Question

A proton and an $\alpha$ -particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is $10 \,cm$, then radius of $\alpha$ -particle is

• A. $10 \, cm$
• B. $10 \, \sqrt{2} cm$
• C. $20 \, cm$
• D. $5 \sqrt{2} \, cm$

Answer 1

Answer: (B)

$10 \, \sqrt{2} cm$

Answer 2

Radius of path $r_{i}=\frac{1}{\beta} \sqrt{\frac{2 m v}{q}}$
$\frac{r_{\alpha}}{r_{p}}=\sqrt{\frac{m_{\alpha}}{m_{p}}} \sqrt{\frac{q_{p}}{q_{\alpha}}}$
$\frac{r_{\alpha}}{10}=\sqrt{\frac{4}{2}}$
$r_{\alpha}=10 \sqrt{2}\, cm$