An α particle and a proton are moving along the same direction with the same kinetic energy. They enter a uniform magnetic field acting perpendicular to their velocities. The ratio of radii of their paths is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1:1 \)
In a field perpendicular to its velocity, a charged particle moves in a circle because the magnetic force supplies the centripetal force.
\( \displaystyle qvB = \frac{mv^{2}}{r} \Rightarrow r = \frac{mv}{qB} \)
Writing the momentum in terms of the kinetic energy K, \( mv = \sqrt{2mK} \):
\( \displaystyle r = \frac{\sqrt{2mK}}{qB} \propto \frac{\sqrt{m}}{q} \quad (\text{same } K,\ \text{same } B) \)
An α particle has \( m_\alpha = 4m_p \) and \( q_\alpha = 2e \), while a proton has \( m_p \) and \( e \).
\( \displaystyle \frac{r_\alpha}{r_p} = \sqrt{\frac{m_\alpha}{m_p}}\times\frac{q_p}{q_\alpha} = \sqrt{4}\times\frac{1}{2} = 1 \)
Note: A similar question was also asked in CUET (UG) 2026 on 26-05-2026 (Slot 2), in CUET (UG) 2025 on 29-05-2025 (Slot 2), and in CUET (UG) 2022 on 18-08-2022 (Slot 2).