Question

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 $I$. Choose the correct choice (s).

• A. The particle enters Region III only if its velocity v > $\frac{qlB}{m}$
• B. The particle enters Region III only if its velocity v < $\frac{qlB}{m}$
• 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 1

The Correct Option is D

v $\perp$ B in region II. Therefore, path of particle is circle in region II.
Particle enters in region III if, radius of circular path, r > l
$or \frac{mv}{Bq} > l\, or\, v >\frac{Bql}{m}$
If $v=\frac{Bql}{m},r=\frac{mv}{Bq}=l, $ particle will turn back and path length will be maximum. If particle returns to region I, time spent in region II will be

$t=\frac{T}{2}=\frac{\pi m}{Bq}, $ which is independent of v.
$\therefore $ Correct options are (a), (c) and (d).