  By using the recently generalized version of Newton Shell Theorem [3]
analytical equations are derived to calculate the electric interaction energy
between two charged spheres, a small one is located within a larger one, and
each sphere is surrounded outside and inside by electrolyte. This electric
interaction energy is calculated as a function of the electrolyte ion
concentration, temperature, distance between the centers and size of the
spheres. At the same distance between the centers of 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 result of
the Shell Theorem. Finally, the analytical equation is generalized to calculate
the total electric interaction energy between a large charged sphere and N
small charged spheres (located within the large sphere) where the spheres are
surrounded by electrolyte.
