An α -particle (mass 4 amu ) and a singly charged sulfur ion (mass 32 amu ) are initially at rest.

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4.Moving Charges and Magnetism

easy

An $\alpha$-particle (mass $4 amu$ ) and a singly charged sulfur ion (mass $32 amu$ ) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_\alpha$ and $r_5$, respectively. The ratio $\left(r_s / r_\alpha\right)$ is. . . . .$(4)$

A

$2$

B

$4$

C

$7$

D

$8$

(IIT-2021)

Solution

$r =\frac{ mV }{ qB }=\frac{\sqrt{2 mqV }}{ qB }$

$\frac{ P ^2}{2 m }= K E= qV$

$\frac{ r _{ s }}{ r _\alpha}=\sqrt{\frac{32}{1} \times \frac{2}{4}}=4$

$\frac{ r _{ s }}{ r _\alpha}=4$

Standard 12

Physics

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