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

• A

  $\tan ^{-1}$ (2)
• B

  $\tan ^{-1}\left(\frac{1}{2}\right)$
• Correct answer
  C

  $\tan ^{-1}(\sqrt{2})$
• D

  $\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$

Solution

$\begin{aligned} & \tan \alpha &=\frac{1}{2} \tan \theta \\ & \text { or } & \tan \theta &=2 \tan \alpha \\ & \text { or } & \tan \theta &=2 \tan \left(90^{\circ}-\theta\right) \\ & \text { or } & \tan ^{2} \theta &=2 \\ \tan \theta &=\sqrt{2} \\ \theta &=\tan ^{-1}(\sqrt{2}) \end{aligned}$

Hence, the correct answer is option: 'C'.