Any, even the most exact science, should always be treated with a certain amount of humor and sound skepticism, because, after some time, literally everything can change dramatically in it, for example, the direction of current flow :) With such a mood, we approached the transformer method of energy transfer and found that in the classical explanation of this principle there are significant inconsistencies with the current theory, and the presence of additional obvious fields is not considered there at all. In this note, we will try to eliminate these uncertainties, derive our hypothesis and set up a very unusual experiment for this. And for greater certainty, we will consider here a classical transformer with a ferromagnetic core [1], in which there are no active losses.

Usually, to explain the operation of the transformer, Faraday's law of electromagnetic induction is used [2], from which it follows that with a change in the magnetic flux in the primary winding and the core, a proportional appearance of voltage in the secondary winding follows. But it's just stress. And where does the current come from, which does not lag by 90 degrees, as it should be according to all the laws of electrodynamics, but appears immediately and in proportion to the voltage? The coil itself (the secondary winding of the transformer), at the same time, turns from a reactive element into an active one! How can this be? Here we will try to answer this question, and at the same time we will decide how a conventional transformer still works.

It will not work to apply the Lorentz law [3] in a transformer with a magnetic core, because almost all magnetic lines are concentrated in this core, which means that the turns of the secondary winding are not pierced by them. This, in turn, means that the free electrons in the metal of the turns of the secondary winding are not moved by this force from their places, therefore, the Lorentz current is not formed. There remains only Faraday's law, which assumes the appearance of voltage in the secondary winding. The current should lag behind this voltage by 90 degrees, but in reality, as you know, we observe a completely different picture.

Let's look at the general formula of the Lorentz force [3]: \[ \mathbf{F} = q\, \mathbf{E} + q\, \mathbf{v} \times \mathbf{B} \tag{1}\] It has two components: electric (\(q\, \mathbf{E}\)) and magnetic (\(q\, \mathbf{v} \times \mathbf{B}\)). The magnetic component almost does not work here due to the concentration of all magnetic field lines in the core, which we mentioned earlier. And the electrical component is described by the law of electromagnetic induction, where the electric field strength \(\mathbf{E}\), in general terms, is found according to one of the Maxwell-Faraday equations [3]: \[ \operatorname{rot} \, \mathbf{E} = -{\partial {\mathbf{B}} \over \partial t} \tag{2}\] Despite the desolation of these mathematical patterns, their general meaning can still be determined. The Lorentz force arises when the magnetic field changes in time (electrical component) and in space (magnetic component). And since the time coordinate is expanded relative to the spatial coordinates by 90 degrees (details), just like the three spatial coordinates relative to each other, then in formulas (1-2) vector quantities arise with rather complex geometric relationships.

So, no matter what the wonderful electrical component (2), but in the coil of a transformer, it will simply have to first unfold the magnetic domains of the core before the current appears in it. This is the very lag of the current from the voltage in the inductance, which is described in all electrical engineering textbooks. But the current in the secondary winding of a real transformer appears along with the current in the primary, without phase lag. How?

The proposed experiment should break some stereotypes in electrodynamics, and its conclusions should confirm the model of energy transfer in a transformer proposed below. The scheme of this experiment consists of a transmitter and a receiver (Fig. 1a). The transmitter includes a sine wave generator U, an amplifier AM1 and a closed core ferrite transformer L₁. The receiver consists of L₂ coil, C2 resonant capacitor, and OS1 oscilloscope.

The generator of sinusoidal signals can be anything, and give out at least 1 V of the amplitude value at its output. Amplifier AM1 must have a balanced output to eliminate the effect of interference. In this regard, the circuit on the TDA7056B is well suited, which can be assembled, for example, so, where a voltage of 6-7 volts is applied to XS1, a sinusoidal signal of 1 V from any generator is applied to XS2, and the primary winding of the transformer L₁ is connected to XS3. In this case, the regulator R1 is set to the maximum gain in DA1.

The L₁ transformer must be wound on several ferrite rings, for example so, where its primary winding contains two turns of wire, and the secondary - 14-18 turns, the conclusions of which are closed with each other. The coil L₂ is wound on a small piece of ferrite from SV and DV receivers (4-6 cm long), with the number of turns 20-30. With the help of the capacitor C2, it is tuned to resonance with the frequency netransmitter, which can be checked with the oscilloscope OS1. Thus, it turns out that the transmitting transformer has a closed core, and the receiving coil is open.

