Magnetic field at the center of a hairpin wire ($B=\frac{{\mu }_{0}I}{4\pi a}(\pi +2)$)

A semicircular current arc of radius $a$ connected tangentially to two parallel semi-infinite wires has the displayed magnetic field at its centre. The arc contributes ${\mu }_{0}I/(4a)$ and each straight segment ${\mu }_{0}I/(4\pi a)$ by the Biot-Savart law. For the continuous hairpin current all three magnetic fields have the same normal direction by the right-hand rule; they add rather than cancel.