JEE Main 2026 Jan 21 Shift 2, Physics Q17: Magnetic Field due to Electric Current

Three contributions at the centre O:

(i) The two straight semi-infinite parts (AB and DE) end at the points where the circle meets the line, each a perpendicular distance $r$ from O. Each contributes $\frac{{\mu }_{0}I}{4\pi r}$ in the $+\hat{i}$ direction (their fields add).

(ii) The full circular loop at its centre contributes $\frac{{\mu }_{0}I}{2r}$ in the $-\hat{i}$ direction (opposite sense from the straight parts based on the current direction shown).

Net: ${\vec{B}}_0=\frac{{\mu }_{0}I}{4\pi r}\hat{i}+\frac{{\mu }_{0}I}{4\pi r}\hat{i}-\frac{{\mu }_{0}I}{2r}\hat{i}=\frac{{\mu }_{0}I}{2\pi r}\hat{i}-\frac{{\mu }_{0}I}{2r}\hat{i}=\frac{{\mu }_{0}I}{2\pi r}(1-\pi )\hat{i}=-\frac{{\mu }_{0}I}{2\pi r}(\pi -1)\hat{i}$.