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Question

A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is:

A
3B
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B
5B
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C
4B
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D
2B
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Solution

The correct option is D 4B
Let the radius of the circular loop be r

Magnetic field at its centre B=μo2πIr .........(1)

Thus length of the wire L=2πr

But the same wire is looped into a coil of radius r2 of two turns.

L=2(2πr2)=2πr r2=r2

Magnetic field at its centre B2=μo2πIr2×n

B2=μo2πIr/2×2=4×μoI2πr

From (1) we get B2=4B

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