A proton and an alpha particle of the same velocity enter in turn a region of uniform magnetic field, acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the particles, respectively, would be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 2
A charge moving perpendicular to a uniform magnetic field moves in a circle; the magnetic force \( qvB \) supplies the centripetal force.
\( \displaystyle qvB = \frac{mv^{2}}{r} \;\Rightarrow\; r = \frac{mv}{qB} \)
With the same \( v \) and \( B \), \( r \propto m/q \). An alpha particle has 4 times the mass and 2 times the charge of a proton.
\( m_p = m,\; q_p = e \)
\( m_\alpha = 4m,\; q_\alpha = 2e \)
\( \displaystyle \frac{r_p}{r_\alpha} = \frac{m/e}{4m/2e} = \frac{1}{2} \)