We consider a finite-sized dust cloud embedded in an infinite plasma. The dust cloud will generally be at a different potential from that of the ambient plasma, and particles which enter the cloud are accelerated or decelerated. We treat the two limiting cases: in case A, particles are not thermalized within the cloud, and in case B, the plasma is thermalized in the cloud interior to form a Maxwellian plasma with densities given by Boltzmann relations as functions of the local cloud potential. Qualitatively, both cases lead to similar results: In a tenuous cloud the dust cloud potential is low while the dust potentials are close to those of single isolated dust particles. In dense dust clouds the cloud potential approaches a maximum while the dust potentials decreases to zero with increasing dust density. However, the exact values of the potentials can differ considerably for the two cases for the same set of other cloud and ambient plasma parameters. Also, for case A we may have several sets of solutions for the two potentials, all giving charge balance in the cloud and current balance to the dust. We find, however, that case A may not easily be formed for all ranges of dust densities because the charging of dust can take a longer time than the time for scattering processes to lead to internal Boltzmann distributions for both plasma particle types. On the other hand, we expect semistable cases intermediate between case A and case B with multiple solutions to be found. Instabilities through the creation of double layers and transitions between two solutions may occur and lead to events in dust clouds. We suggest that such events may possibly occur in cometary comas and in planetary rings and lead to changes in the dust cloud structure. Conditions relevant for multiple solutions will probably be rather short-lived, at most a few times 10 days, before scattering collisions with diffusion in velocity space turn the plasma velocity distribution into that of case B. In this case there is only one solution for the potentials for each set of cloud and plasma parameters. ¿American Geophysical Union 1987