  We develop a stochastic model for the charge fluctuations on a microscopic
dust particle resting on a surface exposed to plasma. We find in steady state
that the fluctuations are normally distributed with a standard deviation that
is proportional to $CT_{e})^{1/2}$, where $C$ is the particle-surface
capacitance and $T_{e}$ is the plasma electron temperature. The time for an
initially uncharged ensemble of particles to reach the steady state
distribution is directly proportional to $CT_{e}$.
