The forces acting on a spherical conducting particle in a transversely flowing magnetized plasma are calculated in the entire range of magnetization and Debye length, using the particle code SCEPTIC3D (Patacchini and Hutchinson 2010 Plasma Phys. Control. Fusion52 035005, 2011 Plasma Phys. Control. Fusion53 025005). In short Debye length (i.e. high density) plasmas, both the ion-drag and Lorentz force arising from currents circulating inside the dust show strong components antiparallel to the convective electric field, suggesting that a free dust particle should gyrate faster than what predicted by its Larmor frequency. In intermediate to large Debye length conditions, by a downstream depletion effect already reported in unmagnetized strongly collisional regimes, the ion-drag in the direction of transverse flow can become negative. The internal Lorentz force, however, remains in the flow direction, and large enough in magnitude so that no spontaneous dust motion should occur.