In an electrostatics it is possible to allocate two kinds of problems: the field determination at an unknown location of the charges, but the given electric potential at the boundaries of the considered region, and the calculation of the potential and components of the electric field strength in a region free of charges from the known spatially-limited electric charge distribution. In this paper, preference has been given to the second formulation, which has been added by the principle of superposition of electric fields. Further, we consider the problem of the distribution of the electrostatic potential over a thin-walled torus, uniformly charged along the surface. The condition of constancy of the surface charge density is realized only when using a torus with dielectric walls. To find the distribution of the electrostatic potential around a non-conducting torus uniformly charged along the surface, the Poisson equation was considered, which solution was represented as a surface integral. In toroidal coordinates, an expression for the electrostatic potential is obtained, which is calculated in terms of the complete elliptic integral of the first kind. The torus potential is explored on presence of a local extreme. The functions of cylindrical coordinates (paraxial approximation) are constructed, approximating the potential and field intensity in the outer region of the torus, and it is proved that the potential has a saddle shape in the region close to the centre. The spatial distribution of the electrostatic potential in the outer region of a uniformly charged along the torus surface has been visualized, using Matlab environment.
