The spatial factor Φ(x) of the vibratory-state MWB (‘multiple water-bag’) plasma potential Φ = Φ(x) exp (- iwt) in the vicinity of its generating electric charge rgr;(x) exp (- iwt) is proved to be the Poisson potential U(x) of ρ plus an error function ξ(x) whose magnitude can be rendered as small as desired, in relation to │Φ(x)│, by locating the recording point sufficiently close to the charge. How close this should be is independent of ρ, but depends quantitatively on the MWB model and the frequency ω, and qualitatively on whether the frequency of the vibrations is greater or less than the plasma frequency. A high vibration frequency reinforces accuracy in the Poissonian approximation. The question as to whether Φ is weaker or stronger than U(x) is tacked. Shielding efficiency is explored in the vibratory state.