B_X and B_Y are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of B_X and B_Y is :

Solution

Physics sir · 3 steps

Same current, same radius, so the field at the centre just follows the number of turns.

1. Field of a coil. At the centre of a circular coil of N turns, each turn adds the same field, so the total is N times the field of one loop.

   B = (μ₀ N I)/2R

2. Take the ratio. Both coils carry the same current I and have the same radius R = 20 cm. So μ₀, I and 2R all cancel, leaving B_X/B_Y = N_X/N_Y = 200/400.
3. So. B_X/B_Y = 1/2, so the ratio is 1 : 2, option (b).

The idea to keep. For a coil, B at the centre is proportional to NI/R. Before you calculate anything, check which quantities are equal; they cancel in the ratio.

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