Two identical coils of radius $R$ and number of turns $N$ are placed perpendicular to each others in such a way that they have common centre. The current through them are $I$ and $I\sqrt 3$ . The resultant intensity of magnetic field at the centre of the coil will be (in $weber/m^2)2$
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The magnetic field, due the coil, carrying current $I$ Ampere
$B_1=\frac{\mu_0 I}{2 R}$
The magnetic field due to the coil, carrying current $2I$ Ampere
$B_2=\frac{\mu_0(2 I)}{2 R}$
The resultant $B$
$B_{n e t}=\sqrt{B_1^2+B_2^2+2 B_1 B_2 \cos \theta}$
where $\theta=90^{\circ}$
$\Rightarrow B_{\text {net }}=\sqrt{B_1^2+B_2^2+2 B_1 B_2 \cos 90^0}=\frac{\mu_0(2 I)}{2 R} \sqrt{1+4}$
$=\frac{\sqrt{5} \mu_0 I}{2 R}$
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