介质的边界条件（双语）.pptxVIP

Normal ComponentsConstructing a small cylindrical surface about a point on the boundary. Its height is ?h and the end face area is ?S.Then the flux of electric flux density over the cylindrical surface is equal to the amount of net free charge enclosed by the surface, that is?S D ? d S ? qeDn2?h?2? 1?SD1Let ?h ? 0 , the flux through the lateral surface will be zero.And considering ?S to be very small, one has?S D ? d S ? D2n ?S ? D1n ?SThe direction of the normal to the boundary is specified as that from dielectric ① to ② .qD2n ? D1n ? ? ?We haveS?Swhere ? S is the surface density of the free charge at the boundary.In the absence of net surface free charge, one hasD1n ? D2nThe normal components of the electric flux densities at the boundary between two dielectrics are equal. In other words, the normal components of the electric flux densities are continuous at the boundary.For linear isotropic dielectrics, we obtain?1E1n ? ? 2 E2nIn addition, we can find the relationship between the bound charges and the normal component of the electric field intensity as?S? ? ?0 ( E2n ? E1n )7. Boundary Conditions for Dielectric-conductor InterfaceElectrostatic equilibriumA state of electrostatic equilibrium.An electrostatic field cannot exist inside a conductor.The free charge in conductors must be zero, and they are only found on the surface of the conductors.A conductor in electrostatic equilibrium is an equipotential body, and the surface is an equipotential surface.Since the electrostatic field cannot exist inside a conductor, but the tangential component of electric field intensity at any boundary is continuous, and the electric field intensity must be perpendicular to the surface of the conductor, we haveen ? E ? 0E, DIf an electric field exists near to a conductor, surface electric charge ?S will be induced on the surface of the conductorenDielectricConductor? ?S?S ? en ? D orEn??? ?S?n ?Due to E ? ?? , we haven?n? ?Since there is no electrostatic field