Magnetic resonance electrical impedance tomography (MREIT) is a method for reconstructing a three-dimensional image of the conductivity distribution in a target volume using magnetic resonance (MR). In MREIT, currents are applied to the volume through surface electrodes and their effects on the MR induced magnetic fields are analyzed to produce the conductance image. However, current injection through surface electrodes poses technical problems such as the limitation on the safely applicable currents. In this paper, we present a new method called magnetic resonance driven electrical impedance tomography (MRDEIT), where the magnetic resonance in each voxel is used as the applied magnetic field source, and the resultant electromagnetic field is measured through surface electrodes or radio-frequency (RF) detectors placed near the surface. Because the applied magnetic field is at the RF frequency and eddy currents are the integral components in the method, a vector wave equation for the electric field is used as the basis of the analysis instead of a quasi-static approximation. Using computer simulations, it is shown that complex permittivity images can be reconstructed using MRDEIT, but that improvements in signal detection are necessary for detecting moderate complex permittivity changes.