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

Radius of the circular path is given by `r = (mv)/(qB)`
To enter region III radius of circle must be greater than I which is width of region II.
Hence to enter region `III : r = (mv)/(qB) gt l rArr v gt (qBl)/m`
Thus, option (a) is correct.
When `v = (qBl)/m` then particle will just return to region I after completing semi-circle in region II.
This is the maximum possible radius and hence the path length will be maximum.
So, option (c) is also correct.
Time taken to complete a circle is independent of velocity hence particles which return to region I will return in same time. Thus, option (d) is correct too.