Two identical wires A and B, each of length ℓ, carry the same current I. Wire A is bent into a circle of radius R and wire B into a square of side a. If Bₐ and Bᵦ are the magnetic fields at the centres of the circle and square respectively, find Bₐ/Bᵦ.
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Question

Two identical wires A and B, each of length ℓ, carry the same current I. Wire A is bent into a circle of radius R and wire B into a square of side a. If Bₐ and Bᵦ are the magnetic fields at the centres of the circle and square respectively, find Bₐ/Bᵦ.

Options

G1 Physics · Accepted Answer

Equal wire lengths give 2πR=4a, so a=πR/2. At the circle centre Bₐ=μ₀I/(2R). For the square, each side contributes μ₀I√2/(2πa), and four sides add. Therefore Bₐ/Bᵦ=π²/(8√2), option A.