Poynting theorem

M. W. Evans et al., Vacuum energy flow and Poynting theorem from topology and gauge theory (in press). 

The volume Lis arbitrary and, from Eq. (257) standard methods [66], give the vacuum Poynting theorem... 

The Poynting theorem for the true vacuum can be developed as in Eqs. (258)-(262). The true vacuum energy (355) comes from the vacuum current in Eq. (350), which is transformed into a matter current by a minimal prescription as discussed already. This matter current in principle provides an electromotive force in a circuit. It is to be noted that the local Higgs maximum occurs at A = 0 [46], so the local Higgs minimum occurs below the zero value of A. 

On the basis of the Poynting theorem (El.18°), the energy loss of the beam with a cross-sectional area of unity in the thin film. A/, after integration of Eq. (1.25) over the volume of this film is given as [99, 101]... 

Where E is the input value of the electric field intensity, W is the width of the incident plane, f is the fi"equency of the microwave, X. is the X-point of the incident plane, is the wave length of a microwave in the waveguide, and Ej. is the wave impedance. According to the Poynting theorem ... 

The Poynting theorem expresses the conservation of energy in electromagnetism. If one takes the scalar product of Eq. (1.1.1) with E and of Eq. (1.1.2) with H, and adds the results one finds... 

This is the Poynting theorem S is the Poynting vector. The first two terms in Eq. (1.2.4) represent rate of change of the magnetic and electric energy densities... 

Energy conservation follows from Maxwell s equations. The vector identity V (a X 6) = 6 (V X a) - a (V X 6) yields the Poynting theorem in the time domain ... 

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