The penetration of the electric field and associated magnetic perturbations from high latitudes to low latitudes is studied with the Magnetosphere-Thermosphere-Ionosphere-Electrodynamics General Circulation Model (MTIEGCM) of Peymirat et al. [1998> in response to variations of the polar cap potential drop. For a sudden decrease of the polar cap potential of ~40 kV, the model reproduces the well-known overshielding phenomenon corresponding to a sudden reversal of the low-latitude electric field. For quasi-periodic oscillations of the polar cap potential drop of ~40 min period, the model predicts that the poleward electric field and the eastward Hall current in the auroral zone lag slightly in phase (<1 min), while the eastward electric field and current at the magnetic equator are advanced slightly in phase, with respect to the potential-drop oscillations. These phase differences are interpreted as the consequence of the succession of shielding and overshielding episodes induced by the response of the region-2 field-aligned currents to the polar cap variations. The phase differences among the polar cap potential and the auroral and equatorial electric fields and currents increase with the plasma sheet pressure. The amplitude of the associated magnetic perturbations is very dependent on the distribution of the potential along the polar cap boundary. The model predictions are tested against the observations of Kobea et al. [this issue> for two events, one representing simple overshielding and the other associated with polar cap potential oscillations. The model underestimates the decay time of the magnetic perturbations by a factor of 2 during the overshielding event, and the model gives results compatible with the observations during the second event. The disagreements may be due to limitations of the model and uncertainties of the input parameters. ¿ 2000 American Geophysical Union