Question

A proton and an alpha particle enter the same magnetic field which is perpendicular to their velocity. If they have same kinetic energy then ratio of radii of their circular path is

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is A $1:1$

A proton and an alpha particle enter the same magnetic field which is perpendicular to their velocity and have the same kinetic energy.

Given,

$m_{\alpha }=4m_p$

$q_{\alpha }=2q_p$

The radius of the circular path is given by

$r=\frac{\sqrt{2mE}}{qB}$. . . . . . . .(1)

$r\propto \frac{\sqrt{m}}{q}$

$\frac{r_p}{r_{\alpha }}=\sqrt{\frac{m_p}{m_{\alpha }}}.\frac{q_{\alpha }}{q_p}$

$\frac{r_p}{r_{\alpha }}=\sqrt{\frac{m_p}{4m_p}}.\frac{2q_p}{q_p}$

$\frac{r_p}{r_{\alpha }}=2\sqrt{\frac{1}{4}}$

$\frac{r_p}{r_{\alpha }}=1$

$r_p:r_{\alpha }=1:1$

The correct option is A.