Electric Field Due to Charge Distributions - Approach
A proton and ...
Question
A proton and an α-particle enter a uniform magnetic field at right angles to the field with the same speed. The ratio of the periods of α-particle and proton is-
A
2:1
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B
1:1
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C
1:4
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D
1:2
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Solution
The correct option is A2:1 Proton →1H1 and α-particle →2He4
⇒qp=e;qHe=2e;mp=m;mHe=4m
∵→v⊥→B Hence, they will undergo a uniform circular motion.
Fm=Fcentripetal
qvB=mv2r[∵v=rω]
Bqrω=mrω2⇒Bq=mω
Bq=m(2πT)
∴T=2πmBq⇒T∝mq
TαTp=mαmp×qpqα=41×12=21
∴Tα:Tp=2:1
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Hence, (A) is the correct answer.