Test Index

Magnetism

Section: Physics

© examsnet.com

Question : 13 of 48

Marks: +1, -0

An

\alpha

-particle (mass 4 amu) and a singly charged sulfur ion (mass

32\ \text{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}

r_{s}

, respectively. The ratio

\left(\frac{r_{s}}{r_{\alpha}}\right)

[JEE Adv 2021 P1]

Your Answer:

Solution:

Here, force

F = q V B

is balanced by centripetal force

F_{e} = \;\frac{m V^{2}}{r}

\therefore\;\; q V B = \;\frac{m V^{2}}{r}

or

r = \;\frac{m V}{q B} = \;\frac{\sqrt{2 m q V}}{q B}

\;\frac{P^{2}}{2 m} = \text{K.E.} = q V

\;\frac{r_{s}}{r_{\alpha}} = \sqrt{\;\frac{m_{s}}{q_{s}}} \times \sqrt{\;\frac{q_{\alpha}}{m_{\alpha}}} = \sqrt{\;\frac{32}{1} \times \;\frac{2}{4}} = 4 \;\; \therefore \;\frac{r_{s}}{r_{\alpha}} = 4

© examsnet.com

Go to Question:

Prev Question

Next Question