Moscow State University of Printing. Vortex electric field. Self-induction. Self-induced emf. Inductance. Magnetic field energy Law of electromagnetic induction

The electric field that arises when the magnetic field changes has a completely different structure than the electrostatic one. It is not directly connected with electric charges, and its lines of tension cannot begin and end on them. They do not begin or end anywhere at all, but are closed lines, similar to magnetic field induction lines. This is the so-called vortex electric field. The question may arise: why, in fact, is this field called electric? After all, it has a different origin and a different configuration than a static electric field. The answer is simple: the vortex field acts on the charge q just like the electrostatic one, and this is what we considered and still consider to be the main property of the field. The force acting on the charge is still equal to F= qE, Where E- intensity of the vortex field.

If the magnetic flux is created by a uniform magnetic field concentrated in a long narrow cylindrical tube with radius r 0 (Fig. 5.8), then from symmetry considerations it is obvious that the electric field strength lines lie in planes perpendicular to lines B and are circles. In accordance with Lenz's rule, as the magnetic field increases

Induction lines of tension E form a left screw with the direction of magnetic induction B.

Unlike a static or stationary electric field, the work of a vortex field on a closed path is not zero. Indeed, when a charge moves along a closed line of electric field strength, the work on all sections of the path has the same sign, since the force and movement coincide in direction. A vortex electric field, like a magnetic field, is not potential.

The work of a vortex electric field to move a single positive charge along a closed stationary conductor is numerically equal to the induced emf in this conductor.

If alternating current flows through the coil, then the magnetic flux passing through the coil changes. Therefore, an induced emf occurs in the same conductor through which alternating current flows. This phenomenon is called self-induction.

With self-induction, the conductive circuit plays a dual role: a current flows through it, causing induction, and an induced emf appears in it. A changing magnetic field induces an emf in the very conductor through which the current flows, creating this field.

At the moment of current increase, the intensity of the vortex electric field, in accordance with Lenz's rule, is directed against the current. Consequently, at this moment the vortex field prevents the current from increasing. On the contrary, at the moment the current decreases, the vortex field supports it.

This leads to the fact that when a circuit containing a source of constant EMF is closed, a certain current value is not established immediately, but gradually over time (Fig. 5.13). On the other hand, when the source is turned off, the current in closed circuits does not stop instantly. The self-inductive emf that arises in this case can exceed the source emf, since the change in current and its magnetic field occurs very quickly when the source is turned off.

The phenomenon of self-induction can be observed in simple experiments. Figure 5.14 shows a circuit for connecting two identical lamps in parallel. One of them is connected to the source through a resistor R, and the other - in series with the coil L with an iron core. When the key is closed, the first lamp flashes almost immediately, and the second with a noticeable delay. The self-inductive emf in the circuit of this lamp is large, and the current strength does not immediately reach its maximum value. The appearance of self-inductive emf upon opening can be observed experimentally with a circuit schematically shown in Figure 5.15. When the key in the coil is opened L A self-induced emf arises, maintaining the initial current. As a result, at the moment of opening, a current flows through the galvanometer (dashed arrow), directed opposite the initial current before opening (solid arrow). Moreover, the current strength when the circuit is opened exceeds the current strength passing through the galvanometer when the switch is closed. This means that the self-induced emf ξ. more emf ξ is battery elements.

The phenomenon of self-induction is similar to the phenomenon of inertia in mechanics. Thus, inertia leads to the fact that under the influence of force a body does not instantly acquire a certain speed, but gradually. The body cannot be instantly slowed down, no matter how great the braking force. In the same way, due to self-induction, when the circuit is closed, the current strength does not immediately acquire a certain value, but increases gradually. By turning off the source, we do not stop the current immediately. Self-induction maintains it for some time, despite the presence of circuit resistance.

Next, in order to increase the speed of a body, according to the laws of mechanics, work must be done. When braking, the body itself does positive work. In the same way, to create a current, work must be done against the vortex electric field, and when the current disappears, this field itself does positive work.

This is not just a superficial analogy. It has a deep inner meaning. After all, current is a collection of moving charged particles. As the speed of electrons increases, the magnetic field they create changes and generates a vortex electric field that acts on the electrons themselves, preventing an instant increase in their speed under the influence of an external force. During braking, on the contrary, the vortex field tends to maintain the electron speed constant (Lenz's rule). Thus, the inertia of electrons, and therefore their mass, is at least partially of electromagnetic origin. Mass cannot be completely electromagnetic, since there are electrically neutral particles with mass (neutrons, etc.)

Inductance.

Module B of magnetic induction created by current in any closed circuit is proportional to the strength of the current. Since the magnetic flux Ф is proportional to B, then Ф ~ В ~ I.

