c
(c) An electric dipole of moment \(=\bar{p}\)

electric field \(x-\) axis at a point \(=p\)

angle \(=\theta\) with \(x-\) axis

\(\tan a=\frac{1}{2} \tan \theta\)

\((\theta+\alpha)=\) the value of the position vector makes an angle \(\theta\)

\(\theta=60^{\circ}+\alpha\)

now resolving \(E\) into its components

\(E \cos \alpha=\frac{2 p \cos 60^{0}}{4 \pi \epsilon_{0} r^{3}} \quad \longrightarrow(1)\)

\(E \sin \alpha=\frac{p \sin 60^{0}}{4 \pi \epsilon_{0} r^{3}} \quad \longrightarrow(2)\)

Dividing \(2\) by \(1\)

\(\tan \alpha=\frac{1}{2} \tan \theta\)

\(\tan \alpha=\tan (\theta+\alpha)\)

\(\alpha=\theta+\alpha\)