The pair interaction of aerosols having arbitrary electrical charge is evaluated by an exact solution to the Coulomb force equation. A rapidly convergent solution is obtained by casting the expression for the surface charge density in the form of the Fredholm integral equation. Because the electrostatic force is always attractive at close separations, for dissimilar aerosols coagulation rates are always enhanced with increasing charge and size polydispersity. Results for the electrostatic force acting on spherical aerosols and the resulting pair stability values are presented over the full range of aerosol size and charge.