A charged particle is moving on a circular path of radius R in a uniform magnetic field under the Lorentz force F. How much work is done by the force in one round? Is the momentum of the particle changing?

Explanation

When a charged particle moving on a circular path of radius R in a uniform magnetic field, the Lorentz magnetic force `F(=qvB)` acting on the particle, provides the required centripetal force for its circular motion. It means the Lerentz force acts along the radius towards the centre of circular path. While moving on a circular path, the small displacement `dvecr` of the charged particle is always perpendicular to Lerentz force, i.e., `theta=90^@`, therefore work done
`dW=vecF.dvecr=Fdr cos 90^@=0`.
Since the velocity of the charged particle, moving on a circular path is acting tangentially to the path whose direction is changing continuously in circular motion of the particle, therefore, the momentum of the particle is changing.