Question

An electric dipole is placed along the $x$ - axis at the origin $O.A$ point $P$ is at a distance of $20cm$ from this origin such that $OP$ makes an angle $\pi /3$ with the $x$ - axis. If the electric field at point P makes an angle $\theta$ with the $x$ - axis the value of $\theta$ would be.

• A. $\pi /3$
• B. $2\pi /3$
• C. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
• D. $\pi /3+{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Answer 1

Answer: (D)

$\theta =\frac{\pi }{3}+\alpha (i)$
As we known
$\tan \alpha =\frac{1}{2}\tan \theta$
$\frac{1}{2}\tan \frac{\pi }{3}$
$=\frac{1}{2}\times \sqrt{3}=\frac{\sqrt{3}}{2}$
$\alpha ={\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$ put in(i)
$\theta =\frac{\pi }{3}+{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$