We evaluate the stopping and image forces on a charged particle moving
parallel to a doped sheet of graphene by using the dielectric response
formalism for graphene's π-electron bands in the random phase approximation
(RPA). The forces are presented as functions of the particle speed and the
particle distance for a broad range of charge-carrier densities in graphene. A
detailed comparison with the results from a kinetic equation model reveal the
importance of inter-band single-particle excitations in the RPA model for high
particle speeds. We also consider the effects of a finite gap between graphene
and a supporting substrate, as well as the effects of a finite damping rate
that is included through the use of Mermin's procedure. The damping rate is
estimated from a tentative comparison of the Mermin loss function with a HREELS
experiment. In the limit of low particle speeds, several analytical results are
obtained for the friction coefficient that show an intricate relationship
between the charge-carrier density, the damping rate, and the particle
distance, which may be relevant to surface processes and electrochemistry
involving graphene.Comment: 14 pages, 10 figures, accepted for publication in Phys. Rev.