We have examined magnetic field data from POLAR MFE on May 11, 1999, when the solar wind density was well below 1 cm-3 and the IMF was generally weakly northward. The data on the event day are compared with those in the control day of May 14, when the solar wind density was normal and the IMF conditions were similar. The Polar orbit was nearly on the noon-midnight meridian plane on both days. When the Polar magnetic data are compared with the IGRF model without external contributions, the residuals are much smaller on May 11 than on May 14. Thus, the magnetosphere was much more dipolar then usual when the solar wind is unusually tenuous. However, the ring current did not disappear even with the extremely low solar wind mass flux on May 11. In the inner magnetosphere, the residual of the magnetic field was dominated by a ring current contribution. The magnetic field data agreed well with the Tsyganenko 1996 model with a ring current on May 11. The model ring current needed to best fit the data was stronger than that suggested by the Dst index, which provides a way to calibrate the ring current strength and the Dst index. This suggests that the quiet time ring current may be stronger than that currently in the Tsyganenko  model. Weak field aligned currents were present on May 11 and their strength was similar to those observed on May 14, as expected for northward IMF. We conclude that the field-aligned currents are controlled mainly by the IMF direction and affected very little by the solar wind dynamic pressure. The cusp signature of depressed magnetic field, normally seen by POLAR when passing through the high altitude polar cusp, was not seen on May 11, indicating that the energy density of the plasma entering the cusp was much smaller than usual.