The trapping of dust particles with an attendant reduction in beam lifetime and/or increased radiation rates is aperiodically observed in the Cornell Electron/positron Storage Ring CESR. A measurement of the stability of the trapped dust as a function of bunch current with a single bunch of electrons confirmed directly that the dust particles are heavier than any normal constituent of the residual gas in the vacuum chamber. The removal of individual dust particles from the beam via image charge forces were observed and the change in beam lifetime together with the current at which the dust left the beam permitted calculation of the dust mass and charge. The surface electric field of the dust particle as calculated from the experimental data agrees well with a theoretical calculation based upon an equilibrium between charging and discharging rates.