Abstract
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.
Highlights
Classical Electrodynamics (CED), formulated at the end of the nineteenth century, is one of the greatest triumphs of science
This article is devoted to the introduction and implementation of two powerful techniques described subtly in the references [6, 7]. These methods are little explored in undergraduate courses and allow for the resolution of a wide range of electrostatic problems with azimuthal symmetry
In a region without charges, every electrostatic problem with azimuthal symmetry consists in the search of the set of parameters {Al e Bl, l = 0, 1, . . . }
Summary
Classical Electrodynamics (CED), formulated at the end of the nineteenth century, is one of the greatest triumphs of science It unified the already known electric and magnetic phenomena and predicted the existence of electromagnetic waves and, being the first relativistic theory developed, CED served as a foundation for our current understanding of space and time. Electrostatics consists in determining the electric field formed by a previously known macroscopic charge distribution, characterized by the charge density, ρ(x), which does not evolve in time. This article is devoted to the introduction and implementation of two powerful techniques described subtly in the references [6, 7] These methods are little explored in undergraduate courses and allow for the resolution (sometimes only in a partial way) of a wide range of electrostatic problems with azimuthal symmetry.
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