Question

An electric dipole is placed at the origin $O$ and is directed along the $x$ -axis. At a point $P$, far away from the dipole; the electric field is parallel to $y$ -axis. OP makes an angle $\theta$ with the $x$ -axis, then

• A. $\tan \theta=\sqrt{3}$
• B. $\tan \theta=\sqrt{2}$
• C. $\theta=45^{\circ}$
• D. $\tan \theta=\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

We know that in this case electric field makes an angle $\theta+\alpha$ with the direction of dipole.

Also, $\tan \alpha=\frac{1}{2} \tan \theta$
Here, $\theta+\alpha=90^{\circ} \Rightarrow \alpha=90^{\circ}-\theta$
Hence $\tan \left(90^{\circ}-\theta\right)=\frac{1}{2} \tan \theta $
$\Rightarrow \cot \theta=\frac{1}{2} \tan \theta$
$\Rightarrow \tan ^{2} \theta=2 $
$\Rightarrow \tan \theta=\sqrt{2}$