  In association with the Blanford-Znajek mechanism for rotational energy
extraction from Kerr black holes, it is of some interest to explore how much of
magnetic flux can actually penetrate the horizon at least in idealized
situations. For completely uncharged Kerr hole case, it has been known for some
time that the magnetic flux gets entirely expelled when the hole is
maximally-rotating. In the mean time, it is 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 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 charged Kerr hole
depends not only on the hole's angular momentum but on the hole's charge as
well such that it never vanishes for any value of the hole's angular momentum.
