Question

An electric dipole is placed along the x-axis at the origin 0. A point P is at a distance of 20 cm from this origin such that OP makes an angle $\text{/3}$ 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. ${{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)$

Answer 1

Answer: (B)

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

Answer 2

Component of electric field at point P parallel to $X-$ axis, ${{E}_{X}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2(p\cos \pi /3)}{{{r}^{3}}}$ $\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{P}{{{r}^{3}}}$ Component of electric field of point $P$ perpendicular to $X-$ axis, ${{E}_{Y}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{p\sin \pi /3}{{{r}^{3}}}$ $=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{\sqrt{3}p}{2{{r}^{3}}}$ $\therefore$ $\tan \theta =\frac{{{E}_{Y}}}{{{E}_{X}}}=\frac{\sqrt{3}}{2}$ $\therefore$ $\theta ={{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)$