 Solution

The Lorentz force law isIts rate of work is $dT/dt=\mathbf{F}\cdot \mathbf{v}=q\mathbf{E}\cdot \mathbf{v}$, because $\mathbf{v}\cdot (\mathbf{v}\times \mathbf{B})=0$. Thus, with $\mathbf{E}=0$, the kinetic energy cannot increase: a static magnetic field changes the direction of motion but does no work.