Question

In given diagram, two current carrying circular loop of radius $R$ and $2 R$ are arranged in $YZ$ -plane and $XZ$ -plane respectively. Common centre of both are at origin $O$. Then what will be the angle of resultant magnetic field from $X$-axis.

• A. $\tan ^{-1}(2)$
• B. $\sin ^{-1}\left(\frac{1}{\sqrt{5}}\right)$
• C. $\cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)$
• D. $\sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)$

Answer 1

Answer: (B)

$B _{ x }=\frac{\mu_{0} I }{4 R }, B _{ y }=\frac{\mu_{0} I }{8 R }$
$ \Rightarrow \tan \theta=\frac{ B _{ y }}{ B _{ x }}=\frac{1}{2}$
$\sin \theta=\frac{1}{\sqrt{5}} $
$\Rightarrow \theta=\sin ^{-1}\left(\frac{1}{\sqrt{5}}\right)$