Magnetic field B at the centre of arc is obtained by integrating Biot-Savart's law
that is applied to segment legth dl along the length of arc
at each point of arc length segment dl and unit vector along radial direction are perpendicular.
cross product of vectors equals segment length dl
Hence by keeping all parameters constants, integration of length segment becomes length of arc, i.e. (π/2)r .
Hence Magnetic field B =