Electromagnetic fields displacement vector

To illustrate the use of the vector operators described in the previous section, consider the equations of Maxwell. In a vacuum they provide the basic description of an electromagnetic field in terms of the vector quantifies the electric field and 9C the magnetic field The definition of the field in a dielectric medium requires the introduction of two additional quantities, the electric displacement SH and the magnetic induction. The macroscopic electromagnetic properties of the medium are then determined by Maxwell s equations, viz. 

Electric dipole radiation is the most important component involved in normal excitation of atoms and molecules. Ttu electric dipole operator has the form TejXf where e is the electronic charge in esu and xt is the displacement vector for the jth electron in the oscillating electromagnetic field. 

In ionic and partially ionic crystals optic vibrations are associated with strong electric moments and hence can interact directly with the transverse electric field of incident infrared electromagnetic radiation. In terms of the phenomenological theory of infrared dispersion, if , and D are the electric field, polarization and displacement vectors respectively, then... 

Consider a material s body in Figure 4.1 before deformation. After internal or external loading (force, thermal, electromagnetic field, gravity, etc.), the body is deformed, and may also have rigid body displacement, into the deformed spatial body shown in Figure 4.1. A material s point is defined in the Cartesian coordinate system (ei, 62, 63) by a position vector X in the undeformed body and position vector x in the deformed body u is the displacement vector. Throughout this chapter, bold face letters will represent tensors. Obviously,... 

Table 3.1. Balance equations for a polarized reactive fluid medium. H magnetic displacement vector, D electrical displacement vector, B magnetic field, E electrical field, P = D-E E electrical polarization (p per unit mass), M = B-H magnetic polarization (m per unit mass), ( ) following the motion, (2) relative to the dipoles (section 3.1), Jok diffusion flux, q heat flux, i diffusion current, p pressure tensor, pi viscous pressure tensor, chemical production rode, fi distant forces other than those due to the electromagnetic field...

The Interpretation of the electromagnetic field A (x) as the displacement vector of an extensible medium In Minkowski space Is discussed. 

Electromagnetic radiation consists of an electric vector E directed atong the displacement direction of the wave. The associated magnetic field vector H, lies perpendicular to the electric vector and perpendicular to the direction of propagation. The oscillations of the two fields are given by... 

H is the magnetic field vector and D is called the electric induction or displacement field. This equation is known as the Ampere Oersted law and shows that a magnetic field will exist near an electric current density J. The displacement field, D, is necessary to propagate electromagnetic energy through space, /has units charge area-1 t-1... 

An applied electric field can be the electric held component of an electromagnetic wave, in which case electronic excitations or other optical responses may ensue. These are the topic of the next chapter. Here, the concern is with electrostatics, specihcally, the dielectric, or insulative, properties of materials. In an electrical conductor, an applied electric held, E, produces an electric current - ions, in the case of an ionic conductor, or electrons, in the case of an electronic conductor. Electrical conductivity has already been examined in earlier chapters. In insulating solids, the topic of the current discussion, the response to an applied electric held is a static spatial displacement of the bound ions or electrons, resulting in an electrical polarization, P, or net dipole moment (charge separahon) per unit volume, which is a vector quantity. In a homogeneous linear and isotropic medium, the polarization and electric held are aligned. In an anisotropic medium, this need not be so. The fth component of the polarization is related to the jth component of the electric held by ... 

Light beams are represented by electromagnetic waves that are described in a medium by four vector fields the electric field E r, t), the magnetic field H r, t), the electric displacement field D r,t), and B r,t) the magnetic induction field (or magnetic flux density). Throughout this chapter we will use bold symbols to denote vector quantities. All field vectors are functions of position and time. In a dielectric medium they satisfy a set of coupled partial differential equations known as Maxwell s equations. In the CGS system of units, they give... 

The equations of running waves were derived in Chapter 2 (eqs. (2.8.5) and (2.8.7)). In these equations, (x, t) symbolizes the displacement of any point from its equihbrium position X in time instance t. In this chapter we have passed from mechanical to electromagnetic waves by displacement we shall now mean oscillations of the electric field strength E and those of the magnetic field H in mutually perpendicular planes (Figure 5.45). The cross line of these planes coincides with the axis of wave propagation, which coincides with a wave vector k (refer to Section 2.8.2). A plane that is determined by the vector k and the plane of E vector oscillations is a plane of oscillation. 

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