First slide

Force on a charged particle moving in a magnetic field

Question

A proton and an α-particle are projected in a uniform field in a direction perpendicular to the field. If the particles move in circular paths of same radius, then the ratio of linear momentum of proton to that of α-particle is

Moderate

A

$\sqrt{2}$
B

1/ $\sqrt{2}$
C

1/2
D

1/4

Solution

If V be the velocity of projection, then
$r = \frac{V}{ω} = \frac{V}{QB / m} = \frac{mV}{QB} \Rightarrow p = mV = QBr ∴ \frac{p_{P}}{p_{α}} = \frac{Q_{p} . (Br)}{Q_{α} . (Br)} = \frac{Q_{p}}{Qα} = \frac{C}{2 C} = \frac{1}{2} .$

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