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Question

# A particle of mass M and charge q moving with velocity v enters Regionâˆ’2 normal to the boundry as shown in the figure. Regionâˆ’2 has uniform magnetic field B perpendicular to the plane of the paper. The length of the Regionâˆ’2 is l. Choose the correct choice.(A) The particle enters Regionâˆ’3 only, if its velocity v>qlB/m.(B) The particle enters Regionâˆ’3 only, if its velocity v<qlB/m(C) Path length of the particle in Regionâˆ’2 is maximum when velocity v=qlB/m.(D) Time spend in Regionâˆ’2 is same for any velocity v as long as the particle return to Regionâˆ’1.

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 trueWhen 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=mvqBNow, for the particle to enter region III, r>l (path shown by dotted line) ⇒mvqB>l⇒v>qlBmTo 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

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