The Equivalence of the Charge Interaction Sum and the Ionic Strength

Abstract

The electrostatic interaction among a neutral and finite set of point charges is based on the sum of their pairwise charge products, 𝑧 𝑖 𝑧 𝑗 , yet many analyses yield terms which simply contain a sum of the squares of the separate charges, corresponding to the ionic strength, 1/2 Σ𝑚 𝑖 𝑧 2 𝑖 . This submission collects together a number of important instances of this result and explains their equivalence. In effect, the ionic strength-like terms provide conveniently calculated coulomb sums for systems with finite collections of charges.