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

The Correct Option is B

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) $