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Question

A steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is B. If the same wire is bent into a circular loop of n turns, the magnetic field at the centre of the coil is:

A
Bn
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B
nB
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C
nB2
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D
n2B
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Solution

The correct option is C n2B
Let the length of the wire be L and radius of the coil be r
L=2πr
Magnetic field at the centre of coil B=μoI2r ........(1)

Now the same wire is bent into circular loops of n turns.
L=n2πr
2πr=2nπr r=rn ........(2)

Magnetic field at the centre of circular loops of n turns B=μoI4πr×2πn=μoI2rn
Using equation (2), we get B=μoI2rnn=μoI2rn2

B=n2B

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