A particle of mass $m$ and charge $q$ , moving with velocity $V$ enters Region II normal to the boundary as shown in 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).

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The particle enters Region III only if its velocity $V > \frac{q l B}{m}$

The particle enters Region III only if its velocity $V < \frac{q l B}{m}$

Path length of the particle in Region II is maximum when velocity $V = \frac{q l B}{m}$

Time spent in Region II is same for any velocity $V$ as long as the particle returns to Region I

answer is A, C, D.

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Detailed Solution

$\vec{v} ⊥ \vec{B}$ 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 $\frac{m v}{B q} > l o r v > \frac{B q l}{m}$
If $v = \frac{B q l}{m}, r = \frac{m v}{B q} = l,$ particle will turn back and path length
Question Image
Will be maximum. If particle returns to region I, time spent in region II will be
$t = \frac{T}{2} = \frac{π m}{B q},$ which is independent of $v$