Explanation

(b) Field due to a straight wire of infinite length is $\frac{\mu_{0}i}{4\pi r}$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $\frac{\mu_{0}\pi i}{4\pi r}$.
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$\therefore\ \ \ B = B_{a} + B_{b} + B_{c}$
$\ \ \ \ \ \ \ \ \ \ \ = \frac{\mu_{0}}{4\pi}\frac{i}{r} + \ \frac{\mu_{0}}{4\pi}\frac{\pi i}{r} + \frac{\mu_{0}}{4\pi}\frac{i}{r}$
$\ \ \ \ \ \ \ \ = \frac{\mu_{0}}{4\pi}\frac{i}{r}(\pi + 2)$ out of the page