An electric dipole (dipole moment $\vec{p} = p \, \hat{i}$), consisting of charges $-q$ and $q$, separated by distance $2a$, is placed along the $x$-axis, with its center at the origin. Show that the potential $V$, due to this dipole, at a point $x$ ($x \gg a$) is equal to:
\[
V = \frac{1}{4\pi\epsilon_0} \cdot \frac{\vec{p} \cdot \hat{i}}{x^2}.
\]