Electric field generated by a rotating magnetized sphere

Abstract

The electric field outside a steadily rotating, uniformly magnetized sphere is determined for the general case in which the magnetic and rotational axes, though both passing through the center of the sphere, may be oriented at any angle relative to each other. The sphere is perfectly conducting and is surrounded by a conducting plasma of charged particles constrained to move along the magnetic field lines. The electric field generated by the rotating sphere is found to be exactly that required to cause the surrounding plasma to rotate with the sphere. When the magnetic and rotational axes are parallel or antiparallel, co-rotation of sphere and plasma is caused by the E×B drift. For all other orientations Fermi acceleration plays a role in causing co-rotation. The electric field in a reference frame rotating with the sphere is identically zero for the symmetric (dipole) magnetic field under consideration. Therefore, charged particles in the plasma do not change energy in this frame, although they appear alternately to gain and lose small amounts of energy in a nonrotating frame. It is concluded, however, that the electric field generated by the earth's ‘wobbling’ magnetic axis in the real magnetosphere, distorted by the solar wind, probably does cause charged particles to experience net energy changes over a number of revolutions around the earth. It thus provides a mechanism for diffusion of plasma and of higher-energy particles through the magnetosphere. Calculations of such effects must take into account the high conductivity of the plasma in the magnetosphere if they are to give correct results.