  We consider the bound states of the massive scalar field around a rotating
black hole immersed in the asymptotically uniform magnetic field. In the regime
of slow black hole rotation, the Klein-Gordon equation allows separation of
variables. We show that the growth rate of the instability can be amplified a
few times by the magnetic field. The effect occurs because the magnetic field
adds the "effective mass" term $B |m|$ to the scalar field potential for a Kerr
black hole. In addition, and as a by-product, we discuss the behavior of the
quasinormal modes for the magnetized rotating black holes.
