Electrostatic potential and electric field in the $z$ axis of a non centered circular charged ring

TL;DR

This paper calculates the electrostatic potential and electric field along the z-axis of a non-centered charged ring using elliptic integrals, illustrating the application of special functions in electromagnetism.

Contribution

It provides a novel calculation for off-center rings, extending common centered ring analyses with a pedagogical approach using elliptic integrals.

Findings

Explicit formulas for potential and field off the axis of a non-centered ring.

Demonstrates the use of elliptic integrals in electromagnetism problems.

Enhances teaching methods with a new example involving special functions.

Abstract

In introductory level electromagnetism courses the calculation of electrostatic potential and electric field in an arbitrary point is a very common exercise. One of the most viewed cases is the calculation of electrostatic potential and electric field in the symmetry axis of a centered ring and it has been widely studied the potential off the axis of a charged ring centered in the origin coordinate. In this work, we calculated the electrostatic potential and electric field in the $z$ axis of a non centered charged ring using elliptic integrals as an pedagogical example of the application of special functions in electromagnetism.