Electrostatics Question 298

Question: An electric dipole is placed along the $ x- $ axis at the origin $ O $ . A point $ P $ is at a distance of $ 20cm $ 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 [MP PMT 1997]

Options:

A) $ \frac{\pi }{3} $

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

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

D) $ {{\tan }^{-1}}( \frac{\sqrt{3}}{2} ) $

Show Answer

Answer:

Correct Answer: B

Solution:

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

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



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