PX157 - B8b - potential of a point charge

\begin{aligned} V_{a} - V_{b} & = \int_{a}^{b} \frac{q}{4 π ϵ_{0} r^{2}} \hat{r} \cdot \hat{r} d r \\ = \frac{q}{4 π ϵ_{0}} \int_{r_{a}}^{r_{b}} \frac{1}{r^{2}} d r \\ = \frac{q}{4 π ϵ_{0}} (\frac{1}{r_{a}} - \frac{1}{r_{b}}) \end{aligned}

V_{a} - V (r \to \infty) = \frac{q}{4 π ϵ_{0} r_{a}}

V (r) = \frac{q}{4 π ϵ_{0} r}