Both the Q3 model (dipole and quadrupole) and OCT model (Q3 plus octupole) of Uranus' magnetic field within 5 RU are expressed in α and β (Euler potentials) coordinate systems. By using the α and β coordinates of magnetic fields, we calculate the drift paths and velocities for the zero second invariant (J=0) charged particles with different total energies. Many aspects of Uranus' magnetic field are similar to those of Neptune <Ho et al., 1997>, such as a warped zero magnetic scalar potential surface and a region of local distorted magnetic field lines that gives rise to a large open area on the planetary surface when the field lines are mapped from this region. It is found that the OCT model gives a map of magnetic field coordinates on the planetary surface that better explains the Voyager 2 ultraviolet spectrometer (UVS) data of Herbert and Sandel <1994> than the Q3 model. The grossly distorted α and β contours on the planetary surface may explain the incomplete aurora circles around both magnetic poles, and weak UV emissions are found lying along a belt that coincides remarkably well with the OCT magnetic equator. In addition, tracing of drift paths of J=0 charged particles shows that the weak emission along the magnetic equator is due to the precipitation of J=0 particles, or particles with a large equatorial pitch angle. In particular, the low-energy J=0 particles tend to drift toward a planet in three concentrated regions where UV emissions are observed. ¿ 1998 American Geophysical Union