Classical linearized Debye–Hückel theory is formulated for a finite fluid system, of arbitrary shape, composed of rigid particles with arbitrary internal electrical structure. The multipole description is eschewed in favor of the more basic description of a particle in terms of its charge density function. This function is left arbitrary, so the particles may be charged or neutral, polar or nonpolar, etc. The theory implies that the direct correlation function c(12)=−v(12)/k T, where v(12) is the Coulomb interaction energy between the charge densities of particles 1 and 2. In the case of uncharged polar molecules, the dielectric constant may be evaluated in closed form from c(12); the result is the Langevin–Debye equation. This development removes the nonuniqueness in the original formulation of dipolar Debye–Hückel theory [J. Chem. Phys. 64, 3666 (1976)], and demonstrates that this nonuniqueness was an artifact of the multipole description rather than the mean‐field approximation. Specialization to the case of simple finite dipoles shows that the nonuniqueness is associated with premature passage to the point dipole limit.