An electric dipole is placed along x -axis at origin O. A point P is at a distance of 20,

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1. Electric Charges and Fields

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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 $\frac{\pi}{3}$ with the $x$ -axis. If the electric field at $P$ makes an angle $\theta$ with the $x$ -axis, the value of $\theta$ would be

A

$\frac{\pi}{3}$

B

$\frac{\pi}{3} + \tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$

C

$\frac{2 \pi}{3}$

D

$\tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$

Solution

$\theta=\frac{\pi}{3}+\alpha$ where $\tan \alpha=\frac{1}{2} \tan \frac{\pi}{3}$

$\Rightarrow \alpha=\tan ^{-1} \frac{\sqrt{3}}{2}$ so, $\theta=\frac{\pi}{3}+\tan ^{-1} \frac{\sqrt{3}}{2}$

Standard 12

Physics

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