In paper I, we showed that time-dependent general relativistic magnetohydrodynamic (GRMHD) numerical models of accretion disks, although being highly turbulent, have surprisingly simple electromagnetic properties. In particular, the toroidal current density in the disk takes the form $dI_phi/dr propto r^{-5/4}$. Guided by this simplicity, we use a time-dependent general relativistic force-free electrodynamics (GRFFE) code to study an idealized problem in which the accretion disk is replaced by an infinitely thin rotating equatorial current sheet. We consider both an $r^{-5/4}$ current profile and an $r^{-1}$ profile, the latter corresponding to the paraboloidal model of Blandford & Znajek (1977). The force-free magnetosphere we obtain with the $r^{-5/4}$ current sheet matches remarkably well to the Poynting-dominated jet seen in GRMHD numerical models. By comparing to the non-rotating force-free model studied in paper I, rotation is seen to lead to mild decollimation of the jet suggesting that hoop-stress forces nearly cancel centrifugal forces. In order to study the process that generates the corona and disk wind and destroys the ordered field in the corona in GRMHD numerical models, the force-free field with the $r^{-5/4}$ current distribution is embedded in an accretion disk and followed in a GRMHD simulation. Reconnection and magnetic stresses contribute to a magnetized, thermal wind without the aid of an ordered field threading the disk.
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