Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

Solution

Physics sir · 3 steps

Same mass, so the radius depends only on v over q: put in both ratios and divide.

1. Force gives radius. For an ion moving perpendicular to the field, the magnetic force qvB supplies the centripetal force mv²/r. Setting them equal gives r = mv/qB.
2. Take the ratio. Both ions have the same m and are in the same B, so these cancel. The radius is proportional to speed and inversely proportional to charge.

   r₁/r₂ = v₁/v₂ × q₂/q₁ = 2/3 × 2/1 = 4/3

3. So. The radii are in the ratio 4 : 3, which is option (b).

The idea to keep. In a magnetic field, r = mv/qB. Charge sits in the denominator, so flip the charge ratio before you multiply it with the other ratios.

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