= Electric dipole field
{title2=$\mathbf E=[3(\mathbf p\cdot\hat{\mathbf r})\hat{\mathbf r}-\mathbf p]/(4\pi\epsilon_0r^3)$}
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 $E_r=2p\cos\theta/(4\pi\epsilon_0r^3)$ and $E_\theta=p\sin\theta/(4\pi\epsilon_0r^3)$, giving $|\mathbf E|=p\sqrt{1+3\cos^2\theta}/(4\pi\epsilon_0r^3)$. 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>.
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