The origin of the Earth's magnetic field constitutes one of the most fascinating problems of modern physics. Ever since the works of the physicist W. Gilbert in 1600, we have known that the magnetic field detected with a compass has a terrestrial origin, but a precise understanding of its production (together with the good regime of parameters) remains elusive. The generation of the Earth's magnetic field by electric currents inside our planet was proposed by Amp`ere just after the famous experiment done by Ørsted in 1820 (a wire carrying an electric current is able to move the needle of a compass). These currents cross the Earth's outer core, which is made of liquid metal (mainly iron) at several thousand degrees. If it were not maintained by a source these currents would disappear within several thousand years through Ohmic dissipation. Indeed, in the absence of any regenerative mechanism the Earth's magnetic field would decay in a time τdiff that can be estimated with the simple relation τdiff ~ l2/η. Since the Earth's metallic envelope is characterized by a thickness of ~ 2000 km and a magnetic diffusivity η ~ 1m2 s-1, we obtain τdiff ~ 30 000 years. Also, in order to explain the presence of a large-scale magnetic field on Earth since several million years ago, it is necessary to introduce the dynamo mechanism. It was Sir J. Larmor in 1919 who first suggested that the solar magnetic field could be maintained by what he called a self-excited dynamo, a theory explaining the formation of sunspots. Generally speaking, the dynamo effect explains the solar, stellar, and even galactic magnetic fields.

Geophysics, Astrophysics, and Experiments

Experimental Dynamos

The simplest experiment concerning a self-excited dynamo is Bullard's dynamo as shown in Figure 5.1: it is made of a conducting disk which rotates in a medium

where an axial magnetic field B0 is present. An electric wire going around the axis is connected on one side to the axis and on the other side to the disk (the electric contacts do not prevent the rotation). Because of the Lorentz force an electric potential is induced between the center and the side of the disk. The induced electromotive force e1 generates a current i1 in the loop, which in turn generates an axial induced magnetic field B1, which adds to the initial field.