  We study charged particle motion in weakly charged higher dimensional black
holes. To describe the electromagnetic field we use a test field approximation
and use the higher dimensional Kerr-NUT-(A)dS metric as a background geometry.
It is shown that for a special configuration of the electromagnetic field the
equations of motion of charged particles are completely integrable. The vector
potential of such a field is proportional to one of the Killing vectors (called
primary Killing vector) from the `Killing tower' of symmetry generating objects
which exists in the background geometry. A free constant in the definition of
the adopted electromagnetic potential is proportional to the electric charge of
the higher dimensional black hole. The full set of independent conserved
quantities in involution is found. It is demonstrated, that Hamilton-Jacobi
equations are separable, as well as the corresponding Klein-Gordon equation and
its symmetry operators.
