This paper treats the magnetic properties of the quiescent prominence as a part of the larger coronal structure made up of the prominence, cavity, and helmet dome. A rigorous analysis of the mechanical support of a vertical prominence sheet suspended in equilibrium by magnetic fields in uniform gravity shows that the finite vertical extension of the prominence sheet has an important dynamic constraint. For the inverse topology with the prominence magnetic field pointing opposite to the held implied by the bipolar photospheric region below, this constraint requires the prominence sheet to be embedded in a horizontal, nearly force-free, magnetic flux rope which crucially supports a part of the prominence weight by current attraction from above. A similar analysis of the support problem is carried out for the prominence in the normal topology in which both prominence and photospheric magnetic fields point in the same sense. Starting with the observation that most prominences are of the inverse topology, a recent model is extended to show that this topology implies that the prominence sits in a two-flux magnetic system, one flux connecting the bipolar magnetic sources in the photosphere below and the other forming a rope which embeds the prominence and runs above and parallel to the photospheric polarity-inversion line. This model physically relates several pieces of well-known but hitherto disjoint observations. The prominence flux rope manifests itself as the cavity in the corona and as the filament channel in the chromosphere. The chromospheric fibril patterns associated with prominences and filament channels can, for the first time, be modeled faithfully. Several physical implications on the origin of the prominence and questions deriving from the results are discussed.