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 $\tan \left(90^{\circ }-\theta \right)=\frac{1}{2}\tan \theta$
$\Rightarrow \cot \theta =\frac{1}{2}\tan \theta$
$\Rightarrow {\tan }^2\theta =2$
$\Rightarrow \tan \theta =\sqrt{2}$