We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.