Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6: 5 and their respective masses ratio is 9: 4. Then, the ratio of their charges will be :

Solution

Physics sir · 4 steps

Same kinetic energy means momentum goes as √m, so put p = √2mK into r = p/qB.

1. Radius in a field. The magnetic force supplies the centripetal force, qvB = mv²/r, so r = mv/qB = p/qB.
2. Bring in K. Since K = p²/2m, the momentum is p = √2mK. Both particles have the same K and see the same B, so only m, q and r change.

   r = √2mK/qB ⇒ q ∝ √m/r

3. Put in ratios. q₁/q₂ = √(m₁/m₂) × r₂/r₁ = √(9/4) × 5/6 = 3/2 × 5/6 = 15/12.
4. So. 15/12 reduces to 5/4, so the charges are in the ratio 5 : 4, option (b).

The idea to keep. In a magnetic field r = p/qB. Turn whatever is held equal (speed, K or accelerating voltage) into momentum first. For equal kinetic energy, p = √2mK.

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