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The phenomenon of surface charging, known as contact electrification or tribocharging, has wide-ranging applications but also notable hazards. Precisely measuring surface charge density in insulating materials is crucial for optimizing tribocharging and mitigating adverse effects. Although the vibrating capacitor method is commonly used for this purpose, its principle, designed for conductive materials, limits direct application to insulating surfaces, leaving the relationship between measured surface potential and surface charge density unclear. To address this issue, this study simulated the process of measuring the surface potential of insulating materials using Comsol simulations. It analyzed the effects of charged area size, probe height, and probe position, and utilized the spatial distribution of potential measurement values of surface point charges to derive an integral relationship between the distribution of measured surface potential values and the distribution of surface charge density. The integral relationship of surface potential distribution under different forms of surface charge density distributions calculated from this formula largely matches the numerical simulation results. Based on this, a relationship between the distribution of surface charge density and surface potential measurement values was further derived. This relationship can be used for measuring the surface charge density of insulating materials.
Fan et al. (Tue,) studied this question.