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Q.

Two identical wires A and B have the same length l and carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If B1 and B2 are the values of magnetic induction at the centre of the circle and the centre of the square respectively, thenthe ratio B1/B2 is

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a

π2/8

b

π2/82

c

π2/16

d

π2/162

answer is B.

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Detailed Solution

B1 = μ04π× 2πIR= μ04π× 2πI × 2πL                         ….(1)∵    L=2πR,  for  circular  loopB2 =  μ04π×  Ia/2   sin 450  +  sin 450 ×  4where  a=L/4∴   B2 =  μ0I4πL× 8  × 4 × 12 + 12=  μ0I4πL× 642∴    B1B2  =  μ04π  4π2IL  /  μ0I4πL× 642or   B1B2  = π282
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