Biot-Savart Law & Circular Coils question from NEET 2012 (AIPMT, Prelims)

Answer: (a)

1. Each coil gives $B = \frac{\mu_0 I}{2R}$ at the centre, along its own axis.
2. $B_1 = \frac{\mu_0 I}{2R}$, $B_2 = \frac{\mu_0 (2I)}{2R}$; the two fields are perpendicular.
3. $B = \sqrt{B_1^2 + B_2^2} = \sqrt{1 + 4}\,\frac{\mu_0 I}{2R}$
4. So the answer is (a) $\frac{\sqrt{5}\mu_0 I}{2R}$.