A portion of a conductive wire is bent in the form of a semicircle of radius r as shown below in fig. At the centre of semicircle, the magnetic induction will be

The straight part will not contribute magnetic field at the centre of the semicircle because every element of the straight part will be 0° or 180°with the line joining the centre and the element. Due to circular portion, the field is
$\frac{1}{2}\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{r}}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}}$
Hence total field at O $=\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}} \mathrm{tesla}$