The equilibrium of a field reversed configuration (FRC) with a rotating magnetic field (RMF) applied externally for maintaining steady state is studied theoretically. The momentum balance equations of ions and electrons as well as the mass balance equations have been solved analytically and a solution of a steady equilibrium of the FRC with the RMF, in which the ions and electrons rotate at different velocities, has been found. It has been revealed that the particle source and the radial flow neglected in previous studies plays an important role in the equilibrium