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By using the recently generalized version of Newton Shell Theorem [3]analytical equations are derived to calculate the electric interaction energybetween two charged spheres, a small one is located within a larger one, andeach sphere is surrounded outside and inside by electrolyte. This electricinteraction energy is calculated as a function of the electrolyte ionconcentration, temperature, distance between the centers and size of thespheres. At the same distance between the centers of the spheres the absolutevalue of the interaction energy decreases with increasing electrolyte ionconcentration and increases with increasing temperature. At zero electrolyteion concentration the derived analytical equation transforms into the result ofthe Shell Theorem. Finally, the analytical equation is generalized to calculatethe total electric interaction energy between a large charged sphere and Nsmall charged spheres (located within the large sphere) where the spheres aresurrounded by electrolyte.

Interaction energy between two charged spheres surrounded by electrolyte. The smaller sphere located inside the larger sphere