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Q.

Two circular coils X and Y have equal number of turns and carry equal currents in the same sense and subtend same solid angle at point O. The smaller coil X is midway between O and Y. If we represent the magnetic induction due to bigger coil Y at O as BY and that due to smaller coilX at O as BX, then

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a

BYBX  =1

b

BYBX  =2

c

BYBX  =12

d

BYBX  =14

answer is C.

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Detailed Solution

As two coils subtend the same solid angle at O, hence Area of coil Y = 4 x Area of coil XSolid  angle = area⊥  distance2i. e., Radius of coil Y = 2 x Radius of coil X∴   By =  μ04π×  2π I 2r22r2 + d23/2Bx =  μ04π×  2π  r2r2 + d223/2∴   ByBx =   44r2+d23/2 ×  4r2+d243/2=  443/2  =  48=12
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