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. $\theta =45^{{}^{\circ }}$
• 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.
$\theta +{\tan }^{-1}\left(\frac{\tan \theta }{2}\right)=\frac{\pi }{2}$


$\frac{\text{tan}\theta }{2}=\text{cot}\theta$
$\text{tan}\theta =2cot\theta \Rightarrow {\text{tan}}^2\theta =2$
$\therefore \text{tan}\theta =\sqrt{2}$