We studied the dynamic evolution of the geomagnetic tail in response to a dawn-to-dusk electric field Ey applied at the high-latitude boundary by means of a two-dimensional nonlinear MHD code. We found that the electric field propagates inward through the lobes toward the plasma sheet. Only a small fraction, however, penetrates into the interior of the plasma sheet, and eventually an almost linear decrease from the boundary to the equatorial plane is assumed. There was no tendency to evolve toward a steady or nearly steady state which would require Ey ≈ const in a larger area. The resulting time-dependent changes are consistent with quasi-static analytic models of Schindler and Birn (1982) and Birn and Schindler (1983) and with observed substorm growth phase effects in the near tail. If the external electric field Ey is constant or varies only slightly along the tail, the convection speed within the plasma sheet remains small. A strongly nonuniform external electric field Ey leads to similar spatial and temporal variation of Ey. It does, however, produce a locally much stronger thinning which favors the onset of a tail instability such as the tearing mode. It can also produce stronger flows primarily parallel to the magnetic field.