In association with the Blandford-Znajek mechanism for rotational energy ex
traction from Kerr black holes, it is of some interest to explore how much
magnetic flux can actually penetrate the horizon at least in idealized situ
ations. For the completely uncharged Kerr hole case, it has been known for
some time that the magnetic flux gets entirely expelled when the hole is ma
ximally rotating. In the mean time, it is also known that when the rotating
hole is immersed in an originally uniform magnetic field surrounded by an
ionized interstellar medium (plasma), which is a more realistic situation,
the hole accretes a certain amount of electric charge. In the present work,
it is demonstrated that, as a result of this accretion charge small enough
not to disturb the geometry, the magnetic flux through this slightly charg
ed Kerr hole depends not only on the hole's angular momentum but on the hol
e's charge as well, such that it never vanishes for any value of the hole's
angular momentum.