Question

An $\alpha$ particle and a proton travel with same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular paths.

• A. 4:1
• B. 1:4
• C. 2:1
• D. 1:2

Answer 1

Answer: (C)

2:1

As $r=\frac{mv}{Bq}$
Hence, $\frac{r_{\alpha }}{r_p}=\frac{m_{\alpha }}{m_p}\times \frac{q_p}{q_a}$

We know, $m_{\alpha }=4m_p$ and $q_{\alpha }=2q_p$
$\frac{r_{\alpha }}{r_p}=\left(\frac{4}{1}\right)\times \left(\frac{1}{2}\right)=\frac{2}{1}=2:1$