Law of electromagnetic induction. Vortex electric field. Eddy currents

INFOFIZ

A vortex electric field is an electric field that is generated by an alternating magnetic field and whose tension lines are closed.

An alternating magnetic field generates an induced electric field
.
If the magnetic field is constant, then there will be no induced electric field. Therefore, the induced electric field is not associated with charges
, as is the case with an electrostatic field;
its lines of force do not begin or end on charges, but are closed on themselves
, like the lines of force of a magnetic field.
This means that the induced electric field
, like a magnetic field,
is vortex.
If a stationary conductor is placed in an alternating magnetic field, then an e is induced in it. d.s. The electrons are driven in directional 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 free electrons in the conductor and thereby reveals itself. Now we can say that even without a conductor this field exists, possessing 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 unit positive charge along a closed circuit is equal to e. d.s. induction, not zero.

The direction of the vortex electric field intensity vector is established in accordance with Faraday's law of electromagnetic induction and Lenz's rule. Direction of force lines of vortex electric. field coincides with the direction of the induction current.

Since the vortex electric field 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 operation of electron accelerators - betatrons - is based.

An inductive electric field has completely different properties compared to an electrostatic field.

The difference between a vortex electric field and an electrostatic one

1) It is not associated with electric charges; 2) The lines of force of this field are always closed; 3) The work done by the vortex field forces to move charges along a closed trajectory is not zero.

electrostatic field	induction electric field (vortex electric field)
1. created by stationary electric. 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 electric. charges	3. field sources cannot be specified
4. work done by field forces to move a test charge along a closed path = 0.	4. work of field forces to move a test charge along a closed path = induced emf

Electromagnetic induction

According to the law of electromagnetic induction, when the magnetic flux changes through a closed loop, an induced emf is induced in it. Its formula:

$$\mathscr{E}= -{Δ\Phi \over Δt}$$

What is the mechanism for the occurrence of EMF in the circuit?

The occurrence of EMF means that forces appear in the circuit that move free charge carriers in the circuit material. The magnetic field penetrating the circuit does not interact with carriers: it does not affect charges at rest. Thus, the only forces that can move charges in it are the forces of the electric field.

Consequently, when the magnetic field changes, an electric field appears in the circuit, which moves charges and creates an induced emf.

Rice. 1. Electromagnetic induction.

Vortex electric field

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One of the consequences of Maxwell's equations of electrodynamics is the existence of an electric field that has no sources - charges. Such an electric field is called a vortex field. Let's talk briefly about the vortex electric field.

Vortex electric field

However, the field arising in the circuit has an important difference from the electric field generated by charges (static electric field). The lines of force of a static field begin and end on charges, but in this case there are no charges, which means that the lines of the resulting electric field do not have a beginning and an end - they are closed.

A field with closed lines of force is called a vortex field. For example, all existing magnetic fields are vortex. The theory does not prohibit the existence of a static magnetic field, but magnetic charges have not yet been discovered. Exactly the same vortex field is the one that arises in the circuit when the magnetic flux through the circuit changes.

The essence of the mechanism of electromagnetic induction is that a change in the magnetic field generates a vortex electric field, which sets the charges in the circuit in motion, creating an induced emf.

The faster the flow through the circuit changes, the greater the intensity of the electric field generated by it. The direction of the electric field coincides with the direction of the induction current in the circuit, which means it is also determined by Lenz’s rule: the induction current arising in a closed circuit is directed so as to counteract the cause that causes it.

As the magnetic flux through the circuit increases, the direction of the vortex electric field can be determined by the right hand grip rule: if the thumb of the right hand points to the direction of the magnetic field, then the four wrapping fingers will indicate the direction of the vortex electric field. As the magnetic flux decreases, the direction of the vortex field will change to the opposite.

What have we learned?

A change in the magnetic flux through the circuit causes the appearance of a vortex electric field in it. It is this vortex field that is the source of EMF of electromagnetic induction. Lenz's rule is used to determine its direction.

