Biot-Savart Law & Circular Coils question from MHT CET 2023 (12 May, Shift 1)

Answer: (d)

1. Field at the centre of a coil: $B = \frac{\mu_0 I}{2R}$, along the coil's axis.
2. $B_1 = \frac{\mu_0 I}{2R}$ and $B_2 = \frac{\mu_0 (2I)}{2R} = 2B_1$.
3. The planes are perpendicular, so the two fields are perpendicular: $B = \sqrt{B_1^2 + B_2^2} = \sqrt{5}\,B_1$.
4. So the answer is (d) $\frac{\sqrt{5}\mu_0 I}{2R}$.