  Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall,
are studied. A general two-point charge correlation function is considered.
Valid for any fixed position of one of the points, a new relation is found
between the algebraic tail of the correlation function along the wall and the
dipole moment of that function. The relation is tested first in the
weak-coupling (Debye-H\"uckel) limit, and afterwards, for the special case of a
plain hard wall, on the exactly solvable two-dimensional two-component plasma
at coupling $\Gamma=2$, and on the two-dimensional one-component plasma at an
arbitrary even integer $\Gamma$.
