Question

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

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

Answer 1

The correct option is A $\frac{\pi }{3}+{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

$E_1=\frac{2p\cos 60}{{4\pi {\epsilon }_{0}r}^3}{E}_2=\frac{2p\sin 60}{{4\pi {\epsilon }_{0}r}^3}\tan \alpha =\frac{E_2}{E_1}=\frac{\sqrt{3}}{2},\alpha ={\tan }^{-1}\frac{E_2}{E_1}=\alpha ={41}^O$

Angle with the x axis

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