Electrostatics of two charged spheres at small separation

Abstract

There are many examples of electrostatic phenomena in our daily lives, from those as simple as the sparks that accompany the taking off of our sweaters, to the formation of clouds and rain droplets. Moreover, electrostatics are widely used in modern industry, such as laser printing and automotive spray painting. Our research project focuses on analyzing the electrostatic interaction between two charged conducting spheres in the limit when they are about to touch each other. By using analytical techniques, we obtain dimensionless expressions of capacitances for those two spheres. Furthermore, we derive the electrostatic force between two spheres. When the two spheres are of the same size, our results show that the electrostatic force can be expressed as a linear combination of two parts, one is always attractive and the other one is always repulsive. The attractive part always dominates the repulsive part at sufficiently small distances, thus the electrostatic force is always attractive at small distances, even for positively charged spheres!