A new approach is proposed to calculate the self-consistent parallel electric field associated with the response of a plasma to quasi-static electromagnetic perturbations (&ohgr;&ohgr; (&ohgr;d being the bounce averaged magnetic drift frequency equal to kyvd, where ky is the wave number in the y direction and vd the bounce averaged magnetic drift velocity). The first regime (&ohgr;d&ohgr;) is adapted to large energies and/or large ky. In particular, in the limit &ohgr;d<&ohgr; and |vd|<|uy|, where uy is the diamagnetic velocity proportional to the pressure gradient, we find a parallel electric field proportional to the pressure gradient and directed toward the ionosphere in the dusk sector and toward the equator in the dawn sector. This parallel electric field corresponds to a potential drop of a few hundred volts that can accelerate electrons and produce a differential drift between electrons and ions. ¿ 2000 American Geophysical Union