\(V_A=\frac{k q}{r}+\frac{k(-q)}{d-r}\)

\(V_B=\frac{-k q}{r}+\frac{k q}{d-r}\)

\(V=V_A-V_B=\frac{2 k q}{r}-\frac{2 k q}{d-r}=\frac{2 q}{4 \pi \varepsilon_0}\left[\frac{1}{r}-\frac{1}{d-r}\right]\)

\(V=\frac{q}{2 \pi \varepsilon_0}\left[\frac{d-2 r}{(r)(d-r)}\right]\)

\(d \gg r\)

\(V=\frac{q}{2 \pi \varepsilon_0}\)

\(\frac{q}{V}=2 \pi \varepsilon_0 r=C\)