question_answer

The electric field at a point due to an electric dipole, on an axis inclined at an angle \[\theta \left( <\text{ }90{}^\circ  \right)\] 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 \[\tan \theta =2\tan \alpha ({{90}^{o}}-\theta )\] or \[{{\tan }^{2}}\theta =2\] or \[\tan \theta =\sqrt{2}\]