A novel approach to the design of gradient coils for MRI is introduced which takes into account from the start the effects of induced E-fields and hence currents in a patient subjected to time dependent magnetic field gradients. The approach has led to conceptually novel designs of gradient coils which comprise distributions of electrodes or tessellae placed around the basic coil structure. When properly energised the electrode arrays are able, in the simplest case, to reduce the maximum E-field experienced by the patient by approximately a factor of three over that experienced with a standard fingerprint or distributed transverse gradient coil, the comparison being done for the same gradient strength, same coil diameter and same ROI.