A long conducting wire carrying current I is bent into a circular coil of N turns. Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in both cases. The ratio of magnetic field in first case to that in second case is:
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Question

A long conducting wire carrying current I is bent into a circular coil of N turns. Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in both cases. The ratio of magnetic field in first case to that in second case is:

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G1 Physics · Accepted Answer

For fixed wire length L, radius of an N-turn coil is R = L/(2πN). Field at centre B = μ₀NI/(2R) ∝ N². Therefore B₁/B₂ = N²/n².