Electrostatic energy for a circular charged configuration: discrete vs. dontinuum

The concept of electrostatic potential energy has served as a starting point for a deeper understanding of several models in electromagnetic theory. We use this concept looking for a connection between some of those models, in particular, we analyze the contribution of electrostatic potential energy for different configurations of electric charge with circular symmetry. We study models corresponding to a discrete set of point charges arranged in a polygonal figure, a uni-dimensional continuously charged ring and a continuously charged torus, considering the existing analogies between them. In addition, we contrast the situation between the discrete and continuum models.