The nonlinear generation of a steady magnetic field in a conducting sphere placed in an oscillatory magnetic field

Abstract

It is shown that the nonlinear ‘‘Hall’’ force generated in a conducting sphere placed in an oscillatory (ac) magnetic field has a nonzero curl. It, therefore, drives a poloidal current which has a steady (dc) component and a second harmonic component. A general analytic expression for the dc toroidal magnetic field generated by the Hall current is obtained for the weakly nonlinear case: ωce/ν ≪1, where ωce =eB/m is the electron cyclotron frequency in the ac magnetic field and ν is the effective collision frequency. The dc magnetic field is evaluated numerically (using the general analytic formulae) for the special case where the applied ac magnetic field is uniform.