Electrostatic effects in nanosystems are understood via a physical picture built on their multiscale character and the distinct behavior of mobile ions versus charge groups fixed to the nanostructure. The Poisson-Boltzmann equation is nondimensionalized to introduce a factor lambda that measures the density of mobile ion charge versus that due to fixed charges; the diffusive smearing and volume exclusion effects of the former tend to diminish its value relative to that from the fixed charges. We introduce the ratio sigma of the average nearest-neighbor atom distance to the characteristic size of the features of the nanostructure of interest (e.g., a viral capsomer). We show that a unified treatment (i.e., lambda proportional to sigma) and a perturbation expansion around sigma=0 yields, through analytic continuation, an approximation to the electrostatic potential of high accuracy and computational efficiency. The approach was analyzed via Padé approximants and demonstrated on viral system electrostatics; it can be generalized to accommodate extended Poisson-Boltzmann models, and has wider applicability to nonequilibrium electrodiffusion and many-particle quantum systems.