Physics - Magnetism Question with Solution | TestHub

Magnetic field at centre $O=$ magnetic field due to reaction $AB+$ magnetic field due to section $PQR$ $$B_0=B_{AB}+B_{PQR}$$
but $B_{AB}=\frac{{\mu }_{0}i}{2\pi R}$ (upside the plane of paper) and $B_{PQR}=\frac{{\mu }_{0}i}{2R}$ (inside the plane of paper) Hence $B_0=\frac{{\mu }_{0}i}{2R}-\frac{{\mu }_{0}i}{2\pi R}$ $$B_0=\frac{{\mu }_{0}i(\pi -1)}{2\pi R}$$