 Electric dipole field

At distances large compared with the separation of a neutral charge pair, its electric field has the displayed leading form in terms of the electric dipole moment $\mathbf{p}$. Measure the polar angle from $\mathbf{p}$. The radial and angular components are $E_r=2p\cos \theta /(4\pi {ϵ}_0{r}^3)$ and $E_{\theta }=p\sin \theta /(4\pi {ϵ}_0{r}^3)$, giving $|\mathbf{E}|=p\sqrt{1+3{\cos }^2\theta }/(4\pi {ϵ}_0{r}^3)$. At fixed radius the polar field magnitude is twice the equatorial one. This leading neutral-pair field falls as $r^{-3}$, faster than the $r^{-2}$ electric field of an isolated point charge.