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Question

# Two circular coils P and Q are made from similar wire but radius of Q is twice that of P. Relation between the values of potential difference across them so that the magnetic induction at their centers may be the same is :

A
VQ=2VP
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B
VQ=3VP
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C
VQ=4VP
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D
VQ=14VP
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Solution

## The correct option is D VQ=4VPMagnetic field at the center of a circular coli is B=μ04π×2πirWhere i is flowing in the coil and r is the radius of coil.At the center of the coil PB1=μ04π×2πi1r1........(1)At the center of the coil QB2=μ04π×2πi2r2........(2)But B1=B2∴μ04π×2πi1r1=μ04π×2πi2r2Or i1r1=i2r2As r1=2r2i12r2=i2r2Or i1=2i2................(3)Now , Potential differencesVQVP=i2×r2i1×r1=i2×r22i2×2r2=14VPVQ=41VQ=4VPHence the correct answer is VQ=4VP

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