Abstract Finding the electrostatic potential produced by a point load is an easy task, when that point load is replaced by a load distribution this task is complicated, the difficulty of this procedure depends on the place where you want to know the potential, it is not the same to find the potential at a given point to find it in any place in space. In this case we will work with a uniformly charged two-dimensional ring, the problem that arises is the obtaining of the electrostatic potential at any point around the ring, for this we will look for the conditions that must be met to pose the problem, a theoretical solution for this problem, in which we find the Legendre polynomials and finally proceeds to make this same solution using the two dimensional finite element method.