In this paper we study the trajectories of charged particles in an electromagnetic field superimposed on the Kerr background. The electromagnetic fields considered are of two types: (i) a dipole magnetic field with an associated quadrupole electric field, (ii) a uniform magnetic field. The contribution of the background geometry to the electromagnetic field is taken through the solutions of Petterson and Wald respectively. The effective potential is studied in detail for ther-motion of the particles in the equatorial plane and the orbits are obtained. The most interesting aspect of the study is the illustration of the effect of inertial frame dragging due to the rotation of the central star. This appears through the existence of nongyrating bound orbits at and inside the ergo surface. The presence of the magnetic field seems to increase the range of stable orbits, as was found in a previous study involving the Schwarzschild background.