First slide

Motion of a charged particle

Question

A proton, a deuteron and an α particle whose kinetic energies are same enter at right angles to a uniform magnetic field. Then the ratio of the radii of their circular paths is

Moderate

A

$1 : \sqrt{2} : 1$
B

$\sqrt{2} : 1 : 1$
C

$1 : 2 : 1$
D

$2 : 2 : 1$

Solution

$R a d i u s o f c i r c u l a r p a t h = r = \frac{\sqrt{2 m K}}{B q} \Rightarrow r \propto \frac{\sqrt{m}}{q} \Rightarrow r_{p} : r_{D} : r_{α} = \frac{\sqrt{m_{p}}}{q_{p}} : \frac{\sqrt{m_{D}}}{q_{D}} : \frac{\sqrt{m_{α}}}{q_{α}} = \frac{\sqrt{1}}{1} : \frac{\sqrt{2}}{1} : \frac{\sqrt{4}}{2} = 1 : \sqrt{2} : 1$

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