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Question

A steady current is flowing in a circular coil of radius R, made up of a thin conducting wire. The magnetic field at the center of the loop is BL. Now, a circular loop of radius R/n is made from the same wire without changing its length, by unfolding and refolding the loop, and the same current is passed through it. If new magnetic field at the center of the coil is BC, then the ratio BLBC is

A
1:n2
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B
n1/2
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C
n:1
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D
none of these.
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Solution

The correct option is A 1:n2
BL=μ0I2πR
If the radius is R/n, then number of turns will be n
BC=nμ0I2π(R/n)=n2μ0I2πR
Hence ,BLBC=1n2

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