The stationary multipole solutions of the Einstein-Maxwell equations representing coupled electromagnetic and gravitational perturbations of the extreme Reissner-Nordstrom black hole are simple rational functions of the radial coordinate. These solutions are used to construct the axially symmetric field of a current loop in the equatorial plane and of a small current loop on the polar axis. The magnetic lines of force are calculated numerically and exhibited graphically. The field representing a general Reissner-Nordstrom black hole in an asymptotically uniform magnetic field is also given, and its relation to the exact solutions of Ernst describing Kerr-Newman black holes in Melvin's magnetic universe is discussed.

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The work on black holes immersed in external stationary magnetic fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and rotating black holes which are approaching extremal states. Recently this effect has been shown to occur for black hole solutions in string theory and Kaluza-Klein theory. PACS 04.70.-s -Physics of black holes. PACS 97.60.Lf -Black holes. PACS 04.40.Nr -Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields.

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