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:

$\frac{μ_0I}{\sqrt{2}R}$

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

Magnetic field at the center is,

$B = \frac{\mu_0I}{2R}$

$∴B_P=B_Q=\frac{\mu_0I}{2R}$

Also, these loops are perpendicular to each other because the loops are in perpendicular planes.

$B_{net}=\sqrt{{B_P}^2+{B_Q}^2}$

$=\sqrt{\left(\frac{\mu_0I}{2R}\right)^2+\left(\frac{\mu_0I}{2R}\right)^2}$

$=\frac{\mu_0I}{2R}\sqrt{2}=\frac{μ_0I}{\sqrt{2}R}$