The spectral properties of low frequency electrostatic waves in the polar cap E region over northern Scandinavia were studied experimentally by instruments on the Rocket and Scatter Experiment (ROSE) rockets. Fluctuations in plasma density were detected as well as potential differences between boom-mounted probes. By comparison of the spectral index for fluctuations in the potential signal and plasma density, evidence is obtained for deviations from Boltzmann distributions in the electron dynamics, which would predict fluctuations in density and potential to be proportional, with the same constant of proportionality at all frequencies. Investigations of the cross correlation between density and potential signals demonstrate that the phase between the two increases approximately linearly with frequency. Empirical relations are obtained for the frequency dependence of the amplitude and phase relations between fluctuations in density and potential. ¿ 2000 American Geophysical Union