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IIT JEE Advanced 2008 Paper 1
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© examsnet.com
Question : 8
Total: 69
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).
The particle enters Region III only if its velocity is V >
q
l
B
m
.
The particle enters Region III only if its velocity V <
q
l
B
m
.
Path length of the particle in Region II is maximum when velocity V =
q
l
B
m
.
Time spent in Region II is same for any velocity V as long as the particle returns to Region I.
Validate
Solution:
The particle enters the Region III only when the cyclotron radius r is greater than l, that is, r > l.
v >
q
B
l
m
⇒
m
v
q
B
> l
The path length is maximum when the radius of curvature r = l.
If r < l, particle traces a semi-circle inside
→
B
. The time taken t =
T
2
=
π
m
q
B
is independent of velocity, v. So the time spent in Region II is independent of velocity.
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