$B_{1}=\frac{\mu_{0} I}{2 R}$

It acts in horizontal direction.

Magnetic field induction due to horizontal loop at the centre $O$ is

$B_{2}=\frac{\mu_{0} 2 I}{2 R}$

It acts in vertically upward direction.

As $B_{1}$ and $B_{2}$ are perpendicular to each other, therefore the resultant magnetic field induction at the centre $O$ is

${B_{\text {net }}=\sqrt{B_{1}^{2}+B_{2}^{2}}=\sqrt{\left(\frac{\mu_{0} I}{2 R}\right)^{2}+\left(\frac{\mu_{0} 2 I}{2 R}\right)^{2}}}$

${B_{\text {net }}=\frac{\mu_{0} I}{2 R} \sqrt{(1)^{2}+(2)^{2}}=\frac{\sqrt{5} \mu_{0} I}{2 R}}$