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

The radius of circle of path of charged particle of `R=(mV)/(qB)`
For particle to enter region `III R gt l`. Or `(mV)/(qB) gt l`
For path length of particle in region `II` to be maximum
`l=R` or `V=(qlB)/m`
The period of revolution of charged particle is `omega=(qB)/m`
The time spent in region `II` is `t=pi/omega=(pim)/(qB)`,which same for all the cases when it returns to region `II`.