Question

A proton and an alpha particle enter into a uniform magnetic field with the same velocity. The period of rotation of the alpha particle will be

Answer 1

Given,

Uniform magnetic field.

For proton: time period,

$T_1=\frac{2\pi m_p}{B{q}_p}=\frac{2\pi m}{Bq}$

For alpha particle: time period

$T_2=\frac{2\pi m_{\alpha }}{B{q}_{\alpha }}=\frac{2\pi \left(4m\right)}{B\left(2q\right)}=2\times \frac{2\pi m}{Bq}=2T_1$

Hence, period of alpha particle is twice the time period of proton.