The electric-field and wave experiment (EFW) on Cluster is designed to measure the electric-field and density fluctuations with sampling rates up to 36 000 samples s-1. Langmuir probe sweeps can also be made to determine the electron density and temperature. The instrument has several important capabilities. These include (1) measurements of quasi-static electric fields of amplitudes up to 700 mV m-1 with high amplitude and time resolution, (2) measurements over short periods of time of up to five simualtaneous waveforms (two electric signals and three magnetic signals from the seach coil magnetometer sensors) of a bandwidth of 4 kHz with high time resolution, (3) measurements of density fluctuations in four points with high time resolution. Among the more interesting scientific objectives of the experiment are studies of nonlinear wave phenomena that result in acceleration of plasma as well as large- and small-scale interferometric measurements. By using four spacecraft for large-scale differential measurements and several Langmuir probes on one spacecraft for small-scale interferometry, it will be possible to study motion and shape of plasma structures on a wide range of spatial and temporal scales. This paper describes the primary scientific objectives of the EFW experiment and the technical capabilities of the instrument.