Although solar wind and solar flare electrons can have direct access to low altitudes on open field lines, low-energy electron fluxes over the polar caps may at times be accelerated and trapped by a large-scale potential barrier in the magnetotail. If the effective potential difference at the barrier fluctuates randomly about an average value, a fraction of the beam flux accelerated toward the earth from beyond the barrier can be trapped between the barrier and the earth. Additional low-energy electrons diffusing onto field lines closed to particle losses by the potential barrier would also be quasi-trapped. The effects of such a fluctuating magnetotail barrier potential are described with a simple model. When the observed tail lobe spectrum is taken to be the electron source distribution beyond the barrier, the model adequately simulates the electron intensity, energy spectrum, and pitch angle distribution observed at low altitudes over the polar cap.