A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

Solution

Physics sir · 3 steps

Same speed, same field, so the radius goes as mass over charge. Compare m/q for the two particles.

1. Radius formula. The magnetic force qvB supplies the centripetal force mv²/r. Setting them equal gives the radius of the circle.

   r = mv/qB

2. Compare m and q. Here v and B are the same for both, so r ∝ m/q. An alpha particle has mass 4mₚ and charge 2e, while a proton has mass mₚ and charge e.
3. So. r_α/rₚ = (4mₚ/2e)/(mₚ/e) = 2, so the ratio is 2 : 1, option (c).

The idea to keep. In a uniform field, r = mv/qB. Always check what is held equal: same velocity means r ∝ m/q, but same kinetic energy or same accelerating voltage gives a different dependence.

Answer from the NTA final answer key. Solution by PrepWiser.