  A model of a finite cylindrical ion channel through a phospholipid membrane
of width $L$ separating two electrolyte reservoirs is studied. Analytical
solution of the Poisson equation is obtained for an arbitrary distribution of
ions inside the trans-membrane pore. The solution is asymptotically exact in
the limit of large ionic strength of electrolyte on the two sides of membrane.
However, even for physiological concentrations of electrolyte, the
electrostatic barrier sizes found using the theory are in excellent agreement
with the numerical solution of the Poisson equation. The analytical solution is
used to calculate the electrostatic potential energy profiles for pores
containing charged protein residues. Availability of a semi-exact interionic
potential should greatly facilitate the study of ionic transport through
nanopores and ion channels.
