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Question

A proton and an α - particle (Helium nucleus) enters a uniform magnetic field with their direction of velocity perpendicular to the direction of magnetic field.

(iii) If proton and α - particle enter the magnetic field, perpendicular to it with same momentum, then the ratio of the radii of curvature of proton and α - particle will be

​​​​​​​[1 Mark]

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

The correct option is B 2:1
When v and B are perpendicular, the path will be circle.
The radius of the circle is given by r=MvqB r=pqB

For proton, let MP=m,qP=q
Radius of proton is
rP=pqB

For α - particle, Mα=4m,qα=2q
Radius of alpha particle is
rα=p2qB

Ratio of radii is
rPrα=21

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