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Displacement current and electromagnetic wave

Since the eddy magnetic field is generated by a current flowing through a conductor, J. Maxwell, when developing the theory of electromagnetism, suggested that the eddy electric field is also generated by a similar process, which was called displacement current (as opposed to the usual conduction current). Just as conduction current is the "motion" of an electric field, displacement current can be thought of as the "motion" of a magnetic field. It is the displacement current that generates the vortex electric field. And the electric field, in turn creating an ordinary electric current, generates a vortex magnetic field.

As a result, when the electric and magnetic fields change in space, a propagating structure of mutually generating magnetic and electric fields, called an electromagnetic wave, immediately forms.

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Swirls and skin effect

In the case when very strong eddy currents arise (at high-frequency current), the current density in bodies becomes significantly less than on their surfaces. This is the so-called skin effect, its methods are used to create special coatings for wires and pipes, which are developed specifically for eddy currents and tested under extreme conditions.

This was proven by the scientist Eckert, who studied EMF and transformer installations.

Induction heating circuit

§ 32-1. Vortex electric field. Induction EMF in moving conductors

Vortex electric field. When the magnetic flux changes through a surface bounded by a conducting closed fixed (relative to the selected inertial reference frame) contour, an electric current arises in it.
This indicates that forces act on free charged particles in the circuit. But for randomly moving charged particles, the average value of the Lorentz force is zero, therefore, such particles are affected by an electric field. J. Maxwell was the first to suggest that with any change in time of the magnetic field in the surrounding space, an electric field arises. It is called inductive or induced. It is this inductive electric field that acts on charged particles, bringing them into ordered motion and creating an inductive electric current. We emphasize that the inductive electric field is not associated with electric charges; its source is a magnetic field that changes over time. The inductive electric field strength lines are closed. The electric field that arises with any change in time of the magnetic field is one of the vortex fields.

The vortex, i.e. non-potential, nature of the induction electric field is the reason that when a charge moves along a closed circuit, this field does work that is not equal to zero.

Thus, the induced emf arising in a stationary closed loop located in a time-varying magnetic field is equal to the work of the forces of the vortex electric field in moving a single positive charge along this loop. If such a circuit turns out to be conductive, then the induced emf that arises in it leads to the appearance of an induced current.

Maxwell in 1873 established that the induced emf that occurs in a stationary circuit when the magnetic field changes over time does not depend on the characteristics of this circuit (substance, type of free charge carriers, resistance, temperature, etc.). Based on this, he concluded that the role of the circuit is reduced only to the indication of the vortex electric field created by an alternating magnetic field.

So, the essence of the phenomenon of electromagnetic induction is that a vortex electric field arises at any point in space if there is a time-varying magnetic field at that point, regardless of whether there is a conducting circuit there or not.

The intensity lines of the vortex electric field cover the induction lines of the time-varying magnetic field. The direction of the vortex electric field intensity lines is determined by Lenz's rule. Indeed, if you place a closed conducting circuit in a time-varying magnetic field, then an inductive electric current will flow along it in the direction of the electric field strength lines.

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Eddy currents (Foucault currents).

In a massive conductor located in an alternating magnetic field, an eddy electric field causes an induced current. Because the lines of tension

are closed, then the current lines inside this massive conductor are closed, so they are called
eddy currents , or Foucault currents .
In 1855, J. B. L. Foucault discovered the heating of ferromagnetic cores, as well as other metallic bodies, in an alternating magnetic field. He explained this effect by the excitation of induced currents. Foucault proposed a way to reduce energy losses due to heating - to manufacture cores and other magnetic circuits in the form of plates separated by thin insulating films, and to orient the surfaces of these plates perpendicular to the vector of the eddy electric field strength (i.e., so that they intersect possible lines of eddy currents). Eddy current heating of massive conductors is used in induction furnaces for melting metals and making alloys.