It can be shown that the currents in the earth's core which give rise to the externally observable magnetic field do not form a complete set of solutions of the field equations. There exists a second set of solutions composed of the modes of the electric type which produce a magnetic field inside the metallic sphere, but appear at the outside only through an electric field too weak to be measured. For reasons of symmetry the most important terms among the electric modes are the quadrupoles. The theory of inductive coupling by fluid motion, developed previously, is here applied to the interaction of the magnetic and electric modes. The system again is non-conservative, and work is done on the field by the fluid, or vice versa. It is shown that the interaction between the magnetic dipole and electric quadrupole modes constitutes a basic amplifier mechanism which amplifies the quadrupole mode until the magneto-mechanical forces exerted by the field upon the fluid begin to slow down the motion, thus prohibiting further increase of the field. This internal quadrupole field is likely to be much larger than the ordinary magnetic dipole field. Further analysis leads one to interpret the couplings between the magnetic and electric modes as a feed-back amplifier whereby the field can be maintained through the power delivered to it by the fluid motion. A survey of possible sources of power for this process indicates that the power for the maintenance of the field is provided from the rotational energy lost by the earth as it is slowed down through the action of the lunar tide.

• Received 27 March 1947

DOI:https://doi.org/10.1103/PhysRev.72.821