  The electrostatic potential of a moving dust grain in a complex plasma with
magnetized ions is computed using linear response theory, thereby extending our
previous work for unmagnetized plasmas [P. Ludwig et al., New J. Phys. 14,
053016 (2012)]. In addition to the magnetic field, our approach accounts for a
finite ion temperature as well as ion-neutral collisions. Our recently
introduced code \texttt{Kielstream} is used for an efficient calculation of the
dust potential. Increasing the magnetization of the ions, we find that the
shape of the potential crucially depends on the Mach number $M$. In the regime
of subsonic ion flow ($M<1$), a strong magnetization gives rise to a potential
distribution that is qualitatively different from the unmagnetized limit, while
for $M>1$ the magnetic field effectively suppresses the plasma wakefield.
