Radial equation for an accretion flow driven by Poynting flux

Using a toy model of a two dimensional accretion disk, we discuss further the radial equation of the accretion flow dominated by the Poynting flux. Assuming the force-free condition is valid around the accretion disk, the relation between the fluid angular velocity of the disk, $\Omega_D$, and the angular velocity of the magnetic field lines, $\Omega_F$, is also discussed.