2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186442A special test electromagnetic field in the spacetime of the higher-dimensional generally rotating NUT-(A)dS black hole is found. It is adjusted to the hidden symmetries of the background represented by the principal Killing-Yano tensor. Such electromagnetic field generalizes the field of charged black hole in four dimensions. In higher dimensions, however, the gravitational back reaction of such a field cannot be consistently solved.8 pages, no figures; presented at the Black hole VI conference in White Point, Canada, May 12-16 2007, and at the GRG18 conference in Sydney, Australia, July 8-13 2007High Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext