A α particle and a proton enters a region of uniform magnetic field B with same momentum at right angle to magnetic field. The ratio of the radii of the circular paths of α particle to proton is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 2
A charged particle moving at right angles to a uniform magnetic field moves in a circle, with the magnetic force supplying the centripetal force: \( qvB = mv^{2}/r \), which gives \( r = mv/(qB) = p/(qB) \).
The momentum p and the field B are the same for both particles, so \( r\propto 1/q \). The charge of the α particle is \( 2e \) and that of the proton is \( e \).
\( \displaystyle \frac{r_\alpha}{r_p} = \frac{q_p}{q_\alpha} = \frac{e}{2e} = \frac{1}{2} \)