Electromagnetic induction in rotating conductors

Abstract

This paper describes an experimental and theoretical investigation of induction in a rotating conductor surrounded by a rigid conductor of finite or infinite extent. The results are applied to a discussion of induction in rotating eddies in the fluid core of the earth as a possible origin of the geomagnetic non-dipole field. Model experiments were made with rigid rotators in a steady magnetic field; the induced magnetic field was measured outside the conductors. The results confirmed the appropriate parts of the theoretical work. In the theoretical work solutions are first obtained for a rotator embedded in a solid conductor of infinite extent; a method is then developed for extending this solution to a finite surrounding conductor. Charts are given for the induced field on the surface of the earth due to a hypothetical rotator in the earth’s core. The analysis is based on integral solutions of the field equations; wherever possible the field vectors themselves are used rather than a vector potential. The induced magnetic fields depend on the relative symmetry of the rotator, the surrounding conductor, and the applied magnetic field. For an applied field parallel to the axis of rotation, the induced field is proportional to the angular velocity; for an applied field perpendicular to the axis, the induced field reaches a limit at high angular velocities. If both the surrounding conductor and the applied magnetic field have rotational symmetry about the axis there is no induced field outside the surrounding conductor. The conclusion of the geophysical discussion is that eddies must have radii of several hundred kilometres if they are to account for the observed magnitude of the non-dipole field. Because of the skin effect such large radii would not be tenable if the core material were effectively rigid. However, fluid motions must occur due to the electromagnetic forces, and the consequent magneto-hydrodynamic disturbances probably have decay lengths much larger than the rigid conductor skin depth; therefore arguments based on the rigid conductor skin depth are not applicable. Thus the eddy model might be satisfactory if the fluid motion does not seriously alter the basic induction mechanism.