Problem of electrostatic of the interaction of two charged spheres at close distances

The electrostatic interaction between two conducting balls was studied by numerical method. The strength of the interaction was found from the potential distribution of the electrostatic field, which is determined by solving the finite-difference equations for the Laplace's equation in cylindrical coordinates. Used method to obtain complete information about the potential distribution described in detail. Analytical functions were built for describing the amendment to the Coulomb's law in the case of the same charges.