Two methods for solving electrostatic problems with azimuthal symmetry

Abstract

The study of electrostatic phenomena is the gateway to the physics described by Classical Electrodynamics. In this paper, we discuss in detail two methods based on the Uniqueness Theorem for solving electrostatic problems with azimuthal symmetry. The first one is the electrostatic potential extension from the axis of symmetry to an arbitrary point. The other consists in the mutual mapping between two potentials through an inversion transformation. We have prepared a list of six examples for which we calculate, completely or partially, the electrostatic potentials for different charge distributions using both methods. The electric field lines are analyzed and presented graphically in all cases.