  Large-scale magnetic field is believed to play a key role in launching and
collimating jets/outflows. It was found that advection of external field by a
geometrically thin disk is rather inefficient, while the external weak field
may be dragged inwards by fast radially moving tenuous or/and hot gas above the
thin disk. We investigate the field advection in a thin (cold) accretion disk
covered with hot corona, in which turbulence is responsible for the angular
momentum transfer of the gas in the disk and corona. The radial velocity of the
gas in the corona is significantly higher than that in the thin disk. Our
calculations show that the external magnetic flux is efficiently transported
inwards by the corona, and the field line is strongly inclined towards the disk
surface, which help launching outflows. The field configurations are consistent
with those observed in the numerical simulations. The strength of the field is
substantially enhanced in the inner region of the disk (usually several orders
of magnitude higher than the external field strength), which is able to drive a
fraction of gas in the corona into outflows. This mechanism may be useful in
explaining the observational features in X-ray binaries and active galactic
nuclei. Our results may help understanding the physics of the
magneto-hydrodynamic (MHD) simulations.
