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A long conductor carries a constant current. When it is shaped into a single-turn circular loop, the magnetic field at the centre is B. If the same wire is then formed into a circular coil having n turns, the magnetic field at the centre becomes

1. 2nB
2. n²B
3. nB
4. 2n²B

Correct answer: n²B

Solution

Fixed wire length L = 2*pi*R. With n turns each radius r = R/n. B' = n*mu0*I/(2r) = n*mu0*I/(2R/n) = n^2 * mu0*I/(2R) = n^2 B.

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