电磁场与电磁波第7讲静电场中的导体介质电通密度介电常数-wb...ppt

1、Field and Wave Electromagnetics 电磁场与电磁波,2012. 3. 9,2,Review,1. Fundamental Postulates of Electrostatics in Free Space,3,2. Coulombs Law,4,3. Gausss Law and Applications,Gausss law is particularly useful in determining the E-field of charge distributions with some symmetry conditions, such that the n

2、ormal component of the electric field intensity is constant over an enclosed surface. The essence of applying Gausss law lies first in the recognition of symmetry conditions and second in the suitable choice of a surface over which the normal component of E resulting from a given charge distribution

3、 is a constant. Such a surface is referred to as a Gaussian surface.,5,4. Electric Potential,6,Main topic,1. Conductors in Static Electric Field,2. Dielectrics in Static Electric Field,3. Electric Flux Density and Dielectric Constant,7,1. Conductors in Static Electric Field,Conductors, semiconductor

4、s, and insulators (or dielectrics); conductivity,Assume for the present that some positive (or negative) charges are introduced in the interior of a conductor. An electric field will be set up in the conductor, the field exerting a force on the charges and making them move away from one another. Thi

5、s movement will continue until all the charges reach the conductor surface and redistribute themselves in such a way that both the charge and the field inside vansih, then the static (equilibrium) is reached.,8,Under static conditions the E field on a conductor surface is everywhere normal to the su

6、rface. In other words, the surface of a conductor is an equipotential surface under static conditions. The normal component of the E field at a conductor/free space boundary is equal to the surface charge density on the conductor divided by the permittivity of free space.,9,静电感应现象,Now let us assume

7、that we place an isolated conductor in an electric field. The externally applied electric field exerts a force on the free electrons and causes them to move in a direction opposite to the field. One side of the conductor becomes negatively charged, and the other side becomes positively charged. We r

8、efer to such a separation of charges as induced charges. The effect of these induced charges is to produce an electric field within the conductor which is finally equal and opposite to the externally applied electric field. In other words ,the net electric field inside the conductor is zero then the

9、 equilibrium state is reached.,10,Example 3-11 P103-104,11,Dielectric molecules : polar and nonpolar molecules.,Conductor： free electrons， free charges，,Dielectric： bound charges，dielectric breakdown, dielectric strength,正负中心重合,2. Dielectrics in Static Electric Field,12,Polarization of dielectrics,d

10、isplacement polarization,orientation polarization,位移极化,取向极化,13,（a）电介质正常状态下正负电荷中心重合 （b）电介质极化状态下正负电荷对中心分离,（a）电介质正常状态下正负电荷中心重合 （b）电介质极化状态下正负电荷对中心分离,无极分子：位移极化,有极分子：取向极化（同时有微小的位移极化）,均匀极化，非均匀极化，面极化电荷，体极化电荷,14,Equivalent charge distributions of polarized dielectrics,as where n is the number of molecules pe

11、r unit volume and the numerator represents the vector sum of the induced dipole moments contained in a very small volume v. The vector P is the volume density of electric dipole moment.,The dipole moment dp of an elemental volume dv is dp=Pdv , which produces an electrostatic potential (see Eq.3-53b

12、):,15,Integrating over the volume V of the dielectric, we obtain the potential due to the polarized dielectric,Where R is the distance from the elemental volume dv to a fixed field point. In Cartesian coordinates,And it is readily verified that the gradient of 1/R with respect to the primed coordina

13、tes is,16,Hence,Recalling the vector identity,Divergence theorem, we have,and letting A=P and f=1/R, we can rewrite as,17,Comprison of the next two integrals,reveals that the electric potential (and therefore the electric field intensity also) due to a polarized dielectric may be calculated from the

14、 contributions of surface and volume charge distributions having, respectively, densities,18,These are referred to as polarization charge densities or bound-charge densities. In other words, a polarized dielectric may be replaced by an equivalent polarization surface charge density ps and an equival

15、ent polarization volume charge density p for field calculations:,3. Electric Flux Density and Dielectric Constant,We expect the electric field intensity due to a given source distribution in a dielectric to be different from that in free space. In particular, the divergence postulated must be modifi

16、ed to include the effect of p ; that is,19,Integral form,Differential form,The above Equations are the two fundamental governing differential equations for electrostatics in any medium.,The equation, another form of Gausss law, states that the total outward flux of the electric displacement (or, sim

17、ply, the total outward electric flux) over any closed surface is equal to the total free charge enclosed in the surface.,20,When the dielectric properties of the medium are linear and isotropic, the polarization is directly proportional to the electric field intensity, and the proportionality consta

18、nt is independent of the direction of the field. We write,Where e is a dimensionless quantity called electric susceptibility. We have,where, r = 1+ e = /0 , is a dimensionless constant known as the relative permittivity or the dielectric constant of the medium. The coefficient = 0r is the absolute permittivity (often called simply permittivity) of the medium and is measured in farads per meter (F/m). Air has a dielectric constant of 1.00059; hence its permittiv