Energy of electromagnetic field

The free electromagnetic waves have the transverse polarization. The longitudinal and scalar polarization are introduced in Eq(54) artificially and should vanish in the expression for any observable. This can be achieved by imposing the Lorentz condition (40). Then the contributions of the longitudinal and scalar polarizations cancel in the expressions (42), (43) for the field strength and for the energy of electromagnetic field ... 

If the effect of the temperature on reaction rate is well known, and is very easy to express, the problem is very different for effects of electromagnetic waves. What can be expected from the orienting action of electromagnetic fields at molecular levels Are electromagnetic fields able to enhance or modify collisions between reagents All these questions are raised by the use of microwaves energy in chemistry. 

FIGURE A.5 An electromagnetic field oscillates in time and space. The magnetic field is perpendicular to the electric field. The length of an arrow at any point represents the strength of the field at that point. The energy of the field is proportional to the square of the maximum height of the arrows. 

Varani K, De Mattei M, Vincenzi F, Gessi S, Merighi S, Pellati A, Ongaro A, Caruso A, Cadossi R, Borea PA (2008a) Characterization of adenosine receptors in bovine chondrocytes and fibroblast-like synoviocytes exposed to low frequency low energy pulsed electromagnetic fields. Osteoarthritis Cartilage 16(3) 292-304... 

Since the energy of the electromagnetic field fluctuates during one cycle, it is the 1 cycle-averaged energy HR that represents the energy of the field after many cycles. Hence, this is the quantity that we now proceed to quantize. We do so, in the 4 coordinate representation, by replacing the classical momenta with the operators r7 ... 

We can run the cause-effect connection the other way. The natural motions of the charges within a material will necessarily create electric fields whose time-varying spectral properties are those known from how the materials absorb the energy of applied fields (the "fluctuation-dissipation theorem"). It is the correlations between these spontaneously occurring electric fields and their source charges that create van der Waals forces. At a deeper level, we can even think of all these charge or field fluctuations as results or distortions of the electromagnetic fields that would occur spontaneously in vacuum devoid of matter. 

Formula (8.100) has a clear physical interpretation the total energy radiated out of the domain with sources of electromagnetic field, over the time period from the initial field generation until any time t, is always non-negative. Thus, the electromagnetic sources continuously radiate energy outside these. sources ... 

For example, the total energy flow of electromagnetic field through the surface Si of the domain Vi, containing domain Q (Figure 8-1), is equal to... 

Thus we see that four of the conservation equations in (24) correspond to all four conservation equations of the standard theory one is the conservation of energy (25a) (Poynting s equation), and the other three are the conservation of the three components of momentum (25b) of the standard form of electromagnetic field theory. But since (24) are eight real-number valued equations rather than four, the spinor formalism predicts more facts than the standard vector Maxwell formalism—it is a true generalization. 

The absorption cross section for x-rays in the range 100-20000 eV is determined by photoexcitation of electrons from atomic core levels. In this energy range pair production is forbidden and the weakness of electromagnetic field is such that only first order processes are important. 

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