The problem with the penetration of electric fields from atmospheric near-Earth electric current sources to the ionosphere is investigated both within the dynamic simulations of the Maxwell equations in the frequency domain and within the simplified quasi-electrostatic approach. Two cases of the geomagnetic field lines are considered. The first case is the penetration of the geomagnetic field lines deeply into the magnetosphere (open field lines), whereas the second one is the return of these lines into the Earth’s surface (closed field lines). The proper boundary conditions are formulated. It is demonstrated that in the case of the open field lines the results of the dynamic simulations differ essentially from the quasi-electrostatic approach, which is not valid there. In the case of the closed field lines, the results of simulations are practically the same both within the dynamic approach and within the quasi-electrostatic one. From realistic values of the densities of atmospheric electric currents ~0.1 µA/m2, the values of the electric fields within the ionosphere F-layer may reach about 1–10 mV/m.