Question: Consider two opposite charges, of magnitudes q and −q, separated by the vector d. Compute the scalar potential at all points in space, in the limit in which q becomes very large and d very small, with p ≡ qd kept constant.

My attempt: So I have picked a general point r = $(x,y,z)^T$ and labelled the origin at the point charge q.

Then I have taken the formula for an electric potential:

$$ \phi(\mathbb{r})= \frac{1}{4\pi\epsilon_{0}} (\frac{q} {\mathbb{|r|}} -\frac{q}{|\mathbb{r} - \mathbb{d}|}) $$

However I'm not sure how to manipulate this further to reach a point where I can use p ≡ qd is constant. Any help would be greatly appreciated.

Question: Consider two opposite charges, of magnitudes $q$ and $−q$, separated by the vector $\vec{d}$. 
Compute the scalar potential at all points in space, in the limit in which $q$ becomes very large and d very small, with $\vec{p}\equiv q\vec{d}$ kept constant.

My attempt: So I have picked a general point $\vec{r} = (x,y,z)^T$ and labelled the origin at the point charge $q$.

Then I have taken the formula for an electric potential:

$$ \phi(\mathbb{r})= \frac{1}{4\pi\epsilon_{0}} \left(\frac{q} {\mathbb{|\vec{r}|}} -\frac{q}{|\mathbb{\vec{r}} - \mathbb{\vec{d}}|}\right) $$

However I'm not sure how to manipulate this further to reach a point where I can use $\vec{p}\equiv q\vec{d}$ is constant. Any help would be greatly appreciated.