What will be the magnitude of magnetic induction at the centre oi a square loop of side l, if a current i is  flowing in the loop ?

The magnetic induction due to the loop at O is
B= 4x B_AB
Here B_AB= $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{\pi }(\mathrm{l}/2)}\left[\sin {45}^{\circ }+\sin {45}^{\circ }\right]$
$\begin{array}{r}=\frac{2{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{\pi l}}\times \left[\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right]=\frac{2\sqrt{2}{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{\pi l}}\\ \therefore \mathrm{B}=4\times {\mathrm{B}}_{\mathrm{AB}}=\frac{4\times 2\sqrt{2}{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{\pi l}}=\frac{2\sqrt{2}{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{\pi l}}\end{array}$