The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be:
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Question

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be:

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G1 Physics · Accepted Answer

Initially B = μ₀NI/(2R) with N = 4. When rewound into one turn using the same wire, the new radius becomes R′ = 4R. Thus B′ = μ₀I/(2R′) = μ₀I/(8R). Initially B = 2μ₀I/R. Therefore B′/B = 1/16, so B′ = 32/16 = 2 T.