Effects of Shielding and Guarding Electrodes on Electrostatic-Force Balance Measurements in a Coaxial Cylindrical Capacitor

This article reports on a numerical simulation using the finite-element method (FEM) on the effects of shielding and guarding electrodes of a vacuum-gap capacitor using coaxial cylindrical electrodes on the capacitance gradient measurements for an electrostatic-force balance apparatus. The electric field of the coaxial cylindrical capacitor with a shielding electrode was computed when the capacitor was open or semi-closed using a grounded-guarding electrode placed around the positive-terminal electrode. The capacitance and unwanted capacitive coefficients between the positive-terminal and grounded electrodes were calculated using the computed electric fields. The FEM results suggested that, under given conditions, there is an optimal overlapping length in the longitudinal direction of the coaxial cylindrical electrodes of the capacitor. This is based on the linearity of the capacitance gradient and parasitic capacitances that resulted in an error in the determination of the capacitance gradient using a three-terminal capacitance bridge in the electrostatic-force balance measurement. The FEM simulations also suggested that the use of a guarding electrode reduced the unwanted parasitic capacitive coefficients between the terminal and shielding electrodes, whereas the guarding electrode had no significant impact on the linearity of the capacitance gradient. Experiments were also conducted to confirm the consistency of the FEM results, which showed good agreement with the measurement uncertainties.