JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Magnetic Effects of Current

The magnetic force on a charge is $\vec{F}=Q\vec{v}\times \vec{B}$, which is perpendicular to $\vec{v}$, while the element of path $d\vec{\ell }$ is along $\vec{v}$. The work done over that element is therefore

and this holds at every point of the path, so the total work is zero as well. A magnetic field can change the direction of a charge's motion but never its speed, and the work done by it on the moving charge is zero.