Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle α at the centre C. The magnitude of magnetic field due to PQRS at centre C is

The straight portions PQ and RS do not produce magnetic field at C. Only the curved portion QR produces a magnetic field at C. Refer to Fig.Since the current dl is perpendicular to position vector r, the magnetic field at C by Biot-Savart law isdB=μ04πIdl sin⁡90r2=μ04πI×(rdθ)r2 (∵dl=rdθ_)=μ0I4πrdθB=∫0α1dB=μ0I4πr∫0αdθ=μ0Iα4πrSo the correct choice is (4).