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