A particle of mass `m`and charge `q`, moving with velocity `v` enters Region `II` normal to the boundary as shown in the figure. Region `II` has a uniform magnetic field `B` perpendicular to the plane of the paper . The length of the region `II` is `l`. Choose the correct choice(s).

Options

A. The particle enters Region III only if its velocity `Vgt(qlB)/m`
B. The particle enters Region III only if its velocity `Vlt(qlB)/m`
C. Path length of the particle in Region II is maximum when velocity `V=(qlB)/m`
D. Time spent in Region II is same for any velocity V as long as the particle returns to Regions I

Answer

(a,c,d)

Explanation

`vec(v) bot vec(B)` in region II. Therefore, path of particle is circle in region II. Particle enters in region III, if radius of circular path, rgtl
or `(mv)/(Bq)gtl or vgt(Bql)/m`
If `v=(Bql)/m, r=(mv)/(Bq) =l`, particle will turn back and path length will be maximum. If particle returns to region I, time spent in region II will be
`t=T/2 =(pim)/(Bq)`, which is independent of v