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 `v gt qlB//m`
B. The particle enters region III only if its velocity `v lt 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 region I

Answer

A, C, D

Explanation

In region II, the magnetic field is uniform and velocity of the particle in region II is normal to the magnetic field, so the particle will describe a circular path of radius r given by, `r=(mv)/(Bq)`
For particle to enter region III, figure.

`rgtl` or `(mv)/(Bq)gtl` or `vgt(Bql)/(m)`
For path length of particle in region II to be maximum, `l=r` or `m=(Bql)/(m)`
The time of revolution of charged particle in region II is `t=(pir)/(v)=(pil)/(v)=(pim)/(Bq)` which is independent of v. Therefore, all those particles moving with any velocity, which return to region I, spend the same time in region II.