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 centers Region III only if its velocity `v gt(qIB)/m`
B. The particle enters Region III only if its velocity `v lt (qIB)/m`
C. Path length of the particle in Region II is maximum when velocity `v=qIB//m`
D. Time spent in Region II is same for any velocity v as long as the particle returns to Region I

Answer

A, C, D

Explanation

`v_|_B` in region II. Therfore path of particle is circle in region II.
Particle enters in region III. If radius of circular patn `r gt l` or `(mv)/(Bq)gt1` or `v gt(Bql)/m`
If `v(Bq1)/m, r(mv)/(Bq)=1`, 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 `:.` Correct.