A proton, a deuteron and an α particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

Solution

Physics sir · 3 steps

Same momentum means v = p/m, so speed goes as 1/m and force qvB goes as q/m.

1. Speed from momentum. All three have the same momentum p, so v = p/m. The heavier the particle, the slower it moves, and v ∝ 1/m.

   F = qvB = q(p/m)B ⇒ F ∝ q/m

2. Force on each. With p and B the same for all three, and each moving at the same angle to the field, the force depends only on charge divided by mass. Take the proton's charge as e and its mass as m.

   Particle	Charge	Mass	v ∝ 1/m	F ∝ q/m
   Proton	e	m	1	1
   Deuteron	e	2m	1/2	1/2
   α particle	2e	4m	1/4	2/4 = 1/2

3. So. Multiply each column by 4. Forces are 1 : 1/2 : 1/2 = 2 : 1 : 1 and speeds are 1 : 1/2 : 1/4 = 4 : 2 : 1, which is option (a).

The idea to keep. When the momentum is fixed, rewrite v as p/m before comparing. Then F = qvB becomes qpB/m, and only the ratio q/m decides the force.

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