A method for measuring the interactions of charged dust particles within a three-dimensional dust cloud in a plasma is presented. The measurements have been performed with the help of gravity-driven heavy charged probe particles, which moved through a dust cloud levitating at the diffuse edge of an inductively coupled rf discharge plasma. Assuming a screened Coulomb potential surrounding each particle, both the particle charge and the effective screening length were calculated from an analysis of the elastic particle interactions for 20, 30, and 50 Pa of neon pressure. The basic parameters of the bulk discharge plasma have been diagnosed with a Langmuir probe to compare the experimental data with those deriving from different theoretical approaches. The observed discrepancies are discussed.