Interpretation of surface potential measurements performed with the vibrating capacitive probe of an electrostatic voltmeter

In case that the vibrating capacitive probe of an electrostatic voltmeter is facing a metallic plate of known electric potential V, which can be easily imposed by connecting it to a DC high-voltage supply, the value displayed by the instrument is equal to V. The same surface potential measurement technique is employed to characterize the charging state of insulating materials, such as films or non-woven media. The aim of the paper is to give some elements of answer to the following question: What significance can be attributed to the value displayed by the electrostatic voltmeter when the charge is non-uniformly distributed at the surface of the bodies examined by the probe and no constant surface potential can be defined? The measurements were performed for some simple experimental models that simulate surface potential non-uniformity. Thus, a copper wire, a copper rod, and two aluminium strips, connected to a high-voltage supply (V = 875 V) were located at 5 mm above a grounded metal plate. The vibrating capacitive probe was placed at various distances h above the grounded plate and at various distances x from the axial plan of the high-voltage strip/rod/wire - grounded plate system. Different V(x) curves obtained for each of the situations under study, pointing out that the value displayed by the instrument depends on the distribution of the potential across the surface examined by the probe. A commercial computer program based on the superficial charge simulation method was employed for the numerical analysis of the electric field in a simplified model of the geometric system formed by the probe, the high-voltage strip/rod/wire, and the grounded plate. The potential that anneals the electric field at the surface of the probe (to simulate its principle of operation) was calculated by an iterative method. A good agreement was found between the results of the numerical simulations and the experimental data.