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Question

The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire is

A
π22
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B
π42
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C
π242
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D
π282
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Solution

The correct option is D π282
Magnetic field at the centre of a circular coil
BCircular=μ04π2πir=μ04π4π2iL[L=2πr and r=12π]
Magnetic field at the centre of square coil
BSquare=μ04π82ia=μ04π322iL[L=4a and a=L4]
Hence, BCircularBSquare=mu04π4π2iLμ04π322iL=π282.

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