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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. (iv) If proton and α - particle enter the magnetic field, perpendicular to it with same kinetic energy, then the ratio of the radii of curvature of proton and α - particle will be ​​​​​​​[1 Mark]

A
2:1
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B
1:2
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C
1:1
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D
1:22
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Solution

## The correct option is C 1:1When 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 Radius of proton is rP=√2m(KE)qB For α - particle, Mα=4m,qα=2q Radis of alpha particle is rα=√2(4m)(KE)2qB ⇒rα=2√2m(KE)2qB ⇒rα=√2m(KE)qB Ratio of radii ∴rPrα=11

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