Electric field of electromagnetic

The electric field of electromagnetic radiation completes 4.00 x lO - " complete cycles in 1.00 s. What are the period and frequency of the oscillation, and what is its wavelength What is the frequency in units of cm ... 

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

We have not failed to recognize that appropriately designed (6,0) carbon and C/B/N nanotubes may display considerably enhanced nonlinear optical activity. This term refers to the response of the dipole moment of a molecule (or the polarization of bulk material) to the oscillating electric field of electromagnetic radiation.82 85 The component of the dipole moment along an axis i in the presence of an electric field e can be represented by a Taylor series ... 

Another inherent property of polyacetylene chains, associated with the highly de-locahzed rc-system, is the polarizability in an electromagnetic field. The dipole moment induced by the oscillating electric field of electromagnetic radiation may be expressed as the sum of the hnear polarizabihty and nonlinear higher terms (hy-... 

When the electric field of electromagnetic radiation interacts with a material, it induces a dipole moment in the material. The dipole moment induced per unit volume is called "polarization." At low electric fields, the inacroscopic polarization or polarization of the bulk medium. P. is linearly related to the field by the proportionality constant, knovm as the linear electric susceptibility. At high fields, typically those associated with lasers, contribution of the nonlinear (second- and... 

If a molecule is placed in the electric field of electromagnetic radiation then the electrons and protons will experience oppositely directed forces exerted by the electric field. As a result the electrons are displaced relative to the protons and the polarized molecule has an induced dipole moment caused by the... 

When electric fields of electromagnetic waves interact with a polarizable medium (dielectric) three main effects may be... 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

Near the outlet from the torch, at the end of the concentric tubes, a radio high-frequency coil produces a rapidly oscillating electromagnetic field in the flowing gas. The applied high-frequency field couples inductively with the electric fields of the electrons and ions in the plasma, hence the name inductively coupled plasma or ICP. 

To eliminate the ambiguities in the subject of electricity and magnetism, it is convenient to add charge q to the traditional I, m and t dimensions of mechanics to form the reference dimensions. In many situations permittivity S or permeabiUty ]1 is used in Heu of charge. For thermal problems temperature Tis considered as a reference dimension. Tables 2 and 3 Hst the exponents of dimensions of some common variables in the fields of electromagnetism and heat. 

A diatomic molecule placed in an electric field of the type present in an electromagnetic wave experiences an induced dipole M at any instant due to the displacement of the electrons with respect to the relatively massive nuclei under the influence of the applied field E. 

Tlie problem of particular interest in physics and chemistry is concerned with the interaction of electromagnetic radiation, and light in particular, with matter. The electric field of the radiation can directly perturb an atomic or molecular system. Then, as in the Stark effect, the energy of interaction - the perturbation - is given by... 

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

A molecule must have a permanent dipole moment to be micro-wave active. As it rotates, the changing dipole moment interacts with the oscillating electric field of the electromagnetic radiation, resulting in absorption or emission of energy. This requirement means that homonuclear molecules such as H2 are microwave inactive, but heteronuclear molecules such as SO3, S02, NO and, of course, H20 are active. 

Only those vibrations that result in a rhythmical change in the dipole moment of the molecule are observed in the IR. The alternating electric field, produced by the changing charge distribution accompanying a vibration, couples the molecule vibration with the oscillating electric field of the electromagnetic radiation. 

Figure 3.1 Creation of an oscillating dipole by interaction between the charge cloud of an atom, (a) an oscillating electric field (b) electromagnetic radiation wave.

If the field oscillates between the upper and the lower positions, the induced dipole will also oscillate with the frequency of oscillation of the field. The oscillating electric field of the electromagnetic radiation acts in a similar fashion to create an oscillating dipole in the atom or the molecule with Which it is interacting. The dipole is generated in the direction of the electric vector of the incident radiation. 

The principal interaction of an electromagnetic wave, such as visible light, with a substance is that of the electric field of the wave and the electric charges of the substance. The dielectric constant of the substance determines the magnitude of this interaction in fact, it is equal to the square of the dielectric constant ... 

Figure 18-1 Plane-polarized electromagnetic radiation of wavelength K. propagating along the x-axis. The electric field of plane-polarized light is confined to a single plane. Ordinary, unpolarized light has electric field components in all planes.

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