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,

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

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