Electrostatic field potential or vortex. Vortex electric field - Hypermarket of knowledge. Didactic features of the computer
In accordance with Faraday's law for electromagnetic induction in a circuit that moves in a magnetic field, an emf arises proportional to the rate of change of the magnetic flux in this circuit
Faraday's experiments also established that the EMF of electromagnetic induction, defined by expression (67), also occurs when a fixed circuit penetrates a changing magnetic field (Figure 48).
If in a moving circuit the cause of the EMF is the Lorentz force, then the mechanism of its occurrence in a stationary circuit (conductor) becomes unclear. Obviously, the external force that separates the charges in the circuit cannot be of electrostatic origin, since the Coulomb forces do not lead to an increase in the potential difference, to its equalization.
Figure 48
According to the general definition of the EMF source ε , (68)
where is the field strength of external forces.
On the other side 
. (69)
The partial derivative symbol in expression (69) indicates that, in the general case, the magnetic field induction depends not only on time, but also on the coordinates.
Taking into account formulas (69) and (68), Faraday's law for electromagnetic induction is transformed to the form 
. (70)
In accordance with the obtained expression (70), any change in the magnetic field penetrating the circuit leads to the appearance of the field strength of external forces u. as a result, to the occurrence of electromagnetic induction in the EMF circuit. In this case, the change in the magnetic field is not accompanied by mechanical, chemical, thermal and other changes in the circuit. English physicist J. Maxwell proposed a hypothesis according to which the external forces that separate the charges in the circuit are of an electrical nature. Then relation (70) can also be written as 
. (71)
According to formula (71), in a changing magnetic field, the circulation of the electric field strength vector is not equal to zero, that is, the electric field is vortex (Figure 49).
It is important to note that a vortex electric field arises in any space, that is, for its existence, the presence of a conducting circuit is not necessary. But if this field arose in a conducting medium, then it leads to the appearance of eddy currents or Foucault currents (Figure 50).
In conductors with low resistivity, these currents can reach large values. In this regard, they are often used for induction heating of metal parts during hardening, outgassing of fittings for electronic devices, etc.
Figure 49 Figure 50
During the operation of electrical machines (electric motors, generators, transformers), these currents lead to undesirable heat losses in metal magnetic circuits. To reduce losses, the cores of transformers, stators and rotors of electrical machines are recruited from thin electrical steel plates isolated from each other. In other cases, high-resistance magnetic materials - ferrites - are used as magnetic circuits.
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Electric motors
From Figure 23 it follows that with the chosen orientation of the magnet poles and the direction of the current in the circuit, the torque is directed “on us”, that is, it tends to turn the circuit counterclockwise
The work of the magnetic field
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EMF induction occurs either in a stationary conductor placed in a time-varying field, or in a conductor moving in a magnetic field that may not change with time. The value of the EMF in both cases is determined by the law (12.2), but the origin of the EMF is different. Consider first the first case.
Let us have a transformer in front of us - two coils put on a core. By including the primary winding in the network, we will get the current in the secondary winding (Fig. 246), if it is closed. The electrons in the secondary wires will move. But what forces make them move? The magnetic field itself, penetrating the coil, cannot do this, since the magnetic field acts exclusively on moving charges (this is what it differs from the electric one), and the conductor with the electrons in it is motionless.
In addition to the magnetic field, the charges are also affected by the electric field. Moreover, it can also act on stationary charges. But after all, the field that has been discussed so far (electrostatic and stationary field) is created by electric charges, and the induction current appears under the action of an alternating magnetic field. This suggests that the electrons in a fixed conductor are set in motion by an electric field and this field is directly generated by an alternating magnetic field. Thus, a new fundamental property of the field is affirmed: changing in time, the magnetic field generates an electric field. This conclusion was first reached by Maxwell.
Now the phenomenon of electromagnetic induction appears before us in a new light. The main thing in it is the process of generating an electric field by a magnetic field. In this case, the presence of a conducting circuit, for example, a coil, does not change the essence of the matter. A conductor with a supply of free electrons (or other particles) only allows you to detect the emerging electric field. The field sets the electrons in motion in the conductor and thereby reveals itself. The essence of the phenomenon of electromagnetic induction in a fixed conductor is not so much in the appearance of an induction current, but in the appearance of an electric field that sets electric charges in motion.
