We calculate the averge charge on a particle in a particle-plasma cloud, the plasma potential inside the cloud and the Coulomb force acting on the particle. The net repulsive electrostatic force on a particle depends on the plasma density, temperature, density of particles, particle size and the gradient of the particle density. In a uniformly dense ring the electrostatic repulsion is zero. We also show that the electrostatic force acts like a pressure force and that even a collisionless ring can be stable against gravitational collapse and a finite ring thickness does not necessarily imply a finite velocity dispersion. In this paper we derive a simple criterion for the importance of electrostatic forces in planetary rings which involves the calculation of ther vertical ring thickness which would result if only electrostatic repulsion were responsible for the finite ring thickness. Electrostatic forces are entirely negligible in the main rings of Saturn and the E and G rings. They may also be negligible in the F ring. However, the Uranium rings and especially Jupiter's ring seem to be very much influenced by electrostatic repulsion. In fact electrostatic forces could support a Jovian ring which is an order of magnitude more dense than observed. ¿ American Geophysical Union 1988