Electric energies of a charged sphere surrounded by electrolyte

By using the recently generalized version of Newton’s Shell Theorem [6] analytical equations are derived to calculate the electric potential energy needed to build up a charged sphere, and the field and polarization energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the electrolyte’s ion concentration and the radius of the charged sphere. The work needed to build up the charged sphere, E_cc (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the electrolyte ions’ increasing screening effect on the charge-charge interaction. The work needed to build up the charged sphere appears as a sum of the field and polarization energy of the electrolyte. At zero ion concentration the electrolyte’s field energy is equal with E_cc while the polarization energy is zero. At high electrolyte ion concentrations (C>10mol/m³) 50% of E_cc appears as the polarization energy of the electrolyte, 25% as the electrolyte’s field energy inside the sphere and 25% as the electrolyte’s field energy around the sphere.