Dusty plasmas are present in comets, in the ring systems of the outer
planets, and in the interstellar medium. A two-dimensional particle-in
-cell (PIC) model of a dusty plasma is presented in this paper. The PI
C code is best suited for modeling the plasma-dust interaction for lar
ge grains, with diameters of the order of a centimeter. We have modele
d the charging process for an individual dust grain and the associated
potential pattern in the surrounding plasma. We have also considered
the case of a large number of grains in a plasma, with intergrain sepa
rations of the order of the Debye length; and have shown that the plas
ma becomes depleted and the charge on a dust grain is reduced, as othe
r workers in this field have predicted (cf. C.K. Goertz, 1989). We exa
mine the electron and ion distribution functions in the vicinity of a
charged grain and demonstrate that the ions near a grain have clearly
been accelerated by the electrostatic potential.