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  4. A proton and an alpha particle of the same enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the circular paths described by the alpha particle and proton is:

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Q. A proton and an alpha particle of the same enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the circular paths described by the alpha particle and proton is:

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Solution:

When a charged particle enters a field, it takes a circular path. The radius of circular path is given by the relation
$ r =\frac{ mv }{ Bq } $
For proton, $r _1=\frac{ mv }{ Bq }$
For $\alpha$-particle, $r _2=\frac{4 m \times v }{ B \times 2 q }=\frac{2 mv }{ Bq }$
$ \Rightarrow r_1: r_2:: 1: 2 $