The technique of driving a steady Hall current in plasmas using a rotating magnetic field is studied both numerically and analytically in the approximation of negligible ion flow. The authors consider a spherical plasma bounded by an insulating wall and immersed in a uniform magnetic field which has both a rotating component (for current drive) and a constant 'vertical' component (for MHD equilibrium). They formulate the problem in terms of an expansion of field quantities in vector spherical harmonics. The numerical code SPHERE solves the resulting pseudo-harmonic equations by a multiple shooting technique. The results presented, in addition to being relevant to non-inductive current drive generally, have a direct relevance to the rotamak experiments.