Question

A proton and an $\alpha$ particle enter a uniform magnetic field with same velocity, then ratio of the radii of path describe by them will be?

• A. 1 : 2
• B. 1 : 1
• C. 2 : 1
• D. None of these

Answer 1

The correct option is A 1 : 2

By using $r=\frac{mv}{qB}$; $v\to$ same, $B\to$ same $\Rightarrow r\propto \frac{m}{q}\Rightarrow \frac{r_p}{r_{\alpha }}=\frac{m_p}{m_{\alpha }}\times \frac{q_{\alpha }}{q_p}=\frac{m_p}{4m_p}\times \frac{2q_p}{q_p}=\frac{1}{2}$