We have derived a generalization of Poisson’s equation, a fourth-order partial differential equation, to describe the electrostatic behavior of polarizable, quadrupolar fluids. Our theory is in accord with the approach of Evangelista and Barbero. This equation was solved for the case of multipoles of arbitrary order placed at the center of a spherical cavity in a quadrupolar fluid. Our solution indicates that the quadrupolar portion of the disturbance created by an electrostatic probe in a polarizable quadrupolar fluid is localized to a distance of about a bohr, while asymptotically the fluid behaves as a polarizable medium. Internal field corrections as well as internal field gradient corrections have been computed. Fairly good agreement is found between our theory and the experimentally determined dielectric constant for carbon dioxide. The cavity model solution has been applied toward understanding the solvation of ions and dipolar molecules in supercritical carbon dioxide. We have used our theory to show that ions do not dissolve in supercritical carbon dioxide. Our theory displays improving agreement with data on the solubility of water molecules in supercritical carbon dioxide as pressure and temperature are increased. Ways to enhance agreement with experiments are suggested. We speculate on generalizations of our approach to fluids composed of higher-order multipoles, e.g., methane, whose first nonvanishing moment is an octupole.