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Question

A proton and an electron, with same momenta, enter a magnetic field in a direction at right angles to the lines of force. If the radii of their circular paths arc rp and re respectively then the value of rp:re will be

A
1:1
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B
1:2
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C
2:1
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D
4:1
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Solution

The correct option is B 1:1
For a charged particle of mass m, charge q entering into a magnetic field of induction B in a direction at right angles to the lines of force, we can write
mv2r=qBv
r=mvqB
For proton, rp=mpvpqpB
For electron, re=meveqeB
Also, mpvp=meve = constant.
Hence,
rpre=qeqp=11 ......(since, qp=qe)

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