  By using the recently generalized version of Newton Shell Theorem analytical
equations are derived to calculate the electric interaction energy between two
separated charged spheres surrounded outside and inside by electrolyte. This
electric interaction energy is calculated as a function of the electrolyte ion
concentration, temperature, distance between the spheres and size of the
spheres. At the same distance between the spheres the absolute value of the
interaction energy decreases with increasing electrolyte ion concentration and
increases with increasing temperature. At zero electrolyte ion concentration
the derived analytical equation transforms into the Coulomb equation. Finally,
the analytical equation is generalized to calculate the electric interaction
energy of N separated charged spheres surrounded by electrolyte.
