Magnetics 1 Question 7
7. An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r _e, r _p, r _{\alpha}$ respectively, in a uniform magnetic field $B$. The relation between $r _e, r _p, r _{\alpha}$ is
(2018 Main)
(a) $r _e<r _{\alpha}<r _p$
(c) $r _e<r _p=r _{\alpha}$
(b) $r _{\alpha}>r _e=r _p$
(d) $r _e<r _p<r _{\alpha}$
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Answer:
Correct Answer: 7. (c)
Solution:
- For circular path in magnetic field,
$$ r=\frac{\sqrt{2 m K}}{q B} $$
where, $K$ =kinetic energy.
$$ \Rightarrow \quad r \propto \frac{\sqrt{m}}{q} $$
Further,
| $e$ | $p$ | $\alpha$ | |
|---|---|---|---|
| $m$ | $1 / 1836$ | 1 | 14 |
| $q$ | $-e$ | $+e$ | $2 e$ |
$\therefore \quad r _p=r _{\alpha}>r _e$
