We investigate the flow within a liquid-metal battery induced by an externally imposed magnetic field, . An analytical model for laminar flow is proposed and this is found to be in excellent agreement with numerical simulations, not only for weakly forced steady flow, but also for the time-averaged velocity in more strongly forced flows where the motion is either unsteady (but laminar) or else weakly turbulent. Our primary conclusion is that surprisingly weak magnetic fields are capable of destabilizing the flow and inducing turbulence, with turbulence first appearing at . By comparison, the earth's magnetic field is ∼0.5 G. This extreme sensitivity of liquid-metal pools carrying current to an external magnetic field has long been known in the context of other industrial processes.