$$\require{cancel}$$
The field at a distance r from a long charged rod carrying a charge λ coulombs per metre is $$\frac{\lambda}{2\pi\epsilon_0 r}$$. Therefore the potential difference between two points at distances a 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}