We show that, for a reasonable range of choices of ionospheric parameters for Uranus and of solar wind parameters at Uranus orbit, the rings of Uranus are for the most part immersed in the solar wind if Uranus lacks an intrinsic magnetic field. If Uranus ionosphere forms the obstacle to the solar wind, then very low upper bounds (1--4 nT) may be obtained for an intrinsic magnetic field at the polar 1 bar level. In addition, from an examination of the geometric albedos of Jupiter's and of Saturn's rings and moons, we show tht these bodies have characteristically either high albedos in a low radiation environment or low albedos at a high radiation environment. The only exceptions to this pattern are geologically active moons such as Io. We suggest that the moons of Uranus possess a significantly lower albedo than those in the low radiation environment of Saturn and that the rings of Uranus are black because the rings and moons of Uranus may be relatively depleted in their surface stores of ices. In this scenario, immersion of the rings of Uranus in the solar wind would provide a loss mechanism for ring ices and produce the black rings observed. The black rings of Uranus may thus imply the lack of an intrinsic Uranus magnetic field.