Question

In given diagram, two current carrying circular loop of radius $R$ and $2R$ 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)

$B_x=\frac{{\mu }_{0}I}{4R},B_y=\frac{{\mu }_{0}I}{8R}$
$\Rightarrow \tan \theta =\frac{B_y}{B_x}=\frac{1}{2}$
$\sin \theta =\frac{1}{\sqrt{5}}$
$\Rightarrow \theta ={\sin }^{-1}\left(\frac{1}{\sqrt{5}}\right)$