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

Magnetics PYQ — JEE Main 2022 · 26 Jun · Shift 1 · Q54 with Solution

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Correct answer: C

When a charged particle enters a uniform magnetic field perpendicular to its velocity, it moves in a circular path of radius

$r = \frac{mv}{qB}$

where:

The proton and alpha particle have the same velocity and move in the same magnetic field, so from

$r \propto \frac{m}{q}$

So,

$r_p \propto \frac{m_p}{e}$

An alpha particle has:

So,

$r_\alpha \propto \frac{4m_p}{2e} = \frac{2m_p}{e}$

$\frac{r_\alpha}{r_p} = \frac{\frac{2m_p}{e}}{\frac{m_p}{e}} = 2$

Hence,

$r_\alpha : r_p = 2:1$

The correct option is C: $2:1$ .