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

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.