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Lets remember - the beginning of learning magnetism in schools - we imagine solenoid with an image of "magnetic field" power lines (Fig. 1).

Fig.1. Image of solenoid power lines and its illustration with iron filings.

Here is the first step outside of science: the magnetic field lines can not pass on such an intricate curves - they are along the lines of tension, i.e., in circles around the conductors. A picture on the right gives us the vector sum of the existing lines of all conductors. At the head of student information on the vector of tension is already lost , there remain only filings, placed "on power lines."

Fig.2. the real placing of power lines around the turns of selenoid.

It was necessary to present in this way (fig. 2). Between the turns of solenoid the tense is absent because of the opposite vectors. On surface of coil these vectors coincide and form irregular ovals. If instead of arrows, color the power lines by opposite vectors, we would receive same picture for solenoid also (fig. 3). In such simple way easy to explain for students the special features of solenoid, including the appearance of "edge effects", without corruption of meaning.

Fig.3. Illustration for sum of vectors of solenoid magnetic forces

If you look closely at this picture, you can see that the outside of the coil, magnetic fields are of opposite sign, i.e. at small sizes of coil, secondary (increasing) winding of a transformer we should place inside the primary winding. And inside the solenoid is no tension of opposite sign. This is the implementation of the Tesla transformer in which the output voltage exceeds the estimated 60-70%.
Figure 4 shows diagrams of the magnetic intensity inside the solenoid.

Fig.4. Diagrams of tension of magnetic field in solenoid.

   Right figure shows that the effectiveness of such a Tesla transformer is saved in a thin layer adjacent to the primary winding, it's one. We follow the idea of Nikola Tesla: the transformer must be frameless. To coil high-voltage winding with a large number of turns possible only with a very thin wire - it's two, and the coil must be stretched to accommodate a large number of turns in the thin layer is three! All of this creates the most important features of Tesla transformer.
   Meanwhile we have listed a simple misunderstanding, but whether there is a radical misconception of physics in this issue?
- Yes. There is. What theory tells you that Tesla transformer winning is directly connected to the wire diameter of the primary winding? But the steepness of the decline of tension (respectively - also winning thickness of the layer) is determined by the radius of the wire

^(
1).

Yes, the wire radius is mathematically reduced , but this is the case that mathematics must be verified by logic [1] - expression (2)

^(
2).

allow to consider an impossible combination, when the magnetic field moves from the airspace into the metal. And with such a combination not only changes the permeability of the medium, thus changing the current value determined by the flow of electrons within the specified section of the conductor. Hence, common equation (2) needs to be written in other way.

^(
3).

And how do you like approval of textbooks that the solenoid magnetic field lines have a uniform density? Assess the depth of this mistake in chart on the right in Figure 4. Tesla effect lies in the extremely narrow range of distances. Yes, by a stretch of imagination we can speak of a quasi constancy of magnetic intensity, but what is importance of effect that is not covered by science, but used by Tesla? Is it permissible to simplify the way of knowledge?
Even deeper confusion of modern physics in the examples with magnetic wires. But to go to this section, we need to tell about the nature of magnetic forces. Better understanding can be found on this animated site [2], where, very handy, device of an electron is shown.

2.Inductance

But before we should understand - what is inductance. How is created it's feature of momentum of current? As inductance and mutual induction - are parameters of formal describing the processes, that don't have physical interpretation. Enough to say, that inductance of coil (fig. 1) is relative with it's structural parameters by strange empirical formula

Fig.5. Single-layer inductance coil .

Here W - number of turns of coil, - obviously dominant parameter. But why it in second degree and how it defines inertia of processes. Inertia of bodies is born by their movement in space. Somebody need to be blind, not seeing that coil of induction recieves it's features by interaction with free electrons of nearby space. And not seeing that kinetic energy of flying body mv²/2, that enegy of induction storage element Li²/2 - are halfs of full energy (compare with E=mc²).
Enough to examine the appearence of induction in presence of "smooth" change of turns number w from 0 to 1 (Fig. 6), to be surprised by inattention of physicists.

Fig.6. Gradual acquisition of inductive behavior of conductor.

    Giving the form of turn influence only on concentration of force lines of field in the space of solenoid. Spatial electrons can absorb the energy of magnetic field, only by receiving acceleration. For this, the magnetic force should be applied on them. Their current movement velocity proportional to magnetic tension - to the current and number of turns. And number of turns raised to second degree received because that fact, that nearby turns also apply on the same volume of space, i.e. with the increase of density of magnetic lines of force.
    We also see that conception "on the same volume" is fictitious. Turns depose a little the range of magnetic field action. With taking into account of this effect, induction provides to be a function of length of the coil. And ancillary fraction in the denominator reflects the edge effects. where is summarized the action not of all turns.
Naturally arises a question: what happens with inductivity when free electrons receive big acceleration?
-Resistance of environment will decrease and it will not be able to take away half the energy of the field.
    -We can say this, simply need to change the direction of current. Therefore we receive inductive resistance of coil , that depends on the frequency of current change.