When a positive column is submitted to a transverse magnetic field the Lorentz force compresses the electron gas towards one side of the vessel containing the plasma. This phenomenon is analysed in planar geometry at low gas pressure. The ion mean free path is assumed to be at least several times the discharge width. The behavior of the ionic gas is treated using a fluid type version of free fall theory. Plasma density and potential profiles are obtained for various magnetic field strengths. The potential difference between the two insulating discharge walls, or the Hall voltage, is derived and found to be a nonlinear function of the magnetic field. The solution of the free‐fall problem permits to formulate the five equations of balance of a magnetized plasma slab. These are used to determine the electron temperature and the longitudinal electric field of the positive column.