First slide

Force on a charged particle moving in a magnetic field

Question

A proton, a deuteron and an $α$ -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field lf r_p,r_d and r $α$ denote respectively the radii o[ the trajectories of these particles, then

Moderate

A

$r_{α} = r_{p} < r_{d}$
B

$r_{α} > r_{d} > r_{p}$
C

$r_{α} = r_{d} > r_{p}$
D

$r_{p} = r_{d} = r_{α}$

Solution

Given that $K_{p} = K_{d} = K_{α} = K (say)$
We know that $q_{p} = e, q_{d} = e and q_{α} = 2 e$
and $m_{p} = m, m_{d} = 2 m and m_{α} = 4 m$
Further $r = \frac{mV}{qB} = \frac{\sqrt{2 mK}}{qB}$
Hence $r_{p} = \frac{\sqrt{2 mK}}{eB}$
$r_{d} = \frac{\sqrt{2 (2 m) K}}{eB} = \sqrt{2} r_{p}$
and $r_{α} = \frac{\sqrt{2 (4 m) K}}{(2 e) B} = r_{p}$
Hence $r_{α} = r_{p} < r_{d}$

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