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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.

(ii) If proton and α - particle enter the magnetic field, perpendicular to it with same velocity, 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
4:1
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D
1:4
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Solution

The correct option is A 1:2
When V and B are perpendicular, the path will be circle.

The radius of the circle is given by r=MVqB

For proton, let MP=m,qP=q

For α - particle, Mα=4m,qα=2q

Radius of proton is
rP=mVqB
Radius of alpha particle is
rα=4mV2qB=2mVqB

Ratio of radii
rPrα=12

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