Interaction between two point-like charges in nonlinear electrostatics

We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r : with the linear accuracy with respect to the ratio R / r, and in the opposite approximation, where R≫ r, up to the term quadratic in the ratio r / R. The consideration proposes the law a+ bR^{1 / 3} for the energy, when the charges are close to one another, R→ 0. This leads to the singularity of the force between them to be R^{- 2 / 3}, which is weaker than the Coulomb law, R^{- 2}.