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