Spherical robots are mobile systems whose spherical geometry enables locomotion by rolling. Various actuation principles have been explored for such robots; here, we propose an electromagnetic drive that resembles a spherical motor and combines permanent magnets with electromagnets, generating motion through their interaction. The feasibility of this approach is demonstrated through the development of a mathematical model of quasi-stationary electromagnetic interactions between magnets located on different moving shells. From this model, the torque acting on the inner spherical shell is derived as a function of the angular displacement between the permanent magnet and the electromagnet, allowing the identification of an efficient configuration and the computation of energy-optimal current distributions. Using Kirchhoff’s equations together with results from previous studies on optimal control of mechanically driven spherical robots, we further derive current and voltage equations that enable locomotion over uneven surfaces without slipping. The robot’s motion on a bell-shaped surface is also analyzed, and the resulting current and voltage profiles reveal the dynamic and frequency ranges of the control signals. In addition, a trajectory-tracking controller by linearizing the system dynamics around a reference trajectory, is employed. This controller is complemented with a regulator synthesized within the generalized \(H_{2}\) norm, improving robustness to disturbances and reducing tracking errors.