Relative permittivity of dielectrics from scaling relation of capacitance

A scaling relation is established between capacitance and relative permittivity for a wide range of electrode separations and relative permittivity through extensive FEM based calculations. While an electrostatic energy-based approach involving charge density distributions is found to provide a reasonable assessment of capacitance at very small and very large electrode separations in the absence of dielectric media, the scaling relation emerging from the charge distribution trends, with and without a dielectric medium, appears as an attractive alternative. Experiments with two electrode shapes, circular and rectangular, demonstrate the validity of the scaling relation. Significantly, the task of determining relative permittivity of unknown dielectrics, particularly when aspect ratios are large, is made simple by the scaling relation requiring only one measurement.