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. Path length of the particle in region `ii` is maximum when velocity `V=(qlB)/(m)`
C. Time spent in Region `II` is same for any veloicty `V` as long as the particle returens to Region `I`.
D. All the above are correct.

Answer

4

Explanation

`bar(v)_|_bar(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 `II` will be
`t=(T)/(2)=(pim)/(Bq)`, which is independent of `v`.