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Question

A particle of mass M and charge q moving with velocity v enters Region2 normal to the boundry as shown in the figure. Region2 has uniform magnetic field B perpendicular to the plane of the paper. The length of the Region2 is l. Choose the correct choice.
(A) The particle enters Region3 only, if its velocity v>qlB/m.
(B) The particle enters Region3 only, if its velocity v<qlB/m
(C) Path length of the particle in Region2 is maximum when velocity v=qlB/m.
(D) Time spend in Region2 is same for any velocity v as long as the particle return to Region1.
714038_fcb4ced8e8bb49b2bdc8d45d3db82328.png

A
A only true
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B
A,C true
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C
A,C,D true
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D
All are true
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Solution

The correct option is C A,C,D true
When the particles enter in magnetic field, a force tends to move the particle in circular path.

The radius of the circular path is given by:
R=mvqB

Now, for the particle to enter region III, r>l (path shown by dotted line)
mvqB>lv>qlBm

To cover maximum pat in region II, r=l

1=(mv)(q(B))rArr v=(qlB)(m)

The time taken by the particle at any velocity in the region II will be same if the particle returns back to the region I because the radius of the particle will adjust accordingly.
Hence, the correct option is Option(c) - (A),(C) and (D) true

1523338_714038_ans_1076618a55454b91b62bfdb4f408cd27.png

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