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Question

# A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic filed at the centre of the loop is B. It is them bent into circular coil of n turns. The magnetic field at the centre of this cold of n turns will be.

A
2n2B
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B
nB
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C
n2B
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D
2n=B
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Solution

## The correct option is B n2BThe circumference of the first loop is the length of the wire=2πRThe magnetic field at the center of this wire=B=μ0I2RThe same wire is bent into n circular coils.Thus new radius is found out byn×2πr=2πR⟹r=RnThus magnetic field at the center of these loops=nμ0I2r=n2μ0I2R=n2B

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