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# PowerPedia:Energy-dependent Electromagnetic Wave

## Types of electromagnetic waves

Electromagnetic waves can be divided into three types depending on the nature of the energetic processes that occur in them.

### Notations and formulas

Sinusoidal traveling electromagnetic wave:
$E=E_o \cdot \sin(vt-kz), H=H_o \cdot \sin(vt-kz)$,
Standing electromagnetic wave:
$E=E_o \cdot \sin(kz) \cdot \sin(vt), H=H_o \cdot \cos(kz) \cdot \cos(vt)$,
Energy-dependent standing electromagnetic wave:
$E=E_o \cdot \sin(kz) \cdot \sin(vt), H=H_o \cdot \sin(kz) \cdot \sin(vt)$,
Eo - amplitude of oscillations for electric intensity field,
Ho - amplitude of oscillations for magnetic intensity field,
E - oscillations for electric intensity field,
H - oscillations for magnetic intensity field,
k, v - constants,
z - coordinate,
t - time.

### Traveling electromagnetic wave

There exist traveling electromagnetic waves, i.e. an electromagnetic field spreading in space and in time. Electromagnetic waves spread in a substance with a finite speed. In a traveling electromagnetic wave we see mutual transformations of electric and magnetic fields. in any point electromagnetic energy varies in time from zero to a certain maximum. In this way electromagnetic wave transfers energy. When it spreads with the speed v a flow of electromagnetic energy is generated. The energy flow in an electromagnetic wave may be set with the aid of Pointing’s vector, whose direction coincides with the direction of wave spreading. The energy flow goes from the source of traveling electromagnetic wave.

### Standing Electromagnetic Wave

A standing electromagnetic wave (which may be obtained by adding together two waves – one falling on an ideal mirror, another reflected from it. In this wave the intensity in all points changes with time with equal frequency and in one phase, and the amplitude changes according to harmonic law depending on the coordinate Z. Ooscillations E and H are shifted in phase by a quarter of period. It means that when the electric field intensity E reaches maximum, the values of H are equal to zero. the flow density of electromagnetic waves energy is determined by Pointing’s vector. As in the nodes the values E or H are equal to zero, it means that in this points the flow is equal to zero. The nodes for E coincide with antinodes for H and vice verse. This means that through nodes and antinodes there is no flow of electromagnetic energy. However, as E and H in other points are variable in time, we may conclude that with time energy moves between adjoining nodes and antinodes. Here we see the conversion of electric field energy into magnetic field energy and back. The total energy enclosed between two adjoining nodes and antinodes remains constant. The preservation of standing wave does not need any inflow of external energy.

### Energy-dependent Standing Electromagnetic Wave [1, 2]

In this wave the oscillations of electric and magnetic fields are in-phased along the axes ox and oz (if this condition is met, other combinations of Sin и Cos may be possible). The flow density of electromagnetic waves energy is determined by Pointing’s vector. As in the nodes E and H are equal to zero then in these points the flow is also equal to zero. It means that through the nodes there is no electromagnetic energy flow. Evidently, the energy periodically varies in time from zero to a certain maximum. Consequently, for the existence of energy-dependent standing wave the energy must get to it from the outside and transform into electromagnetic energy.

## Experiments

Experimentally the existence of energy-dependent standing waves is confirmed by observing the so called magnetic walls

## The formation of energy-dependent standing waves

In [2,3] is shown that at the change of permanent magnets induction in a given point of space (for example, at rotation) a standing electromagnetic wave is generated. More exactly, in the direction of axis ох (perpendicular to the magnet's face) there appear variations of magnetic intensity as the result of a "splash" of charges on the magnet face surface. Their amplitude depends on х, which means that along the axis ох there appears a electromagnetic field which represents a standing electromagnetic wave. This follows directly from the solution of symmetric Maxwell Equations with Magnetic Charges. This is acceptable, beсause the cylindrical long permanent magnet face may be treated as the bearer of magnetic charges whose density is equal to density of induction.

## The conditions of energy-dependent wave existence

In [2,4,5] proves the following.

