Question

Two concentric coils of radius $r$ are kept mutually perpendicular to each other. If current flowing through both the coils is $I$, then the resultant magnetic moment due to the two coils will be

• A. $\sqrt{2}I\pi r^2$
• B. $\sqrt{2}I{r}^2$
• C. $\sqrt{2}Ir$
• D. $2\pi r^2$

Answer 1

Answer: (A)

$\sqrt{2}I\pi r^2$

As the two coils are held perpendicular to each other, so their normals are also perpendicular to each other, further since magnetic moments are directed along normals, therefore the two magnetic moments are perpendicular to each other.
Now, $M_1=M_2=IA=I\pi r^2$
$M=\sqrt{M_1^2+M_2^2}=M\sqrt{2}=\sqrt{2}I\pi r^2$