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The grand potential of a classical Coulomb system has universal finite-sizecorrections similar to the ones which occur in the free energy of a simplecritical system : the massless Gaussian field. Here, the Coulomb system isassumed to be confined by walls made of an ideal conductor material; thischoice corresponds to simple (Dirichlet) boundary conditions for the Gaussianfield. For a $d$-dimensional ($d>or=2$) Coulomb system confined in a slab ofthickness $W$, the grand potential (in units of $kT$) per unit area has theuniversal term $Gamma(d/2) zeta(d)/2^d pi^{d/2}W^{d-1}$. For a two-dimensionalCoulomb system confined in a disk of radius $R$, the grand potential (in unitsof $kT$) has the universal term $(1/6) ln R$. These results, of generalvalidity, are checked on two-dimensional solvable models.Comment: 26 pages,TE

Coulomb systems seen as critical systems: Ideal conductor boundaries