A necessary condition for the generation of magnetic fields by fluid motions in a sphere is derived in terms of the magnetic Reynolds number on the basis of the radial component of the velocity field. A second parameter entering the criterion is the ratio between the energy of the poloidal component of the magnetic field and the total magnetic energy. Since bounds on this ratio can be obtained from energetic considerations, the criterion can be used as a restriction on possible dynamo mechanisms. Several recent suggestions for the origin of the geodynamo in a stratified outer core are critically reviewed.