Magnetics 1 Question 21
21. 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).
$(2008,4 M)$
(a) The particle enters Region III only if its velocity $v>\frac{q l B}{m}$ (b) The particle enters Region III only if its velocity $v<\frac{q l B}{m}$
(c) Path length of the particle in Region II is maximum when velocity $v=q l B / m$
(d) Time spent in Region II is same for any velocity $v$ as long as the particle returns to Region I.
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Answer:
Correct Answer: 21. (a, c, d)
Solution:
- $\mathbf{v} \perp \mathbf{B}$ 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 $\frac{m v}{B q}>l$ or $v>\frac{B q l}{m}$
If $v=\frac{B q l}{m}, r=\frac{m v}{B q}=l$, particle will turn back
and path length will be maximum. If particle returns to region I, time spent in region II will be
$t=\frac{T}{2}=\frac{\pi m}{B q}$, which is independent of $v$.
