Biot-Savart Law & Circular Coils question from MHT CET 2023 (14 May, Shift 2)

Answer: (a)

1. Straight parts lie along a line through O, so they give no field at O.
2. Going round the single loop, the upper arc ($R_1$) and lower arc ($R_2$) are both traversed clockwise, so both fields at O are into the page.
3. $B = \dfrac{\mu_0 I}{4R_1} + \dfrac{\mu_0 I}{4R_2} = \dfrac{\mu_0 I}{4}\left(\dfrac{1}{R_1}+\dfrac{1}{R_2}\right)$
4. So the answer is (a).