A rotation-dominated model of the Jovian magnetosphere is constructed in which the plasma current distribution is dynamically consistent with the magnetic field. We assume an ionospheric plasma source with no pitch angle scattering, magnetically aligned rotation, loss-free radial transport through flux tube interchange diffusion, and a static balance between centrifugal force and magnetic stress. From these assumptions a dynamical equation is derived for a self-consistent magnetic field configuration having a single adjustable parameter that is related to the plasma source strength. An iterative numerical method is used to solve this equation. The self-consistent field resembles a radially distorted dipole field and does not resemble the flat 'magnetodisc' configuration that has often been inferred from the Pioneer data. The implication is that such a magnetodisc field would require an equatorial plasma source (for example, the Galilean satellites) rather than a source at the feet of the field lines. The centrifugal force opens the field at a radial distance approximately 10% greater than that expected for a pure dipole field for a given source strength. For expected source strengths this opening radius is found to lie in the range 40-75 Rj.