Magnetic field at the centre due to semicircular loop lying in \(x-y\) plane, \(B_{x y}=\frac{1}{2}\left(\frac{\mu_{0} i}{2 R}\right) \quad\) negative \(z\) direction. 

Similarly field due to loop in \(x-z\) plane, 

\(B_{x z}=\frac{1}{2}\left(\frac{\mu_{0} i}{2 R}\right)\) in negative \(y\) direction.

\(\therefore\) Magnitude of resultant magnetic field,

\(B =\sqrt{B_{x y}^{2}+B_{x z}^{2}}=\sqrt{\left(\frac{\mu_{0} i}{4 R}\right)^{2}+\left(\frac{\mu_{0} i}{4 R}\right)^{2}}\)

\(=\frac{\mu_{0} i}{4 R} \sqrt{2}=\frac{\mu_{0} i}{2 \sqrt{2} R}\)