First slide

Force on a charged particle moving in a magnetic field

Question

A proton and an $α -particle$ enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25 μs to make 5 revolutions, then the periodic time for the $α -particle$ would be

Moderate

A

50 μs
B

25 μs
C

10 μs
D

5 μs

Solution

$\begin{matrix} Time period of proton, T_{p} = \frac{25}{5} = 5 μ s \\ ∵ T = \frac{2 πm}{qB} \Rightarrow \frac{T_{α}}{T_{p}} = \frac{m_{α}}{m_{p}} \times \frac{q_{p}}{q_{α}} = \frac{4 m_{p}}{m_{p}} \times \frac{q_{p}}{2 q_{p}} \end{matrix}$
$\Rightarrow T_{α} = 2 T_{P} = 10 μs$

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