A method is proposed for measuring the real part of the Clausius-Mossotti factor (Kr) of dielectrophoresis for Brownian particles based on a solution of the Smoluchowski equation using a designed polydimethysilloxane microchannel with planar hyperbolic electrodes on its glass substrate. An approximate two-dimensional spring-like dielectrophoretic force is generated in the device, and the data necessarily measured is the time evolution of the in-plane particle displacement undergoing confined Brownian motion. Validity of the measurement was checked against the zeta potentials in the literature based on the classical theory of surface conductance using polystyrene particles of size of one micron. As the dielectrophoretic force depends on Kr, which is usually unknown for bio-particles and some engineered particles, and is seldom measured; this study is important from the academic point of view and could be helpful for the manipulation and characterization of sub-micron particles using dielectrophoresis. Extension of the method to the measurement of permanent dipole moment and total polarizability of particle was developed theoretically and discussed by incorporating an optical tweezer into the present device.