How does a magnetic field do work on the electrons in a wire? If F = q v x B, the magnetic field is always perpendicular to the velocity of the free charge. After a small time interval, dx = v dt, so that v and x are in the same direction. For the magnetic field to do work on the charge, dW = F dot dx. But F and dx are perpendicular, aren't they?, so no work seems to be done.