The variation of the self-consistent electrostatic potential along the magnetic field is calculated by application of the principle of quasi-neutrality to the plasma components distributed along an auroral field line. The equilibrium plasma consists of hot anisotropic magnetospheric plasma, ionospheric plasma evaporated or extracted upward by the parallel electrostatic field, and backscattered electrons. It is shown that the above charged particle populations can support a potential difference of up to several kilovolts between the equator and the ionosphere along an auroral field line. Moreover, the corresponding parallel electric field has the proper signature to account for electron precipitation characteristics. Comparisons between theoretical and observed electron precipitation fluxes lead to estimates for the various physical parameters in the model.