A long current-carrying wire forms a single circular loop, producing magnetic field B at the centre. The same total length of wire is reshaped into n circular turns carrying the same current. Find the new magnetic field.
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Question

A long current-carrying wire forms a single circular loop, producing magnetic field B at the centre. The same total length of wire is reshaped into n circular turns carrying the same current. Find the new magnetic field.

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G1 Physics · Accepted Answer

Step 1: For a wire of fixed length ℓ, a single circular turn has radius R=ℓ/(2π). Step 2: If the same wire forms n turns, each radius is r=ℓ/(2πn)=R/n. Step 3: New field B′=μ₀nI/(2r)=μ₀nI/(2R/n)=n²B. Answer B. Final answer: (B) n²B.