A positive charge particle of charge q and mass m enters into a uniform magnetic field with velocity v as shown in Fig. There is no magnetic field to the left of PQ. Find (a) time spent, (b) distance travelled in the magnetic field, (c) impulse of magnetic force.

Explanation

The particle will move in the field as shown
Angle subtended by the arc at the centre `=20`
(i)Time spent by the charge in magnetic field
`omegat=theta rArr (qB)/m t=theta rarr t=(mtheta)/(qB)`
(ii)Distance travelled by the charge in magnetic field:
`=r(20)=(mv)/(qB).2theta`
(iii) Impulse =change in momentum of the charge
`(-mv sin theta hatj+mv cos theta hatj)-(mv sin thetahati+mv cos thetahatj)`
`=-2mvsin theta hatj`