 Neutral cylindrical cell model

Confine the counterions of a uniformly charged infinite cylinder within a coaxial cylinder of radius $R$, with total mobile line charge $\lambda$. The electric field vanishes at $R$, while its surface value at $a$ is fixed by the bare line charge. This gives $a{\varphi }^{\prime }(a)=2\lambda /ϵ$ and $R{\varphi }^{\prime }(R)=0$ in Gaussian units. Sending $R/a\to \infty$ defines the infinite-dilution limit of cylindrical counterions.