Question

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

• A. $\text{tan} \theta = \sqrt{3}$
• B. $\text{tan} \theta = \sqrt{2}$
• C. $\theta = 4 5^{^\circ }$
• D. $\text{tan} \theta = \left(1 / \sqrt{2}\right)$

Answer 1

Answer: (B)

Direction of the electric field from the axis of the dipole is given by $=\theta+\tan ^{-1}\left(\frac{\tan \theta}{2}\right)$
Here given that $E$ is along the $y$-axis.
$ \theta+\tan ^{-1}\left(\frac{\tan \theta}{2}\right)=\frac{\pi}{2} $


$\frac{\text{tan} \theta }{2} = \text{cot} \theta $
$\text{tan} \theta = 2 cot \theta \, ⇒ \, \text{tan}^{2} \theta = 2$
$∴ \, \, \, \text{tan} \theta = \sqrt{2}$