The ideal magnetohydrodynamic equations are used to investigate the equilibrium configurations of a plasma when it is subjected to an external rotating magnetic field. It is shown that the rigid rotor model for the steady toroidal current is an exact solution of the equations provided that there are no oscillating secondary currents within the plasma and that there is no toroidal component of the steady magnetic field. Experimental observations of rotamak plasmas indicate that these conditions are often not satisfied. The rigid rotor model may therefore not be applicable to these plasmas. A perturbation method is used to generalise the theory to include the effects of small oscillating secondary currents and small toroidal magnetic fields.