[en] The collective electric excitations in layered two-dimensional electron gases supported by an insulating substrate induced by a moving charged particle are investigated using linearized quantum hydrodynamic (LQHD) theory. General expressions of the induced potential, the stopping and image forces acting on the incident particle are derived by selecting appropriate boundary conditions. The influence of dielectric constant on induced potential, the stopping and image forces is discussed. Numerical results indicate that the substrate property has little influence on the induced electric field at smaller incident particle speed due to the weaker polarized electric field but the influence is remarkable at higher speed due to the stronger polarized electric field; the smaller the distance between the incident charged particle and the electron gas plane connected to the substrate, the more the influence of dielectric constant on relevant physics properties. (authors)