CBSE Class 12 · 2011 · All India · Magnetic Effects of CurrentShort Answer

The magnetic part of the Lorentz force is $\vec{F}=q(\vec{v}\times \vec{B})$, which is always perpendicular to $\vec{v}$. Work done in time $dt$: $dW=\vec{F}\cdot d\vec{r}=\vec{F}\cdot \vec{v}dt=q(\vec{v}\times \vec{B})\cdot \vec{v}dt$. Since $(\vec{v}\times \vec{B})\cdot \vec{v}=0$ (the cross product is perpendicular to $\vec{v}$), $dW=0$. Hence the magnetic force does no work and the kinetic energy of the particle is unchanged.