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  4. The electric field at a point due to an electric dipole, on an axis inclined at an angle θ R(< 90°) to the dipole axis, is perpendicular to the dipole axis, if the angle θ is

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Q. 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

KCETKCET 2011Electric Charges and Fields

Solution:

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