The interdependent problems of determining the current density field and the electron temperature and number density profiles in nonequilibriumJ×Bdevices are formulated realistically, and solved numerically. The two‐dimensional formulation includes the important effects of thermal and concentration diffusion, thermal and velocity boundary layers, and finite reaction rates on the electrical behavior of crossed‐field devices, and allows each effect to be studied separately. As a result, this study predicts and interprets the asymmetry of the current distribution that has often been reported in experimental studies. Computations in potassium‐seeded nitrogen plasmas have shown that streamwise nonuniformities can be very pronounced both in the core and in the electrode boundary regions of high‐current density devices. In the limiting case of instantaneous reaction rates (ionization equilibrium at the electron temperature) and instantaneous energy relaxation, current lines in the core display a striking increase in slope throughout the narrow region between the insulator segments, where they become almost perpendicular to the flow direction and much denser than in the remaining part of the core. Under these conditions, there is no evidence of current ``shorting'' through the boundary layer, although theTedistribution is such that high‐luminosity regions appear over the electrodes, particularly over the cathode. The general and flexible methods developed in this study allow realistic evaluation of suggested designs under various operating conditions.