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Question

A particle of mass m and charge q, moving with velocity v enters region II normal to the boundary as shown in the following figure. Region II has a uniform magnetic field B. Choose the correct choice(s).


A

The particle enters region III only if its velocity v > qIBm

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B

The particle enters region III only if its velocity v < qIBm

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C

Path length of the particle in region II is maximum when velocity v = qIBm

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D

Time spent in region II is same for any velocity v as long as the particle returns to the region I.

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Solution

The correct options are
A

The particle enters region III only if its velocity v > qIBm


C

Path length of the particle in region II is maximum when velocity v = qIBm


D

Time spent in region II is same for any velocity v as long as the particle returns to the region I.


i.e., mvqB > I or v > qlBm

So, (a) is correct and (b) is wrong. It is clear from the diagram that path length of particle in region II is maximum when R=mvqB=1

So, v=qlBm for maximum path length in region II.

If the particle has to return to region I, then time spend by particle in region II is T2

i.e., t = πmqB which is independent of v, therefore (d) is correct.


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