$$\require{cancel}$$
The field at a distance $$r$$ from a long charged rod carrying a charge $$λ$$ coulombs per meter is $$\frac{\lambda}{2\pi\epsilon_0 r}$$. Therefore the potential difference between two points at distances $$a \text{ and }b$$ from the rod $$(a < b)$$ is
\begin{align}V_b-V_a&=-\frac{\lambda}{2\pi\epsilon_0}\int_a^b \frac{dr}{r}. \\ \therefore V_a-V_b&=\frac{\lambda}{2\pi\epsilon_0}\ln (b/a).\tag{2.2.6} \\ \end{align}