High-temperature superconductors (HTS) and MgB2 may potentially improve the usability of superconducting magnets dramatically owing to their large energy margin. When HTS and MgB2 wires are used for magnets operated in the persistent current mode, such as in magnetic resonance imaging (MRI) scanners, the electric field generated in the wires must be lower than 10−10 V m−1. In this paper, critical current density, J c, defined at an electric field criterion of 10−10 V m−1 is evaluated from a magnetisation decay measurement for state-of-the-art monofilamentary MgB2 wires. By using the obtained J c, a critical line of our multifilamentary MgB2 wire is shown on the temperature-magnetic field plane. Here, the critical line is defined as a line on which an electric field of 10−10 V m−1 is generated at a coil current density of 150 A mm−2. The area inside the critical line is demonstrated to be large enough to fulfil the requirement of 1.5 T MRI scanners operated at 10K–15K. In addition, the iso energy-margin lines are shown on the temperature-magnetic field plane and compared with those of NbTi wires. The MgB2 wire has an order of magnitude greater energy margin than the NbTi wires in most of the area inside the critical line. This suggests that the MgB2 wire is highly unlikely to be quenched due to mechanical disturbances.