  For a Coulomb system contained in a domain \Lambda, the dielectric
susceptibility tensor \chi_{\Lambda} is defined as relating the average
polarization in the system to a constant applied electric field, in the linear
limit. According to the phenomenological laws of macroscopic electrostatics,
\chi_{\Lambda} depends on the specific shape of the domain \Lambda. In this
paper we derive, using the methods of equilibrium statistical mechanics in both
canonical and grand-canonical ensembles, the shape dependence of \chi_{\Lambda}
and the corresponding finite-size corrections to the thermodynamic limit, for a
class of general \nu-dimensional (\nu\ge 2) Coulomb systems, of ellipsoidal
shape, being in the conducting state. The microscopic derivation is based on a
general principle: the total force acting on a system in thermal equilibrium is
zero. The results are checked in the Debye-H\"uckel limit. The paper is a
generalization of a previous one [L. \v{S}amaj, J. Stat. Phys. 100:949 (2000)],
dealing with the special case of a one-component plasma in two dimensions. In
that case, the validity of the presented formalism has already been verified at
the exactly solvable (dimensionless) coupling \Gamma = 2.
