During magnetic resonance imaging, there is an interaction between the time-varying magnetic fields and the active implantable medical devices (AIMD). In this study, in order to express the nature of this interaction, simplified analytical expressions for the electric fields induced by time-varying magnetic fields are derived inside a homogeneous cylindrical volume. With these analytical expressions, the gradient induced potential on the electrodes of the AIMD can be approximately calculated if the position of the lead inside the body is known. By utilizing the fact that gradient coils produce linear magnetic field in a volume of interest, the simplified closed form electric field expressions are defined. Using these simplified expressions, the induced potential on an implant electrode has been computed approximately for various lead positions on a cylindrical phantom and verified by comparing with the measured potentials for these sample conditions. In addition, the validity of the method was tested with isolated frog leg stimulation experiments. As a result, these simplified expressions may help in assessing the gradient-induced stimulation risk to the patients with implants.