First slide

Force on a charged particle moving in a magnetic field

Question

A proton and a deuteron, both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deuteron on circular path of radius R_p and R_d, respectively, the correct option is

Moderate

A

$R_{d} = \sqrt{2} R_{p}$
B

$R_{d} = R_{p} / \sqrt{2}$
C

$R_{d} = R_{p}$
D

$R_{d} = 2 R_{p}$

Solution

We know, $\frac{{mv}^{2}}{R} = qvB . For proton,$
$R_{p} = \frac{mv}{qB} = \frac{\sqrt{2 m_{p} K}}{qB}$
$\begin{array}{l} and for deuteron R_{d} = \frac{\sqrt{2 m_{d} K}}{qB} \\ \Rightarrow \frac{R_{d}}{R_{p}} = \sqrt{\frac{m_{d}}{m_{p}}} = \sqrt{2} \Rightarrow R_{d} = \sqrt{2} R_{p} \end{array}$

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