In the theory of electrostatic probes, it is usually assumed that the probe surface potential is uniform. However, nonuniformity of the surface work function produces a nonuniformity in surface potential which may modify the current collection. This effect is examined for an infinite cylinder immersed in a collisionless plasma in the limit when Debye length is much greater than probe radius, by numerically following charged-particle orbits in a Laplace potential. It is shown that only large-scale, macroscopic potential nonuniformities are important for the current collection, and that microscopic nonuniformities are smoothed over relatively short distance by the Laplace equation character of the potential. ¿ American Geophysical Union 1989