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Global magnetohydrodynamic (MHD) simulations of the Earth's magnetosphere must be coupled with a dynamical ionospheric module in order to give realistic results. The usual approach is to compute the field-aligned current (FAC) from the magnetospheric MHD variables at the ionospheric boundary. The ionospheric potential is solved from an elliptic equation using the FAC as a source term. The plasma velocity at the boundary is the <b>E</b> × <b>B</b> velocity associated with the ionospheric potential. Contemporary global MHD simulations which include a serious ionospheric model use this method, which we call the electrostatic approach in this paper. We study the possibility of reversing the flow of information through the ionosphere: the magnetosphere gives the electric field to the ionosphere. The field is not necessarily electrostatic, thus we will call this scheme electromagnetic. The electric field determines the horizontal ionospheric current. The divergence of the horizontal current gives the FAC, which is used as a boundary condition for MHD equations. We derive the necessary formulas and discuss the validity of the approximations necessarily involved. It is concluded that the electromagnetic ionosphere-magnetosphere coupling scheme is a serious candidate for future global MHD simulators, although a few problem areas still remain. At minimum, it should be investigated further to discover whether there are any differences in the simulation using the electrostatic or the electromagnetic ionospheric coupling.<br><br><b>Key words.</b> Ionosphere · Ionosphere-magnetosphere interaction · Magnetospheric physics · Magnetosphere-ionosphere interaction · Space plasma physics · Numerical simulation studies