JEE Advance - Physics (2008 - Paper 1 Offline - No. 9)
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).
Explanation
As the particle enters the magnetic field, a force acts on it due to the magnetic field which moves the particle in a circular path of radius.
$$r={{mv} \over {qB}}$$
For the particle entering in region III, r > $$l$$
$$ \Rightarrow {{mv} \over {qB}} > l$$
$$ \Rightarrow v > qlB/m$$
For maximum path length in region II, r = $$l$$
$$\therefore$$ $$l = {{mv} \over {qB}}$$
$$ \Rightarrow v = {{qlB} \over m}$$
[$$\because$$ $${v_{\max }} = {{qBl} \over m},T = {{2\pi r} \over v} = {{2\pi m} \over {q.B}}$$]
The time taken by the particle to move in region II before coming back in region I is given by $$t=\pi m$$, which is independent of v.
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