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A long straight wire carrying a constant current is shaped first into a single-turn circular loop, producing a magnetic field of magnitude B at its centre. If the same wire, with the same current, is instead wound into a circular coil of n turns having a smaller radius, what will be the magnetic field at the centre?

1. B/n
2. nB
3. B/n²
4. n²B

Correct answer: n²B

Solution

When the wire is wound into a coil with n turns, the magnetic field at the center increases because each turn contributes to the total magnetic field. The magnetic field strength is proportional to the number of turns squared, resulting in a field strength of n²B at the center.

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