The dc electrical coupling of magnetospheric flow vortices and magnetospheric flow channels to the ionosphere is numerically calculated. The equations governing the coupling are derived from current continuity plus Ohm's laws taken for the regions of field-aligned current between the ionosphere and magnetosphere and for the Pedersen layer of the ionosphere. For vortices the strength of the coupling (as measured by fractional penetration of the magnetospheric electric fields down to the ionosphere and by the amount of power dissipation) varies, as expected, with the size of the vortex footprint in the ionosphere. However, because of the diode-like nature of the field-aligned currents, the coupling also varies with sign of the vorticity: Positive center vortices (vorticity antiparallel to B&vec;) couple much more strongly than do negative center vortices (vorticity parallel to B&vec;). Negative center vortices tend to dissipate most of their energy in parallel currents, whereas positive center vortices dissipate most of their energy in Pedersen currents. The electric fields of positive center vortices spread across B&vec; as they connect to the ionosphere, whereas the electric fields of negative center vortices stay confined to their magnetic footprints. Consequently, positive center vortices in the magnetosphere produce quasi-circular vortices of flow in the ionosphere whereas negative center vortices in the magnetosphere produce narrow east-west-elongated vortices of flow in the ionosphere. Negative center vortices in the magnetosphere could produce east-west-aligned bright arc-like features, and positive center vortices could produce east-west-aligned black-arc features imbedded in large circular patches of aurora. Flow channels in the magnetosphere drive field-aligned currents into the ionosphere: The upward field-aligned current on the negative-charged edge of the channel tends to spread across B&vec;, whereas downward current on the positive charge edge tends to stay confined. In the magnetosphere the current spreading results in a back emf that produces a backward flow outside the flow channel on the negative-charged edge. ¿ 2001 American Geophysical Union