In this paper, we study the relationship between the spatial variations of the perpendicular electric field observed in the topside ionosphere and those of the magnetic field induced by the associated field-aligned currents. The mapping of the magnetospheric electric field down to the ionosphere depends upon the spatial scale of its variations and, consequently, also the amplitude of the perpendicular currents and their divergence. This mapping is modeled using realistic conductivity profiles, and the dependence of the electric and magnetic fields upon the spatial scale is analyzed. We compare the effective integrated Pedersen conductivity &Sgr;P,eff defined in our model to ΔB/&mgr;0 ΔE, where ΔE and ΔB are the correlated variations of the mutually orthogonal electric and magnetic fields in the topside ionosphere. We have studied the variation of &Sgr;P,eff as a function of the scale of ΔE and ΔB fluctuations. ΔP,eff is constant and equal to the classical integrated Pedersen conductivity for scales larger than ≈5 km. At smaller scales, it shows a steep decrease down to the lowest scales considered of 0.1 km. The good agreement between observations made on board the AUREOL 3 satellite and this model calculation suggests that the ULF electromagnetic turbulence observed frequently in the cusp and auroral zone may be essentially due to the crossing of spatially structured field-aligned currents. The limits of the present model and its possible improvements are discussed. ¿American Geophysical Union 1990