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Select the correct answer out of the options given against each question and write in the box provided on rigth hand side bottom:
An `alpha`-particle and a proton having same momentum enter into a region of uniform magnetic field and move in circular paths. The ratio of the radii of curvature of their circular paths. The ratio of the radii of curvature of their circular paths `(r_(alpha))/(r_(p))` in the field is

A

1

B

`(1)/(4)`

C

`(1)/(2)`

D

4

Text Solution

Verified by Experts

The centripetal force for the rotation is supplied by the magnetic force on a moving particle.
`therefore " " (mv^(2))/(r ) = qvB, " " or, " " r = (mv^(2))/(qvB) = (mv)/(qB)`
Hence for `alpha` - particle and proton, momentum mv and magnetic field B are the same.
`therefore " " (r_(a))/(r_(q)) = (q_(p))/(q_(alpha)) = (+e)/(+2e) = (1)/(2) `
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