  . We consider the effect of an external bias voltage and the spatial
variation of the surface potential, on the damping of cantilever vibrations.
The electrostatic friction is due to energy losses in the sample created by the
electromagnetic field from the oscillating charges induced on the surface of
the tip by the bias voltage and spatial variation of the surface potential. A
similar effect arises when the tip is oscillating in the electrostatic field
created by charged defects in a dielectric substrate. The electrostatic
friction is compared with the van der Waals friction originating from the
fluctuating electromagnetic field due to quantum and thermal fluctuation of the
current density inside the bodies. We show that the electrostatic and van der
Waals friction can be greatly enhanced if on the surfaces of the sample and the
tip there are two-dimension (2D) systems, e.g. a 2D-electron system or
incommensurate layers of adsorbed ions exhibiting acoustic vibrations. We show
that the damping of the cantilever vibrations due to the electrostatic friction
may be of similar magnitude as the damping observed in recent experiments of
Stipe \textit{et al} [B.C.Stipe, H.J.Mamin, T.D.Stowe, T.W.Kenny, and D.Rugar,
Phys.Rev. Lett.% \textbf{87}, 0982001]. We also show that at short separation
the van der Waals friction may be large enough to be measured experimentally.
