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  4. A proton and an α-particle (with their masses in the ratio of 1: 4 and charges in the ratio of 1: 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp: rα of the circular paths described by them will be :

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Q. A proton and an $\alpha$-particle (with their masses in the ratio of $1 : 4$ and charges in the ratio of $1 : 2$) are accelerated from rest through a potential difference $V$. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii $r_p : r_\alpha$ of the circular paths described by them will be :

JEE MainJEE Main 2019Moving Charges and Magnetism

Solution:

$KE =q\Delta V$
$ r =\frac{\sqrt{2mq\Delta V}}{qB} $
$r \propto \sqrt{\frac{m}{q}} $
$\frac{r_{p}}{r_{\infty}} = \frac{1}{\sqrt{2}} $