Transformer L₁ and coil L₂ are placed perpendicular to each other (Fig. 1b), but so that the primary winding axis L₁ is parallel to the winding axis L₂, and spread over a distance of 20 cm. The transmitter starts its work, while the power consumption of the amplifier AM1 from the power supply should be about 4-5 W. We must get the receiving coil oscillations on the oscilloscope screen, despite the fact that the transmitting transformer L₁ must not radiate any fields outside. Moreover, if you connect a low-power light bulb instead of an oscilloscope, it will glow if L₁ and L₂ are brought closer to 1-2 cm. Of course, the efficiency of such energy transfer is low, but, from the point of view of the classics, it should not be here at all!

Let's consider the experiment from the point of view of classical electrodynamics. The fields outside the transformer are described by formula (2), equated to zero [4, p. 24]: \[ \operatorname{rot} \, \mathbf{E} = -{\partial {\mathbf{B}} \over \partial t} = 0 \tag{3}\] That is, outside the transformer, there should be neither a vortex electric field nor magnetic induction, which we usually observe. This fact, by the way, determines its sufficiently high efficiency and the absence of influence on the surrounding radio elements. This state of affairs works within certain limits, beyond which other effects begin, one of which is presented in the experiment. It is also confirmed by the Aharonov–Bohm effect, in which the electron experiences a force action outside the classical magnetic field [5, 6].

The magnetic field in physics appeared as a separate entity, although this is just a relativistic effect from the movement of the electric field [7,8]. However, since this field has unique characteristics, it is more convenient to put it in a separate category, which was done by physicists. But when two magnetic fields interact, under certain conditions, one more entity can be formed - the second magnetic field [4,9], which also has a number of unusual characteristics. It is also called a scalar magnetic field (SMF).

The SMF is formed in two cases: when a bias current flows and when ordinary magnetic fields with the same poles collide [9, 10]. Together, these two fields can form a scalar sum of vectors. In fact, in any inductor, when current flows through its turns, both fields are formed, but with different proportions. For example, in a conventional cylindrical coil, the classical magnetic field is more pronounced, and in the flat Tesla coil - SMF.

Next, we need one of the properties of the SMF - to show an electric charge in matter. If this is a biological object, then such a field restores the charge of erythrocytes, which increases their mobility, this is where its healing effect comes from [11]. Also, the effect of SMF on bacterial growth has been experimentally confirmed [12]. In semiconductors and conductors, this field induces electrical charges, which usually manifests itself as a negative effect, leading to various failures, shutdowns and even equipment breakdowns, pickups in its circuits, and incorrect readings of oscilloscopes when measuring it. Moreover, such phenomena are observed not only with dynamic, but also with static SMF, which cannot happen with a classical magnetic field.

Returning to the transformer, we see the following picture. When voltage appears on its primary winding, on the secondary winding, according to the law of electromagnetic induction, an EMF is induced, proportional to the ratio of the turns of these windings. But the electric charges in the secondary winding are those which appear immediately, and not those that must still have time to unfold the domains of the core, and because of which the inductance is a reactive element, - arise due to the presence of the SMF there. So, there is an electromotive force in the secondary winding, there are also charges. EMF moves these charges, which is the reason for the current to appear simultaneously with the voltage in the secondary winding of the transformer!

It remains to figure out due to what in the transformin general, the SMF arises. It all depends on the load in the secondary circuit. When the transformer is not loaded, there is no current in its windings, which means that there is no collision of the magnetic fields of the primary and secondary windings. In this case, there is no SMF, and the voltage transformation occurs according to Faraday's law. With a loaded transformer, the picture is quite different. A small part of the magnetic lines that still go outside the core generate a small Lorentz current flowing through the load. This current causes a collision of the so far weak magnetic fields of the primary and secondary windings, from which, in turn, a weak SMF appears. And then everything happens exponentially: the SMF grows, which causes more current in the secondary winding, and it causes even more resistance to its growth, which means an ever greater SMF. And this happens until the moment when the current becomes equal to the value inversely proportional to the load and EMF (according to the classics). This transient process apparently proceeds quite quickly and is practically imperceptible to an external observer.

By the way, the principle of operation of the transformer differs from the operation of the inductor precisely by the presence of SMF, which almost does not appear in the inductor, and therefore the current there lags behind the voltage in a classical way.

So far, we have considered the transformer and inductor not in resonance mode. Resonance in them can change the ratio of the first and second magnetic fields, in particular - sequential. This principle is, for example, implemented in single-wire system of power transmission, where the SMF in the output resonant transformer generates a longitudinal wave in the transmitting conductor.

This note would be incomplete if we did not remember the free energy seekers who use the transformer principle of SMF generation to build their devices. In some patents of such inventors, there are two transformer windings, where they are the main elements [13,14]. If you do not take into account the SMF, then it is completely incomprehensible why they did this and why they cannot do, for example, with one winding, or even do without inductances. The author hopes that this work has shed some light on the reason for such circuit design solutions.