  A toy model for magnetic connection in black hole (BH) accretion disc is
discussed based on a poloidal magnetic field generated by a single electric
current flowing around a Kerr black hole in the equatorial plane. We discuss
the effects of the coexistence of two kinds of magnetic connection (MC) arising
respectively from (1) the closed field lines connecting the BH horizon with the
disc (henceforth MCHD), and (2) the closed field lines connecting the plunging
region with the disc (henceforth MCPD). The magnetic field configuration is
constrained by conservation of magnetic flux and a criterion of the screw
instability of the magnetic field. Two parameters and are introduced to
describe our model instead of resolving the complicated MHD equations. Compared
with MCHD, energy and angular momentum of the plunging particles are extracted
via MCPD more effectively, provided that the BH spin is not very high. It turns
out that negative energy can be delivered to the BH by the plunging particles
without violating the second law of BH thermodynamics, however it cannot be
realized via MCPD in a stable way.
