The Tesla Currents in Electrodynamics

The paper theoretically shows that the Maxwell equations in the Lorentz gauge deal with not only inertial charged particles, but also charged particles that do not have inertia (virtual charges). Virtual charges appear on the surface of metals. Their movement is the currents of Tesla. Experiments confirming their existence are presented, and some features that reveal them. The influence of virtual currents on the process of transfer of conduction electrons in p-n junctions of semiconductor devices is especially interesting. The results obtained can change our understanding of phenomena in the microcosm.


Introduction
There are not many physicists who will argue that Maxwell's equations describe all phenomena of electromagnetism without exception.Electrodynamics cannot be considered a complete theory.In electrodynamics, there are little studied phenomena.In this paper, we consider the problem of energy transfer by one wire.The effect, discovered by Avramenko (Avramenko, Lisin, & Zaev, 1991), has existed for a long time, the scientists, however, still could not give an adequate explanation of this phenomenon.

Charges and Currents on the Metal Surface
Tesla was an ingenious experimenter.However, his experiments were not supported by equations.Therefore, the Tesla currents have a mystery to this day.Many experimenters closely approached the possibility of repeating Tesla's experiments.One of the researchers was Avramenko, who conducted a number of interesting experiments, transmitting electric energy through one wire.
The problem of explaining the Avramenko effect is not simple, so we will start from afar.In electrodynamics, the boundary conditions for the fields at the interface of two media are strictly deduced.We are interested only in conductors, so we will write down the boundary conditions for the electric and magnetic fields for the conductor surface.When the fields act on the surface of an ideal conductor, surface charges and currents ( ;  ) arise that prevent the penetration of the fields into the metal.

𝐣
= −  ×  and  =   •  , (1) where  is the electric field strength on the metal surface,  is the intensity of the magnetic field on the metal surface,  is the unit normal to the surface,  and  are surface charge density and surface current densities.
When explaining boundary conditions and surface phenomena, there is a question that is not usually considered in textbooks.Assume that electromagnetic or light waves hit the surface of the metal (Landau & Lifshitz, 2010).Suppose that the metal surface reflects electromagnetic or light waves.Then the electromagnetic fields change very quickly.What processes take place on the metal surface?Are the boundary conditions satisfied almost instantly?The authors (Avramenko, Lisin, & Zaev, 1991) avoid a direct answer to this question.They usually refer to "conduction electrons".However, the conduction electrons have a large inertia.So this explanation is rather controversial.
The fields E and H are retarded.Consequently, the surface currents and charges in formulas (1) are also retarded.Like the fields E and H, the surface charges must satisfy the wave equation, and they can move at the speed of Inside the coaxial cable fields E and H are created by moving excess positive and negative charges (Landau & Lifshitz, 2010).Let the pulse propagate along the z axis.Let us calculate some quantities: 1) The charge on the elementary segment  of the outer coaxial cylinder is  = 2  ; where   is the electric field at  = .
2) The charge on the elementary segment  of the interior coaxial cylinder is  = 2  ; where   is the electric field at  = .Hence   =   ⁄ .
Obviously, the law of charge conservation holds: We calculate the values of the surface currents in these conductors.
The surface currents of these conductors are, respectively, | | = | | =  Now we can easily calculate the rate of movement of excess charges, for example, for an internal conductor of a coaxial line.On the one hand, we have: on the other hand: (3) Comparing these expressions and taking into account that     ⁄ =   ⁄ we get:  = .Try to make the "free" conduction electron move at a similar speed!But in waveguides the phase velocity of excess charges exceeds the speed of light in a vacuum!So, the excess charges in the coaxial line move with the speed of light!This is one of the important points.Another point is that positive and negative excess charges are not born in pairs, but separately, ignoring the law of conservation of charge.Therefore, we will call such charges virtual charges.It is the virtual charges that are mainly responsible for the instantaneous fulfillment of the boundary conditions on the surface of the conductors.

Virtual Charges (Or: Surface Charges Without Inertia)
Let the electromagnetic wave fall on the surface of the conductor.We write the boundary conditions.
(3.1a)The wave excites surface currents and charges.On the one hand, the current density  satisfies the continuity equation On the other hand, we have on the surface of an ideal conductor only a common electric field  directed along the normal to the surface.Therefore, we can write: We note th Let us now

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Before we begin From our point ontains doubtf We know that t do not have ine e. without los milliammeter.T ssume that the The same reaso does not practic The authors of xperiment did description of th .2) Since we are dealing with rapidly changing phenomena, it follows from Eq. (3.2) that  = rot − grad  = 0 .( 3 .2 a ) Combining equations (3.1) and (3.2) and taking into account (3.2a) we finally obtain: So, surface charges and currents satisfy homogeneous wave equations.Let  and  are coordinates of a surface element and  =  +  .Then the solutions of these equations will be  =   −  +   +  , (3.5) apr.ccsenet.and where  is Fig Figure 6