We present hydromagnetic equilibrium configurations for the nonrotating ''pole-on'' magnetosphere of Uranus. According to a plasma supply mechanism proposed by Cheng (1984) we assume that charged particle sputtering of the water-ice covered moons of Uranus provides a continuous internal plasma source to the Uranian magnetosphere. We assume further that (1) dynamical changes of the magnetosphere are quasi-static, (2) the internal plasma source fills the Uranian magnetosphere in a homologous manner, and (3) the plasma residence time within the magnetospheric cavity is long enough to allow the Uranian magnetosphere to evolve from a vacuum configuration toward a plasma-dominated equilibrium. With these assumptions, we calculated configurational changes of Uranus's magnetosphere, given the amount of the thermal plasma pressure as a free parameter. In order to include Uranus's dipole in the equilibrium calculations the homogeneous Grad-Shafranov equation for cylindrically symmetric magnetospheres has been complemented by an inhomogeneous source term. We derived linear analytic solutions to the inhomogeneous problem. We found that a plasma ring forms near the equatorial plane of the planet when the thermal pressure reaches about 75% of the maximum amount that would lead to a Harris sheet magnetotail configuration. The appearance of a plasma ring is due to the particular pole-on orientation of Uranus's dipole; such a ring would not exist in an earth-type equilibrium magnetosphere.