Solution: 3D dipole at the origin with orientation in the $+x$ direction.

We proceed the same way we did for the 2D dipole. We first write the superposition of a sorce and sink with the same strength $m$ and a distance $2a$ appart from each other. Then, we take the limit $a \rightarrow 0$. In this limit process we keep the $\mu = 2ma$ constant, otherwise the the source and sink cancel out in the limit.

$$\begin{align}\phi = & \lim\limits_{a \to 0} \mbox{ } - \frac{m}{4\pi }\left( {\f... ...-\nulldelimiterspace} 2}} = - \frac{\mu }{4\pi }\frac{x}{r^3} \notag \end{align}$$

3D dipole (doublet) of moment $\mu$ at the origin oriented in the $+x$ direction.