Question

A proton and an $\alpha$- particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle $\left(\frac{T_{p}}{T_{\alpha}}\right)$ will be

• A. $1: 2$
• B. $1:3$
• C. $2:1$
• D. $3:1$

Answer 1

Answer: (A)

The time period of revolution of a charged particle in a magnetic field is
$T=\frac{2\pi m}{Bq}$
For proton, $m_{p}=m, q_{p}=q$;
$\therefore T_{p}=\frac{2\pi m}{Bq}$
Now, for $\alpha$ -particle, $m_{\alpha} =4m$, $q_{\alpha}=2q$
$\therefore T_{\alpha}=\frac{2\pi\left(4m\right)}{B\left(2q\right)}=2 \left(\frac{2\pi m}{Bq}\right)$
$\Rightarrow \frac{T_{p}}{T_{\alpha}}=\frac{1}{2}$