Two circular coils X and Y, having equal number of turns and carrying currents in the same sense, subtend same solid angle at point O. If the smaller coil X is midway between O and Y and if we represent the magnetic induction due to bigger coil Y at O as `B_y` and the due to smaller coil X at O as `B_x`,then find the ratio `B_x//B_y`.

Options

A. `1:1`
B. `2:1`
C. `1:2`
D. `1:4`

Answer

C

Explanation

Since the two coils subtend the same solid angle at O, hence area of coil `D=4` x area of coil C,
[because solid angle `=(area)/((_|_r distance)^2)`].
Therefore, radius of coil `D=2xx` radius of coil C
`:. B_D=(mu_0)/(4pi)(2piI(2r)^2)/([(2r)^2+a^2]^(3//2))`

`B_C=(mu_0)/(4pi)(2piIr^2)/([r^2+(a//2)^2]^(3//2))`
`:. (B_D)/(B_C)=(4)/((4r^2+a^2)^(3//2))xx[(4r^2+a^2)/(4)]^(3//2)=4/8=1/2`