When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, ca/GMH>0.36 for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk (MH is the mass and aMH is the angular momentum of the black hole). This way, the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from ca/GMH=0.998 to ca/GMH=0.36 by a thin Keplerian disk is ~0.15MHc2. This is larger than ~0.09MHc2, which can be extracted by the Blandford-Znajek mechanism.