Question

An electric dipole is placed along the $x$ - axis at the origin $O. A$ point $P$ is at a distance of $20 cm$ 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)
$\theta=\frac{\pi}{3}+\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$