's mathematical modeling. The multipole system consists of an even number of equiform electrodes of an infinite length. The shape of each electrode can be arbitrary. The constant potential is equal in absolute value and sign-changing at neighboring electrodes. To calculate the potential distribution, each real electrode is changed by a virtual electrode whose surface coincides with an equipotential surface. The variable separation method is used to solve the boundary-value problem in plane polar coordinates. The electrostatic potential distribution is calculated in an analytic form over the entire region of the system. Refs 11. Figs 5.