Moving Charges and Magnetism - Result Question 1
1. Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_H: r _{\alpha}$ will be : [2019]
(a) $2: 1$
(b) $1: 2$
(c) $4: 1$
(d) $1: 4$
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Solution:
- (a) Radius of the path $=r=\frac{m v}{q B}=\frac{P}{q B}$
For $H^{+}$ion, $r_H=\frac{p_H}{e B}$
For $\alpha$ particle
$r _{\alpha}=\frac{p _{\alpha}}{2 e B}$
$\frac{r_H}{r _{\alpha}}=\frac{\frac{p}{e B}}{\frac{p}{2 e B}}$
[as given $p_H=p _{\alpha}=p$ ]
$\Rightarrow \frac{r_H}{r _{\alpha}}=\frac{2}{1}$
