Charge distributions in bipolar particle charging

We consider the process by which a stationary charge distribution develops when spherical particles are immersed in a bipolar charge environment. For particles sufficiently larger than the characteristic electrostatic length e²/4πε{lunate}_oκT this distribution is shown to be a normal Gaussian, regardless of the kinetic details of the charging process or the degree of charge asymmetry. The parameters of the distribution can be easily computed if the kinetic constants of the charging process are known. Under certain conditions the charge distribution is the well-known Boltzmann law. A criterion is presented to determine when the Boltzmann law is the solution to the charging equations.