On the Origin of the Earth's Magnetic Field

The terrestrial field is traced here to the existence of thermoelectric currents in the metallic interior of the earth. The currents owe their existence to inhomogeneities continually created by turbulent convective motions. In order to obtain a nonvanishing resultant angular momentum of the currents around the earth's axis, the current system must exhibit a particular asymmetry. The latter is shown to originate through the preponderant influence of the Coriolis force upon the convective motions. In Part I the well-known proof, based on potential theory, of the fact that the currents must flow inside and not outside the earth, is briefly reproduced. In Part II an analysis of the formal expression for the current density is given. By means of a development in spherical harmonics the conditions for a nonvanishing current momentum can be formulated. It appears that temperature fluctuations in an otherwise homogeneous medium always yield a zero momentum, therefore the existence of inhomogeneities in the material is also required. In Part III it is pointed out that geophysicists have previously obtained evidence of the existence of a metallic core of the earth in which the viscosity is extremely low as compared to the viscosity of the rocks. Radioactive impurities which are very small compared to the total radioactivity of the earth are sufficient to maintain thermally driven convective motions in the metallic core. An estimate of the various terms in the hydrodynamic equations shows that the Coriolis force is much larger than all other dynamical effects. In Part IV we discuss the effect of the Coriolis force in producing that particular asymmetry which leads to a resultant angular momentum of the currents. It is shown that the inhomogeneities in material required according to the analysis of Part II can be accounted for by phase transformations of the material induced by the pressure changes which are connected with the vertical component of the motions. In Part V an attempt is made to estimate numerically the current density, basing the estimate on some general results of the theory of conductivity. For temperature variations of the order of 10° the calculated value of the current is in satisfactory agreement with the observed magnitude of the earth's magnetic moment. At the end, the bearing of these ideas upon the magnetism of sunspots is briefly discussed.