Magnetics 1 Question 15
15. A proton, a deutron and an $\alpha$-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r _p, r _d$ and $r _{\alpha}$ denote, respectively the radii of the trajectories of these particles, then
(1997, 1M)
(a) $r _{\alpha}=r _p<r _d$
(b) $r _{\alpha}>r _d>r _p$
(c) $r _{\alpha}=r _d>r _p$
(d) $r _p=r _d=r _{\alpha}$
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Answer:
Correct Answer: 15. (a)
Solution:
- Radius of the circular path is given by
$$ r=\frac{m v}{B q}=\frac{\sqrt{2 K m}}{B q} $$
Here, $K$ is the kinetic energy to the particle.
Therefore, $r \propto \frac{\sqrt{m}}{q}$ if $K$ and $B$ are same.
$\therefore \quad r _p: r _d: r _{\alpha}=\frac{\sqrt{1}}{1}: \frac{\sqrt{2}}{1}: \frac{\sqrt{4}}{2}=1: \sqrt{2}: 1$
Hence,
$$ r _{\alpha}=r _p<r _d $$
