According to Biot-Savart's law, the magnetic induction at a point to a current carrying element is given
by

Directed normal to plane containing and r, θ being angle between and r.

Field due to semicircular arc

Now, angle between a current element of semicircular arc and the radius vector of the element to point c is .
Therefore, the magnitude of magnetic induction B at O due to this element,

Hence, magnetic induction due to whole semicircular loop is

The magnetic field due to ab and de is zero, because or , so net magnetic field is