(i) Derivation of expression of electric field on the equatorial line of the dipole (ii) Depiction of orientation for stable and unstable equilibrium (i) Let the point ' $P$ ' be at a distance ' $r$ ' from the mid point of the dipole. $\;E_{+q}=\;\frac{q}{4\pi\varepsilon_0(r^2+a^2)}$ $\;E_{-q}=\;\frac{q}{4\pi\varepsilon_0(r^2+a^2)}$ Both are equal and their directions are as shown in the figure. Hence net electric field $E_{+q}= \left[ -(E_{+q}+E_{-q})\cos\theta \right] \hat{p}$ $E_p=-\;\frac{2qa}{4\pi\varepsilon_0(r^2+a^2)^{\frac{3}{2}}} \hat{p}$ (ii) Stable equilibrium, $\theta = 0^{\circ}$