question_answer

The electric field at a point due to an electric dipole, on an axis inclined at an angle\[\theta \left( <{{90}^{0}} \right)\] to the dipole axis, is perpendicular to the dipole axis, if the angle \[\theta \]is

A)  \[{{\tan }^{-1}}\left( 2 \right)\]                

B)  \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]

C)  \[{{\tan }^{-1}}\left( \sqrt{2} \right)\]                   

D)  \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{2}} \right)\]

Correct Answer: C

Solution :

Here, \[\alpha +\theta ={{90}^{o}}\]                                 \[\tan \alpha =\frac{1}{2}\tan \theta \] or            \[\tan \theta =2\tan \alpha \] or            \[\tan \theta =2\tan ({{90}^{o}}-\theta )\] or            \[{{\tan }^{2}}\theta =2\] or            \[\tan \theta =\sqrt{2}\]                 \[\theta ={{\tan }^{-1}}(\sqrt{2})\]