The charge distribution on conducting aerosol particles of arbitrary s
hape in bipolar ion environment is determined, assuming that the mean
free path of ions is small compared to the particle size. It is shown
that the charge balance equations yield the modified Boltzmann distrib
ution as the stationary solution, rather than the standard Boltzmann l
aw. Application of the latter is proved to contradict the irreversibil
ity of the process, as well as the charge balance equations. In the ob
tained analytical solution the particle capacitance acts as a shape fa
ctor, which determines the effective particle radius.