AbstractI‐Vcharacteristics showing high densities and low temperatures are difficult to understand in standard Langmuir probe theory because such a plasma would be highly resistive and would drop more voltage than observed unless the current path were very short. A short current path implies large cross‐field currents, producing largejxBforces. It is shown within the framework of linearized magnetohydrodynamics that this force may be balanced by interaction with the neutrals or by convective accelerations. It is neither appropriate nor necessary to include anomalous diffusivity. The strength of these mechanisms is estimated to be larger than that of classical viscosity and is able to explain theI‐Vcharacteristics observed. With some additional assumptions, it is possible to tentatively relate the results of the linear theory to the level of the electron saturation current and explain a number of trends which have been observed. Analytical expressions for the slope of theI‐Vcharacteristics at floating potential of strip probes have been found and numerical calculations carried out for rectangular