An electricity and magnetism problem by Hammad Shah

The Lorentz force acts on a charged particle and as force is the time derivative of the momentum, it changes. $\frac{dW_{kin}}{dt}=m/2 \frac{d\vec{v}^2}{dt}=\vec{v}\frac{d\vec{p}}{dt}=\vec{v}\vec{F_L}=0$ The last step uses that the force is perpendicular to the particles velocity. This shows that the (kinetic) energy doesn't change.