A square frame of side I carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is
A square frame of side I carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is
- A
$\frac{8 \sqrt{2}}{\pi^2}$
- B
$\frac{8 \sqrt{2}}{\pi^3}$
- C
$\frac{8 \sqrt{2}}{\pi}$
- D
$\frac{4 \sqrt{2}}{\pi^2}$
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