question_answer

An electric dipole is placed along the \[x-\]axis at the origin \[O\]. A point \[P\] is at a distance of \[20\,cm\] 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]

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 :

                   \[\theta =\frac{\pi }{3}+\alpha \] where \[\tan \alpha =\frac{1}{2}\tan \frac{\pi }{3}\] Þ \[\alpha ={{\tan }^{-1}}\sqrt{3}/2\] so, \[\theta =\frac{\pi }{3}+{{\tan }^{-1}}\sqrt{3}/2\]