Abstract The force on a charged dust grain in a plasma due to polarization of thermal ions and degenerate electrons around the grain is derived in the limits of weakly relativistic and ultra-relativistic degeneracy of electrons. It is found that in both these cases, the magnitude of the polarization force is enhanced compared to that in classical plasmas. The in uence of this force on dust-acoustic (DA) modes is examined and discussed. It is shown that the DA wave frequency in degenerate plasmas is signi cantly reduced compared to the classical DA mode.
