The Helmholtz's equations and boundary conditions are set up for study on electrical field induced by oscillation dipole source in layered media from the Maxwell's equations and introducing the Hertz electric vector potential.The equations for calculation of electrical field on surface of the layered media are obtained.The integral equations for calculation of electric field on the surface of the layered media with a fault are derived from the Maxwell's equations and introducing the Green's tensor.The equations can be used in numerical simulation of geoelectric field change on earth surface.