Question

The resultant magnetic moment due to two currents carrying concentric coils of radius $r$, mutually perpendicular to each other will be

• A. $\sqrt{2}ir$
• B. $\sqrt{2}i\pi r^2$
• C. $2\pi r^2$
• D. $\sqrt{2}i{r}^2$

Answer 1

Answer: (B)

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

Magnetic moment of coil-1 ${\mu }_1=i\pi r^2$
Magnetic moment of coil-2 ${\mu }_2=i\pi r^2$
${\mu }_1\perp {\mu }_2$
$\therefore$ resultant of ${\mu }_1$ and ${\mu }_2$ is $\mu =\sqrt{({\mu }_1^2+{\mu }_2^2)}=\sqrt{2}{\mu }_1=\sqrt{2}i\pi r^2$