Question

Two identical wires A and B, each of length ‘l’, 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 $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

For A For B

2πR=L 4a=L

$\Rightarrow R=\frac{L}{2\pi }$ $\Rightarrow a=\frac{L}{4}$

$B_A=\frac{{\mu }_{0}i}{2R}{B}_B=\left[\frac{{\mu }_{0}i}{4\pi a/2}(sin\frac{\pi }{4}+sin\frac{\pi }{4})\right]$

Now $\frac{B_A}{B_B}=\frac{{\pi }^2}{8\sqrt{2}}$