Two similar coils of radius r are placed concentrically with their planes at right angles to each other. The currents flowing in them are I and 3I, respectively. The resultant magnetic induction at the centre is

$\frac{\sqrt{10}μ_0I}{2R}$

The correct answer is Option (2) → $\frac{\sqrt{10}μ_0I}{2R}$

$B = \frac{\mu_0 I}{2r}$

$B_1 = \frac{\mu_0 I}{2r}$

$B_2 = \frac{\mu_0 (3I)}{2r} = \frac{3\mu_0 I}{2r}$

$\text{Fields are perpendicular}$

$B_{\text{net}} = \sqrt{B_1^2 + B_2^2}$

$B_{\text{net}} = \frac{\mu_0 I}{2r}\sqrt{1^2 + 3^2}$

$B_{\text{net}} = \frac{\mu_0 I}{2r}\sqrt{10}$

The resultant magnetic induction is $\frac{\mu_0 I \sqrt{10}}{2r}$.