The electric field arising from a change in the magnetic field has a completely different structure than the electrostatic one. It is not connected directly with electric charges, and its lines of tension cannot begin and end on them. They generally do not begin or end anywhere, but are closed lines, similar to the lines of magnetic field induction. This is the so-called vortex electric field (Fig. 247).
The direction of its lines of force coincides with the direction of the induction current. The force acting from the side of the vortex electric field on the charge is still equal to: But unlike the stationary electric field, the work of the vortex field on a closed path is not equal to zero. Indeed, when a charge moves along a closed line of tension
electric field (Fig. 247), the work on all sections of the path will have the same sign, since the force and displacement coincide in direction. The work of the vortex electric field on the movement of a single positive charge on a closed path is the EMF of induction in a stationary conductor.
Betatron. With a rapid change in the magnetic field of a strong electromagnet, powerful vortices of the electric field appear, which can be used to accelerate electrons to speeds close to the speed of light. The device of the electron accelerator - the betatron is based on this principle. The electrons in the betatron are accelerated by the vortex electric field inside the annular vacuum chamber K, placed in the gap of the electromagnet M (Fig. 248).
An alternating magnetic field generates induced electric field. If the magnetic field is constant, then there will be no induced electric field. Hence, induced electric field is not related to charges, as is the case in the case of an electrostatic field; its lines of force do not begin and end on charges, but are closed on themselves, like the lines of force of a magnetic field. It means that induced electric field, like a magnetic is vortex.
If a stationary conductor is placed in an alternating magnetic field, then e is induced in it. d.s. The electrons are driven in a directed motion by an electric field induced by an alternating magnetic field; an induced electric current occurs. In this case, the conductor is only an indicator of the induced electric field. The field sets in motion the free electrons in the conductor and thereby reveals itself. Now it can be argued that even without a conductor this field exists, having a reserve of energy.
The essence of the phenomenon of electromagnetic induction lies not so much in the appearance of an induced current, but in the appearance of a vortex electric field.
This fundamental position of electrodynamics was established by Maxwell as a generalization of Faraday's law of electromagnetic induction.
Unlike the electrostatic field, the induced electric field is non-potential, since the work done in the induced electric field when moving a single positive charge along a closed circuit is e. d.s. induction, not zero.
The direction of the intensity vector of the vortex electric field is set in accordance with Faraday's law of electromagnetic induction and Lenz's rule. The direction of the lines of force of the vortex el. field coincides with the direction of the induction current.
Since the vortex electric field also exists in the absence of a conductor, it can be used to accelerate charged particles to speeds comparable to the speed of light. It is on the use of this principle that the action of electron accelerators - betatrons is based.
The induction electric field has completely different properties in contrast to the electrostatic field.
The difference between a vortex electric field and an electrostatic one
1) It is not connected with electric charges;
2) The lines of force of this field are always closed;
3) The work of the forces of the vortex field on the movement of charges on a closed trajectory is not equal to zero.
|
electrostatic field |
induction electric field |
| 1. created by motionless electr. charges | 1. caused by changes in the magnetic field |
| 2. field lines are open - potential field | 2. lines of force are closed - vortex field |
| 3. The sources of the field are electr. charges | 3. field sources cannot be specified |
| 4. the work of the field forces in moving the test charge along a closed path = 0. | 4. the work of the field forces on the movement of the test charge along a closed path \u003d induction EMF |
If a closed conductor located in a magnetic field is stationary, then it is impossible to explain the occurrence of the induction EMF by the action of the Lorentz force, since it acts only on moving charges.
It is known that the movement of charges can also occur under the action of an electric field. Therefore, it can be assumed that electrons in a stationary conductor are set in motion by an electric field, and this field is directly generated by an alternating magnetic field. J. Maxwell was the first to come to this conclusion.
