A coil of one turn is made using a given length of wire. The same wire is then reshaped into a two-turn coil. With the same current in both cases, find the ratio of magnetic fields at their centres (one-turn : two-turn).
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Question

A coil of one turn is made using a given length of wire. The same wire is then reshaped into a two-turn coil. With the same current in both cases, find the ratio of magnetic fields at their centres (one-turn : two-turn).

Options

G1 Physics · Accepted Answer

Step 1: For fixed wire length ℓ made into n circular turns, turn radius r=ℓ/(2πn). Step 2: Field at center B(n)=μ₀nI/(2r)=μ₀πI n²/ℓ. Step 3: Changing one turn to two turns gives B₂/B₁=4. So B₁:B₂=1:4, option B. Final answer: (B) 1 : 4.