Here we show the evolution of the magnetic field in a nearly incompressible fluid surrounded by a vacuum exterior. The total energy is composed of the energy stored in the azimuthal magnetic field and the rotational energy of the fluid elements, as well as the energy associated with the constant radial magnetic field. There is no dissipation and no energy flux at the surface; therefore both the evolution of the azimuthal magnetic field and the rotation is periodic.  Throughout the evolution, the total energy is a constant.