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 `B_1 and B_2` are the values of magnetic induction at the centre of the circle and the centre of the square, respectively, then the ratio `B_1//B_2` is

Options

A. `(pi^2//8)`
B. `(pi^2//8sqrt2)`
C. `(pi^2//16)`
D. `(pi^2//16sqrt2)`

Answer

B

Explanation

(b) `B_1=(mu_0)/(4pi)xx(2piI)/R=(mu_0)/(4pi)xx(2piIxx2pi)/L....(i)`
`( :' L=2piR, for circular loop)`
`B_2=(mu_0)/(4pi)xx1/(a//2)[sin45^@+sin45^@]xx4`
where `a=(L//4)`
`:. B_2=(mu_0)/(4piL)xx8xx4xx[1/(sqrt2)+1/(sqrt2)] =(mu_0)/(4piL)xx64/(sqrt2)`
`:. (B_1)/(B_2)=((mu_0)/(4pi)) (4pi^2I)/L// (mu_0I)/(4piL)xx64/(sqrt2)=(pi^2)/(8sqrt2)`