Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle $\mathrm{\alpha }$ at the centre C. The magnitude of magnetic field due to PQRS at centre C is 

The straight portions PQ and RS do not produce magnetic field at C. Only the curved portion QR produces a magnetic field at C. Refer to Fig.

Since the current dl is perpendicular to position vector r, the magnetic field at C by Biot-Savart law is

$\begin{array}{l}\mathrm{dB}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{Idl} \sin 90}{{\mathrm{r}}^2}\\ =\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{I}\times \left(\mathrm{rd\theta }\right)}{{\mathrm{r}}^2}(\because \mathrm{dl}=\mathrm{rd}\underset{\_}{\mathrm{\theta }})\\ =\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}\mathrm{d\theta }\end{array}$

$\mathrm{B}={\int }_0^{\alpha }1dB=\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}{\int }_0^{\alpha }\mathrm{d\theta }=\frac{{\mathrm{\mu }}_0\mathrm{I\alpha }}{4\mathrm{\pi r}}$

So the correct choice is (4).