  In a Coulomb fluid confined to a domain $V$, the dielectric susceptibility
tensor $\chi_V$ depends on the shape of $V$, even in the thermodynamic
$V\to\infty$ limit. This paper deals with the classical two-dimensional
one-component plasma formulated in an elliptic $V$-domain, equilibrium
statistical mechanics is used. For the dimensionless coupling constant $\Gamma
=$ even positive integer, the mapping of the plasma onto a discrete
one-dimensional anticommuting-field theory provides a new sum rule. This sum
rule confirms the limiting value of $\chi_V$ predicted by macroscopic
electrostatics and gives the finite-size correction term to $\chi_V$.
