Question

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

• A. $ta{n}^{-1}(2)$
• B. $ta{n}^{-1}(\frac{1}{2})$
• C. $ta{n}^{-1}\sqrt{2}$
• D. $tan-1(\frac{1}{\sqrt{2}})$

Answer 1

Answer: (C)

Here, $\alpha +\theta =90^{\circ }$

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