By means of a crossed electric field, charged particles can be forced to move from a region where the magnetic field is comparatively weak into a region where the magnetic field is much stronger, which leads to an increase in the density and the temperature of the plasma. However, if the density is not very low, the inertia drift gives rise to space charges, which modify the electric field and thus strongly influence the motion. The motion of the particles is studied in a two-dimensional case with the influence of the space charges taken into account. The results are that the particle trajectories are considerably changed, but the reduction in the drift velocity is of the same order of magnitude as if the space charges are neglected. If the inhomogeneity in the magnetic field is strong enough, a forbidden region will arise. The shape of this region is given and the currents resulting from the particle motion are computed.