  We examine the electromagnetic properties of Kerr-anti-de Sitter (Kerr-AdS)
black holes in four and higher spacetime dimensions. Assuming that the black
holes may carry a test electric charge we show that the Killing one-form which
represents the difference between the timelike generators in the spacetime and
in the reference background can be used as a potential one-form for the
associated electromagnetic field. In four dimensions the potential one-form and
the Kerr-AdS metric with properly re-scaled mass parameter solve the
Einstein-Maxwell equations, thereby resulting in the familiar Kerr-Newman-AdS
solution. We solve the quartic equation governing the location of the event
horizons of the Kerr-Newman-AdS black holes and present closed analytic
expressions for the radii of the horizons. We also compute the gyromagnetic
ratio for these black holes and show that it corresponds to g=2 just as for
ordinary black holes in asymptotically flat spacetime. Next, we compute the
gyromagnetic ratio for the Kerr-AdS black holes with a single angular momentum
and with a test electric charge in all higher dimensions. The gyromagnetic
ratio crucially depends on the dimensionless ratio of the rotation parameter to
the curvature radius of the AdS background. At the critical limit, when the
boundary Einstein universe is rotating at the speed of light, it tends to g=2
irrespective of the spacetime dimension. Finally, we consider the case of a
five dimensional Kerr-AdS black hole with two angular momenta and show that it
possesses two distinct gyromagnetic ratios in accordance with its two
orthogonal 2-planes of rotation. In the special case of two equal angular
momenta, the two gyromagnetic ratios merge into one leading to g=4 at the
maximum angular velocities of rotation.
