A current loop consists of two identical semicircular parts each of...

The magnetic field at centre $O$ for each semicircular parts each of radius $R$, $$\mathrm{B}_1=\mathrm{B}_2=\frac{\mu_0 \mathrm{i}}{4 \mathrm{R}}$$ The magnetic field at their common centre \begin{aligned} \overrightarrow{\mathrm{B}} & =\overrightarrow{\mathrm{B}}_1+\overrightarrow{\mathrm{B}}_2 \\ \mathrm{~B} & =\sqrt{\mathrm{B}_1^2+\mathrm{B}_2^2} \\ & =\sqrt{\left(\frac{\mu_0 \mathrm{i}}{4 \mathrm{R}}\right)^2+\left(\frac{\mu_0 \mathrm{i}}{4 \mathrm{R}}\right)^2} \\ \mathrm{~B} & =\frac{\mu_0 \mathrm{i}}{2 \sqrt{2} \mathrm{R}} \end{aligned}