Magnetic waves
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The magnetic waves are the longitudinal mechanical waves within the aetheric continuum. Since the magnetic field in any case is produced by the matter, the magnetic waves do not exist in the absolute vacuum.
Since the density is proportional to the magnitude of the magnetic flux density, the magnetic field can have any direction with respect to the wave direction. In addition to the usual transversal electromagnetic waves of any polarization, the matter can support the waves with the longitudinal magnetic field oscillations.
The magnetic waves frequency is 2 times lower than the frequency of waves of density and pressure, according to ("Mass and inertia", 2):
\[\delta B=B_A\cos(\omega t-kx)\]
\[\delta \rho=2\rho_A\cos^2(\omega t-kx)=\rho_A(\cos 2(\omega t-kx)+1)\]
The phase velocity ("Waves", 5) of the magnetic waves as well as any other longitudinal waves is:
\[v=\sqrt{\frac{P_A}{\rho_A}}=\frac{c}{n}=\frac{c}{\sqrt{\mu\varepsilon}}\]
\(n\) is the refractive index at a certain frequency.
Similarly with "Pressure of aether", the static pressure of a wave is \(\rho с^2\) (\(с\) is the speed of light in the matter).
There are the following phenomena due to the magnetic waves:
- Scattering and diffraction of the electromagnetic radiation and of the elementary particles.
- Phonons of Debye's theory of heat capacity, which differ from the photons by the third degree of freedom.
- Propagation of the electric potential and current over a conductor at speed many times higher than the charge carriers speed.
- "Gravitational" waves.
The electrical waves within a conductors emerge due to the magnetic waves. The definitions of inductance and capacitance provide a system of Heaviside equations for the one-dimensional perfect conductor, known as telegrapher’s equations:
\[\frac{\partial J}{\partial x}=-C\frac{\partial U}{\partial t}\tag{1}\]
\[\frac{\partial U}{\partial x}=-L\frac{\partial J}{\partial t}\tag{2 – SI}\]
\[c^2\frac{\partial U}{\partial x}=-L\frac{\partial J}{\partial t}\tag{2 – CGS, Sim.}\]
where \(L\) is a distributed inductance per unit length;
\(C\) is a distributed capacitance per unit length.
The one-dimensional conductor here stands for the propagation medium of the electromagnetic field as a function of time and position along the conductor. The conductor cross-section may have any configuration: a single wire, a twisted pair, a coaxial cable, etc.
The wave equations, which follow from telegrapher’s equations (1, 2), are: \[\frac{\partial^2 U}{\partial t^2}=\frac{1}{LC}\frac{\partial^2 U}{\partial x^2}\;\;\;\;\;\frac{\partial^2 J}{\partial t^2}=\frac{1}{LC}\frac{\partial^2 J}{\partial x^2}\tag{3 – SI}\] \[\frac{\partial^2 U}{\partial t^2}=\frac{c^2}{LC}\frac{\partial^2 U}{\partial x^2}\;\;\;\;\;\frac{\partial^2 J}{\partial t^2}=\frac{c^2}{LC}\frac{\partial^2 U}{\partial x^2}\tag{3 – CGS, Sim.}\] The phase difference between the voltage and current waves are determined by the boundary conditions.
The wave velocity: \[v=\frac{1}{\sqrt{LC}}\tag{4 - SI}\] \[v=\frac{c}{\sqrt{LC}}\tag{4 - CGS, Sim.}\] The product \(LC\) for an infinitesimally short conductor segment of length \(\Delta x\) can be written in terms of the inductance and capacitance integral definitions (SI units): \[LC=\lim_{\Delta x\to 0}\frac{1}{\Delta x^2}\frac{\int{\mathbf{\overrightarrow{B}}\mathrm{d}\mathbf{\overrightarrow{S}}}}{\oint{\mathbf{\overrightarrow{H}}\mathrm{d}\mathbf{\overrightarrow{l}}}}\frac{\oint{\mathbf{\overrightarrow{D}}\mathrm{d}\mathbf{\overrightarrow{S}}}}{\int{\mathbf{\overrightarrow{E}}\mathrm{d}\mathbf{\overrightarrow{l}}}}\tag{5}\] Assuming that the aetheric beams velocity \(\mathbf{\overrightarrow{v}}\) is constant over the conductor cross section, and its vector according to the radiation laws is perpendicular to the magnetic and electric fields: \[\Delta x\oint{\mathbf{\overrightarrow{H}}\mathrm{d}\mathbf{\overrightarrow{l}}}=\Delta x\oint{\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{D}}\mathrm{d}\mathbf{\overrightarrow{l}}}=v\oint{\mathbf{\overrightarrow{D}}\mathrm{d}\mathbf{\overrightarrow{S}}}\tag{6}\] \[\Delta x\int{\mathbf{\overrightarrow{E}}\mathrm{d}\mathbf{\overrightarrow{l}}}=\Delta x\int{\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}\mathrm{d}\mathbf{\overrightarrow{l}}}=v\int{\mathbf{\overrightarrow{B}}\mathrm{d}\mathbf{\overrightarrow{S}}}\tag{7}\]
The substitution of equations (6, 7) into (5) minimizes it\[LC=\frac{1}{v^2}\]
Thus, a magnetic wave propagates along the perfect conductor, which has the shape of a straight single wire or a coaxial cable, at speed of light in the medium.
The wave impedance of a conductor is a ratio of the AC voltage to the AC current\[Z=\sqrt{\frac{L}{C}}\tag{8 - SI}\]
\(Z=\frac{1}{c}\sqrt{\frac{L}{C}}\tag{8 - CGS, Sim.}\)
The wave impedance has the same meaning as a refractive index. The waves are reflected at the boundaries (interfaces) between the mediums with the different impedances.
Boundary impedance | \[0\] | \[Z\] | \[\infty\] |
---|---|---|---|
Boundary condition | \[U=0\] | \[J=0\] | |
Phase shift between current and voltage | +90⁰ (inductive) | 0⁰ (active) | –90⁰ (capacitive) |
Wave type | standing | running | standing |
Energy transmission | maybe into aether | point to point | maybe into aether |
Technical solution | short circuit, grounding |
impedance matching | open circuit, break |
In general, a conductor combines both the standing and running waves with an arbitrary phase shift.
The cosine of a phase difference between current and voltage determines the efficiency of power transmission, and it is known in the power industry as the power factor.
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