A proton and an alpha particle enter a uniform magnetic field with the same velocity normal to the direction of the field. If proton makes a circular trajectory of radius \( R \), the radius of the circular trajectory of alpha particles will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2R \)
A charged particle moving at right angles to a uniform magnetic field moves in a circle, with the magnetic force providing the centripetal force.
\( \displaystyle qvB = \frac{mv^{2}}{r} \quad\Rightarrow\quad r = \frac{mv}{qB} \)
With the same v and B, \( r \propto m/q \). An alpha particle has four times the mass and twice the charge of a proton.
\( \displaystyle \frac{r_{\alpha}}{r_p} = \frac{m_{\alpha}/q_{\alpha}}{m_p/q_p} = \frac{4m/2e}{m/e} = 2 \)
\( r_{\alpha} = 2R \)