The paper is based on an analysis by Boda and Sirá[nbreve] (1986) and Boďa (1988) of the instabilities of a horizontal layer of electrically conducting fluid which is rapidly rotating about a vertical axis, parallel to an applied vertical temperature gradient, and permeated by an azimuthal magnetic field that linearly increases with the distance from the axis. In the present configuration, a stably stratified sublayer is also included. This configuration is analysed using mean-field magnetohydrodynamics. The motions and magnetic fields due to the instabilities are considered as fluctuations. The mean electromotive force resulting from these fluctuations is computed, and its dependence on the magnetic field and the width of the unstably stratified sublayer is determined. The results are discussed in the context of the processes in the Earth's liquid core that are responsible for the main geomagnetic field.