where the vector r is the relative position between the charges. This interaction complicates the theoretical treatment of the fluid. For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as 1/"r" 2, the average number of particles at each distance "r" is proportional to "r" , assuming the fluid is fairly isotropic. As a result, a charge fluctuation at any one point has non-negligible effects at large distances.