  After a brief review of previous work, two exactly solvable two-dimensional
models of a finite Coulomb fluid in a disc are studied. The charge correlation
function near the boundary circle is computed. When the disc radius is large
compared to the bulk correlation length, a correlation function of the surface
charge density can be defined. It is checked, on the solvable models, that this
correlation function does have the generic long-range behaviour, decaying as
the inverse square distance, predicted by macroscopic electrostatics. In the
case of a two-component plasma (Coulomb fluid made of two species of particles
of opposite charges), the density correlation function on the boundary circle
itself is conjectured to have a temperature-independent behaviour, decaying as
the -4 power of the distance.
