Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion

To move on circular path in a magnetic field, a centripetal force is provided by the magnetic force. When magnetic field is perpendicular to motion of charged particle, thenCentripetal force = magnetic forceThat is mv2R =Bqv  or R=mvBqFurther, time period of the motionT=2πRv =2πmvBqv  or  T=2πmBqIt is independent of both R and v.