A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{3}+{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
C) \[\frac{2\pi }{3}\]
D) \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
Correct Answer: B
Solution :
Component of electric field at point P parallel to X-axis, \[{{E}_{X}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2(p\,\cos \,\pi /3)}{{{r}^{3}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}\] Component of electric field of point P perpendicular to -X-axis, \[{{E}_{Y}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p\,\sin \,\pi /3}{{{r}^{3}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{\sqrt{3}p}{2{{r}^{3}}}\] \[\therefore \] \[\tan \theta =\frac{{{E}_{Y}}}{{{E}_{X}}}=\frac{\sqrt{3}}{2}\] \[\therefore \] \[\theta ={{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]You need to login to perform this action.
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