Fundamental electromagnetic constants

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

This equation derives directly from the fundamental electromagnetism relations, the Maxwell equations, and relates the electrostatic potential, yr, at any point in space with the charge density (i.e., electrical charge per unit volume), at the same point. In Equation 3.4, is a fixed charge distribution, e is the dielectric coefficient (or constant) of the medium, given by c = e e p where e, is the relative dielectric constant, and q is the vacuum permittivity. 

The smallest unit (packet) of electromagnetic energy (a photon) is related to frequency by the formula, E = hv, in which E is the energy and h is Planck s constant. Alternatively, the relation can be written, E = hc/A,. Frequency (v) is a number with units of cycles per second (cps, the number of times a wavefront passes a given point in unit time, sec ) and is given the name Hertz (Hz), Planck s constant is a fundamental number, measured in J sec or erg-sec. 

In the previous section, it was shown that the constant a must be equal to [hc in order to obtain the right quantization of the electromagnetic helicity. This implies that the topological model predicts that the fundamental charge, either electric or magnetic, has the value... 

Quantum-electrodynamics (QED) as the fundamental theory for electromagnetic interaction seems to be well understood. Numerous experiments in atomic physics as well as in high energy physics do not show any significant discrepancy between theoretical predictions and experimental results. The most striking example of agreement between theory and experiment represents the g factor of the free electron. The experimental value of g = 2.002 319 304 376 6 (87) [1] is confirmed by the calculated value of g = 2.002 319 304 307 0 (280) on the 10 11-level, where the fine structure constant as an input in the theoretical calculation was taken from the quantum Hall effect [2], Up to now uncalculated non-QED contributions play no important role. Indeed today experiment and theory of the free electron yield the most precise fine structure constant. 

Special theory of relativity introduces a fundamental measure of time through signals propagating at a speed independent from the state of uniform motion of sources and sinks. The signal corresponds to electromagnetic radiation (e.g., light). In vacuum, the speed of light is constant. 

Nowadays, spectrophotometry is regarded as an instrumental technique, based on the measurement of the absorption of electromagnetic radiation in the ultraviolet (UV, 200-380 nm), visible (VIS, 380-780 nm), and near infrared region. Inorganic analysis uses UV-VIS spectrophotometry. The UV region is used mostly in the analysis of organic compounds. Irrespective of their usefulness in quantitative analysis, spectrophotometric methods have also been utilized in fundamental studies. They are applied, for example, in the determination of the composition of chemical compounds, dissociation constants of acids and bases, or stability constants of complex compounds. 

This expression shows that a high value of s or the refractive index necessitates a large amount of absorption throughout the electromagnetic spectrum. This is the reason why crystals with a low Eg, for which the fundamental electronic absorption extends far in the infra-red, display high values of the dielectric constant, as shown in Table 3.1. There can be discrepancies in the values reported in different references for the dielectric constants s and TO because they present a small variation with energy. 

The ratio c/u is always greater than 1, and is called the index of refraction of the material (through which the wave travels at the speed u). Note that though c is popularly called the velocity of light, it is the same for any electromagnetic wave. It can be shown that c = l/ y/( Xo o)> where x0 is the permeability of free space (vacuum or air) and e0 is the permittivity of free space. x0 and e0 are fundamental constants, since they represent the properties of our universe. 

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