We report the results of parsec-scale, multi-frequency VLBA observations of the core region of 3C 279 in Stokes I, linear polarization, and circular polarization. These full polarization spectra are modeled by radiative transfer simulations to constrain the magnetic field and particle properties of the parsec-scale jet in 3C 279. The polarization properties of the core region, including the amount of linear polarization, the amount and sign of Faraday rotation, and the amount and sign of circular polarization can be explained by a consistent physical picture. The base of the jet is modeled as an inhomogeneous Blandford-Konigl style conical jet dominated by a vector-ordered poloidal magnetic field along the jet axis, and we estimate its net magnetic flux. This poloidal field is responsible for the linear and circular polarization from this inhomogeneous component. Farther down the jet the magnetic field in two homogeneous features is dominated by local shocks and a smaller fraction of vector-ordered poloidal field remains along the jet axis. In this picture, we find the jet to be kinetically dominated by protons with the radiating particles being dominated by electrons at an approximate fraction of >~ 75%. Based on the amounts of Faraday conversion deduced for the homogeneous components, we find a plausible range for the lower cutoff in the relativistic particle energy spectrum to be 5 <~ gamma_l <~ 35. The physical picture described here is not unique if the observed Faraday rotation and depolarization occur in screens external to the jet; however, we find the joint explanation of linear and circular polarization observations from a single set of magnetic fields and particle properties internal to the jet to be compelling evidence for this picture. (Abridged)
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