We consider a dielectric dust particle immersed in a plasma with one s
pecies lions) drifting relative to the dust particle. The equilibrium
potential around the dust particle is studied with a self consistent f
irst principle kinetic model. The anisotropy of the trajectories of th
e plasma particles is considered and the nonuniformity of the dust cha
rging is described in detail. The simulations show the presence of a d
ipole field around the dust particle, with a significant attractive re
gion. The results of the simulation work are compared successfully wit
h a simple theoretical estimate.