A concentric coplanar capacitive sensor is designed for the quantitative characterization of material properties for dielectrics. The sensor output signal, transcapacitance C_T, is related to the thickness and dielectric constant of the material under test. Electrostatic Green's functions due to point charges over different dielectric structures are derived through the Hankel transform in cylindrical coordinates, given the cylindrical symmetry of the proposed sensor. Numerical implementations based on the Green's functions are presented. Benchmark experiment results are provided and excellent agreement with numerical results is observed.