A positive charge particle of charge q, mass m enters into a uniform magnetic field with velocity v as shown in the figure . There is no magnetic field to the left of PQ . Find (i) time spent,

(ii) distance travelled in the magnetic field
(iii) inpulse of magnetic force.

Explanation

The particle will move in the field as shown Angle subtended by the are at the centre `=2theta`
(i) Time spent by the charge in magnetic field
`omegat=2thetarArr(qB)/(m)t=2thetarArrt=(m2theta)/(qB)`

(ii) Distance travelled by the charge in magnetic field
`=r(2theta)=(mv)/(qB).2theta`
(iii) Impulse = change in momentum of the charge `=(-mvsinthetahati+mvcosthetahatj)-(mvsinthetahati+mvcosthetahatj)=-2mvsinthetahati`