Two identical circular loops P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre as shown in figure. The magnitude of the net magnetic field at the common centre is:

$\frac{μ_0I}{\sqrt{2}R}$

Magnetic field due to one loop is $ B = \frac{\mu_0I}{2R}$

Since magnetic field due to two loops are perpendicular hence net magnetic field at the centre is $ B_{net} = B\sqrt{2} = \frac{\mu_0I}{\sqrt{2}R}$

The correct answer is Option (4) → $\frac{μ_0I}{\sqrt{2}R}$