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).

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

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 D, A, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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 $v$