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Question

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns, find the magnetic field at the centre of this coil.

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Solution

Initially, magnetic field at the centre of the circular loop, B0=μ0I2R
When n turns are made of the wire, 2πR=n×2πRR=Rn
So, B=μ0I2(Rn)=nμ0I2R
B=nB0

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