The charge reduction effect is studied in dense dust clouds. The saturation currents of Langmuir probes are used to derive the density of ions and electrons, which are calibrated with the plasma oscillation method. The plasma potential inside the dust cloud is measured with an emissive probe, which also yields the floating potential in a heated nonemitting mode. The presence of the dust also affects the density and the plasma potential of the ambient plasma. The ion densities inside the dust cloud and in the ambient plasma are found equal, while the electron density is reduced inside the dust cloud. The measured potentials are compared with current models. Inclusion of the bi-Maxwellian distribution of the electrons leads to an improved description in the limit of low dust density. The strong increase of the floating and cloud potential for high dust density, predicted by the constant ion density model, is not confirmed.