Question

A proton and an $\alpha$ - particle enter a uniform magnetic field perpendicularly with same speed. If proton takes $25\mu s$ to make $5$ revolutions, then the time period of the $\alpha$ - particle would be equal to

• A. $25\mu s$
• B. $50\mu s$
• C. $10\mu s$
• D. $5\mu s$

Answer 1

The correct option is C

$10\mu s$

Time period of proton $T_p=\frac{25}{5}=5\mu s$

For a charge moving in Magnetic Field
Timeperiod is given by
$T=\frac{2\pi m}{qB}\Rightarrow \frac{T_{\alpha }}{T_p}=\frac{m_{\alpha }}{m_p}\times \frac{q_p}{q_{\alpha }}=\frac{4m_p}{m_p}\times \frac{q_p}{2q_p}\Rightarrow T_{\alpha }=2T_p=10\mu s$