In many rotamak experiments performed in spherical containment vessels a self-generated toroidal field of substantial magnitude, and opposite polarity in the upper and lower hemispheres, has been observed. In addition, several experiments have observed the formation of a doublet poloidal flux configuration in which the toroidal plasma current flows predominantly above and below the equatorial plane. The authors analyse these phenomena theoretically by considering a spherical uniform density 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 use both a multiple-order perturbation technique and a general numerical technique to solve the vector spherical harmonically expanded MHD equations under the approximation of negligible ion velocity.