Let an electric dipole $A B$ is situated in a vacuum. Let $p$ be a point at a distance $r$ from the dipole when $p$ is electric dipole moment, then electric field intensity is given by
$E=\frac{1}{4 \,\pi \,\varepsilon_{0}} \frac{2 p r}{\left(r^{2}-l^{2}\right)^{2}}$
If $l$ is very small compared to $r(l<< r)$, then $l^{2}$ may be neglected in comparison to $r^{2}$. Then
$ E=\frac{1}{4 \,\pi \,\varepsilon_{0}}\, \frac{2 p}{r^{3}} N / C $
$\Rightarrow \, E \propto \frac{1}{r^{3}}$
