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 in Fig.

Angle subtended by the arc at the centre =`2 theta`
(a) Time spent by the charge in magnetic field
`omegat= 2 theta implies (qB)/mt=2 theta implies t=(m2 theta)/(qB)`
(b) Distance travelled by the charge in magnetic field
`=r(2 theta)=(mv)/(qB)xx2 theta`
(c) Impulse=change in momentum of the charge
`(-mvsin theta hati+mvcos theta hatj)-(-mvsin theta hati+mvcos theta hatj)`
`=-2mvsin theta hati`