• Instantaneous value of induction for the considered wave changes in sinusoidal mode with the time. The wave's instantaneous energy (proportional to square of induction) changes periodically from zero to a certain maximum.
• When the wave's instantaneous energy grows, the instantaneous heat energy of medium 1 (the region of existence of the wave) declines due to magnetic polarization of the air molecules. In this way occurs the transformation of heat energy into magnetic energy.
• When the wave's instantaneous energy declines, the instantaneous heat energy grows. The increase of heat energy of medium 1 occurs due to the heat inflow from the external medium 2, which depolarizes the air molecules. In this way occurs the transformation of magnetic energy into heat energy. It is possible because there exists a difference of temperatures between medium 1 and medium 2.
• Average density of a medium's energy is proportional to its temperature. Average energy density of medium 1 is less than average energy density of medium 2 by a value proportional to the difference of temperatures. This value is also equal to the average energy density of magnetic wave.
• Full magnetic energy of a wave (in all domain of its existence) is equal to the energy of heat flow – just like in an ordinary electromagnetic wave magnetic energy is equal to electric energy.
• The energy of heat flow from medium 2 cannot exceed the magnetic energy of the wave. This exceeding energy may be spent on
- the extension of the wave's existence domain;
- refilling the wave energy, if it partially transforms into other kinds of energy, for instance, into electric energy of a coil entered into the wave domain.
• In the latter case the wave behaves as a heat pump. An important distinction, however, lies in the fact that for such heat pump functioning there is no need for an additional energy source.
• Thus, in an energy-dependent electromagnetic wave the magnetic polarization of the air dipoles is observed, which consists in dipoles polarization by Lorentz forces in the direction perpendicular to the vector of heat speed with which they are moving in the area of this wave. Such polarization limits significantly the degrees of freedom of the air molecules, and this leads to decrease of internal air energy.
• The inflow of heat energy from the environment depolarizes the air molecules. Depolarization means the air molecules rotation under the influence of the heat movement of the surrounding molecules. Such rotation of a molecule - electric dipole creates a magnetic field directed opposite to the magnetic field that polarized this molecule.
• So a oscillatory process takes place: electric dipoles of the air are polarized by magnetic field and the air cools, and then the heat flow (that had arisen due to the air cooling) depolarizes the molecules, which in the process of depolarization increase the induction of magnetic field, and so on.
• The changing electromagnetic wave energy in the sum with changing internal energy of the air fulfill the law of energy conservation. The conditions of this law fulfillment are exactly the conditions of this wave existence. The consequence of this condition is the temperature lowering in the wave area. This phenomenon was observed experimentally.
• The energy-dependent electromagnetic wave keeps existing and propagating as long as this wave exchanges energy with the environment in which this wave exists.

## Longitudinal wave

The energy-dependent electromagnetic wave keeps existing as this wave exchanges energy with the environment in which this wave exists. The wave velocity in this case is 2.5 m/sec (by estimate of [2]). The thermal flow from the environment maintains a certain level of energy.
The thermal flow power grows till the moment when this power becomes equal to the power conveyed by the wave to the generator (this power is lost in the process of area's expansion, due to the inevitable absorption of the wave's energy by the medium 1). With the growth of thermal flow power the radius and the volume of the wave area also grows. There is a formula:

$P \approx 1.3 \triangle T \cdot R^3$,

where

$~ P$ - heat flux equal to the power generator,
$~ R$ - radius of medium 1,
$~ \triangle T$ - temperature decrease near the generator.

The temperature in a certain point of wave area and the induction amplitude associated with this temperature decrease with the distance from this point to generator.
Thus, the wave propagates in the direction of the induction vector, and the value of this vector (as the amplitude of the fluctuating induction) decreases. Such process characterizes a longitudinal wave. This is why the energy depending wave is a longitudinal one. Simultaneously it remains a standing wave, because the wave's nodes do not move (only their quantity increases). The wave velocity in this case is determined by the inertia of the generator (more exactly, by the speed of generator's load power change).
Note that the theory of electromagnetic waves admits the existence of longitudinal waves in the medium (but not in vacuum), and, in particular, the existence of electrical (wthout the magnetic component) longitudinal waves. In our case a magnetic (without electrical component) wave is being observed.

## References

1. Khmelnik S.I., Khmelnik M.I. To the Question of «magnetic walls» in Roschin-Godin experiments. "Papers of Independent Authors", publ. «DNA», printed in USA, Lulu Inc., ID 2221873, Israel-Russia, 2008, iss. 8, ISBN 978-1-4357-1642-1 (in Russian), http://dna.izdatelstwo.com/volum/2221873.pdf
2. Khmelnik S.I. Energy processes in free-full electromagnetic generators. Publisher by “MiC”, printed in USA, Lulu Inc., ID 10292524, Israel, 2011, second edition, ISBN 978-1-257-08919-2, USA, Lulu Inc., ID 10292524
3. Khmelnik S.I. Longitudinal electromagnetic wave as a consequence of the integration of Maxwell's equations. "Papers of Independent Authors", publ. «DNA», printed in USA, Lulu Inc., ID 6334835, Israel-Russia, 2009, iss. 11, ISBN 978-0-557-05831-0 (in Russian), http://dna.izdatelstwo.com/volum/6334835.pdf
4. Khmelnik S.I., Khmelnik M.I. The existence conditions of longitudinal energy-dependent electromagnetic wave. "Papers of Independent Authors", publ. «DNA», printed in USA, Lulu Inc., ID 7157429, Israel-Russia, 2009, iss. 12, ISBN 978-0-557-07401-3, (in Russian), http://dna.izdatelstwo.com/volum/7157429.pdf
5. Khmelnik S.I., Khmelnik M.I. More about the conditions of existence of longitudinal energy- dependent electromagnetic wave. "Papers of Independent Authors", publ. «DNA», printed in USA, Lulu Inc., ID 7803286, Israel-Russia, 2009, iss. 13, ISBN 978-0-557-18185-8 (in Russian), http://dna.izdatelstwo.com/volum/7803286.pdf

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