Physics · Moving Charges and Magnetic Field

JEE Advanced 2021 — Paper 1 — Question 9

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 $r_{s}$ , respectively.

The ratio $\left(r_{s} / r_{\alpha}\right)$ is $\qquad$ .

Answer: 4

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{r}_{a}=\frac{\sqrt{2 \mathrm{~m}_{u} \mathrm{q}_{u} \mathrm{~V}}}{\mathrm{q}_{a} \mathrm{~B}}$

$\mathrm{r}_{\mathrm{s}}=\frac{\sqrt{2 \mathrm{~m}_{\mathrm{s}} \mathrm{q}_{\mathrm{s}} V}}{\mathrm{q}_{\mathrm{s}} \mathrm{B}}$ $\frac{\mathrm{r}_{\mathrm{s}}}{\mathrm{r}_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\mathrm{S}}}{\mathrm{q}_{\mathrm{S}}} \frac{\mathrm{q}_{\alpha}}{\mathrm{m}_{\alpha}}}=\sqrt{\left(\frac{32}{1}\right)\left(\frac{2}{4}\right)}$

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

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2021
Paper: Paper 1
Subject: Physics
Chapter: Moving Charges and Magnetic Field
Topic: Motion of Charged Particles in magnetic Fields