The electric field created by an alternating magnetic field is called induced electric field. It is created at any point in space where there is an alternating magnetic field, regardless of whether there is a conducting circuit there or not. The circuit only allows you to detect the emerging electric field. Thus, J. Maxwell generalized M. Faraday's ideas about the phenomenon of electromagnetic induction, showing that it is precisely in the occurrence of an induced electric field caused by a change in the magnetic field that physical meaning phenomena of electromagnetic induction.
The induced electric field differs from the known electrostatic and stationary electric fields.
1. It is caused not by some distribution of charges, but by an alternating magnetic field.
2. In contrast to the lines of electrostatic and stationary electric fields, which start on positive charges and end on negative charges, induced field strength lines - closed lines. Therefore, this field is vortex field.
Studies have shown that the magnetic field induction lines and the vortex electric field strength lines are located in mutually perpendicular planes. The vortex electric field is related to the alternating magnetic field that induces it by the rule left screw:
if the tip of the left screw moves forward in the direction ΔΒ , then turning the screw head will indicate the direction of the lines of intensity of the induced electric field (Fig. 1).
3. Induced electric field is not potential. The potential difference between any two points of the conductor through which the induction current passes is 0. The work done by this field when the charge moves along a closed path is not equal to zero. The induction emf is the work of the induced electric field on the movement of a unit charge along the considered closed circuit, i.e. not the potential, but the EMF of induction is the energy characteristic of the induced field.
Literature
Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 350-351.
In addition to the potential Coulomb electric field, there is a vortex field in which there are closed lines of tension. Knowing general properties electric field, it is easier to understand the nature of the vortex. It is generated by a changing magnetic field.
What causes the induction current of a conductor in a stationary state? What is electric field induction? The answer to these questions, as well as the difference between vortex and electrostatic and stationary, Foucault currents, ferrites and more, you will learn from the following article.
How does magnetic flux change?
The vortex electric field, which appeared after the magnetic one, is of a completely different kind than the electrostatic one. It has no direct connection with the charges, and the tensions on its lines do not begin and end. These are closed lines, like a magnetic field. Therefore, it is called the vortex electric field.
Magnetic induction
Magnetic induction will change the faster, the greater the intensity. Lenz's rule says: with increasing magnetic induction, the direction of the electric field vector creates a left screw with the direction of another vector. That is, when the left screw rotates in the direction with the lines of tension, its translational movement will become the same as that of the magnetic induction vector.
If the magnetic induction decreases, then the direction of the intensity vector will create a right screw with the direction of another vector.
The lines of force of tension have the same direction as the induction current. The vortex electric field acts on the charge with the same force as before. However, in this case, its work on moving the charge is different from zero, as in a stationary electric field. Since the force and displacement have the same direction, then the work along the entire path along the closed line of tension will be the same. The work of a positive unit charge here will be equal to the electromotive force of induction in the conductor.
Induction currents in massive conductors
In massive conductors, induction currents receive maximum values. This is because they have little resistance.
Such currents are called Foucault currents (this is a French physicist who studied them). They can be used to change the temperature of conductors. It is this principle that is incorporated in induction ovens, for example, household microwave ovens. It is also used to melt metals. Electromagnetic induction is also used in metal detectors located in airport terminals, theaters and other in public places with a large gathering of people.
But Foucault currents lead to energy losses to produce heat. Therefore, the cores of transformers, electric motors, generators and other devices are made of iron not solid, but from different plates, which are isolated from each other. The plates must be strictly perpendicular to the intensity vector, which has a vortex electric field. The plates will then have maximum current resistance, and the minimum amount of heat will be generated.
Ferrites
Radio equipment operates at the highest frequencies, where the number reaches millions of vibrations per second. Core coils will not be effective here, as Foucault currents will appear in each plate.
There are magnet insulators called ferrites. Eddy currents will not appear in them during magnetization reversal. Therefore, energy losses for heat are reduced to a minimum. They are used to make cores used for high-frequency transformers, transistor antennas, and so on. They are obtained from a mixture of original substances, which is pressed and thermally processed.
If the magnetic field in a ferromagnet changes rapidly, this leads to the appearance of induced currents. Their magnetic field will prevent a change in the magnetic flux in the core. Therefore, the flux will not change, and the core will be remagnetized. The eddy currents in ferrites are so small that they can quickly reverse magnetization.
