Correct Answer - C
As two coils subtedn the same solid angle at O, hence area of coi, Y=4`xx` area of coil X
`["solid angel"=("area")/(bot"distance")^(2)]`
i.e. radius of coil Y=2 `xx` radius of coul X
`:. B_(Y)=(mu_(0))/(4pi)xx(2piI(2r)^(2))/([(2r)^(2)+(d^(2))]^(3//2))`
`B_(x)=(mu_(0))/(4pi)xx(2piI(r)^(2))/([r^(2)+((d)/(2))^(2)]^(2//3))`
`(B_(y))/(B_(X))=(4)/((4r^(2)+d^(2))^(3//2))xx[(4r^(2+d^(2)))/(4)]^(3//2)`
`" " (4)/((4)^(3//2))=(4)/(8)=(1)/(2)`