It can therefore be argued that

Where L- coefficient of proportionality between the current in a conducting circuit and the magnetic flux created by it, penetrating this circuit. Size L called the inductance of the circuit or its self-inductance coefficient.

Using the law of electromagnetic induction and expression (5.7.1), we obtain the equality:

(5.7.2)

From formula (5.7.2) it follows that inductance- this is a physical quantity numerically equal to the self-induction emf that occurs in the circuit when the current changes by 1 A per 1 p.

Inductance, like electrical capacitance, depends on geometric factors: the size of the conductor and its shape, but does not depend directly on the current strength in the conductor. Except

geometry of the conductor, inductance depends on the magnetic properties of the environment in which the conductor is located.

The SI unit of inductance is called the henry (H). The conductor inductance is equal to 1 Gn, if in it when the current strength changes by 1 A behind 1s self-induced emf occurs 1 V:

Another special case of electromagnetic induction is mutual induction. Mutual induction is the occurrence of an induced current in a closed circuit(reel) when the current strength changes in the adjacent circuit(reel). In this case, the contours are stationary relative to each other, such as, for example, the coils of a transformer.

Quantitatively, mutual induction is characterized by the coefficient of mutual induction, or mutual inductance.

Figure 5.16 shows two circuits. When the current I 1 changes in the circuit 1 in the circuit 2 an induction current I 2 arises.

The magnetic induction flux Ф 1.2, created by the current in the first circuit and penetrating the surface bounded by the second circuit, is proportional to the current strength I 1:

The proportionality coefficient L 1, 2 is called mutual inductance. It is similar to inductance L.

The induced emf in the second circuit, according to the law of electromagnetic induction, is equal to:

The coefficient L 1.2 is determined by the geometry of both circuits, the distance between them, their relative position and the magnetic properties of the environment. Mutual inductance is expressed L 1.2, like the inductance L, in henry.

If the current changes in the second circuit, then an induced emf occurs in the first circuit

When the current strength changes in a conductor, a vortex electric field appears in the latter. This field slows down electrons when the current increases and accelerates when it decreases.

Current magnetic field energy.

When a circuit containing a source of constant EMF is closed, the energy of the current source is initially spent on creating a current, i.e., on setting in motion the electrons of the conductor and the formation of a magnetic field associated with the current, and also partly on increasing the internal energy of the conductor, i.e. heating it. After a constant current value is established, the energy of the source is spent exclusively on the release of heat. In this case, the current energy does not change.

To create a current, it is necessary to expend energy, i.e., work must be done. This is explained by the fact that when the circuit is closed, when the current begins to increase, a vortex electric field appears in the conductor, acting against the electric field that is created in the conductor due to the current source. In order for the current strength to become equal to I, the current source must do work against the forces of the vortex field. This work goes towards increasing the current energy. The vortex field does negative work.

When the circuit is opened, the current disappears and the vortex field does positive work. The energy stored in the current is released. This is detected by a powerful spark that occurs when a circuit with high inductance is opened.

An expression for the energy of the current I flowing through a circuit with inductance L can be written based on the analogy between inertia and self-induction.

If self-induction is similar to inertia, then inductance in the process of creating current should play the same role as mass when increasing the speed of a body in mechanics. The role of the speed of a body in electrodynamics is played by the current strength I as a quantity characterizing the movement of electric charges. If this is so, then the current energy W m can be considered a quantity similar to the kinetic energy of the body - in mechanics, and write it in the form.

Electric current in a circuit is possible if external forces act on the free charges of the conductor. The work done by these forces to move a single positive charge along a closed loop is called emf. When the magnetic flux changes through the surface limited by the contour, extraneous forces appear in the circuit, the action of which is characterized by the induced emf.

Considering the direction of the induction current, according to Lenz's rule:

The induced emf in a closed loop is equal to the rate of change of the magnetic flux through the surface bounded by the loop, taken with the opposite sign.

Why? - because the induced current counteracts the change in the magnetic flux, the induced emf and the rate of change of the magnetic flux have different signs.

If we consider not a single circuit, but a coil, where N is the number of turns in the coil:

where R is the conductor resistance.

VORTEX ELECTRIC FIELD

The reason for the occurrence of electric current in a stationary conductor is the electric field.
Any change in the magnetic field generates an inductive electric field, regardless of the presence or absence of a closed circuit, and if the conductor is open, then a potential difference arises at its ends; If the conductor is closed, then an induced current is observed in it.

The inductive electric field is vortex.
The direction of the vortex electric field lines coincides with the direction of the induction current
An inductive electric field has completely different properties compared to an electrostatic field.

Electrostatic field- is created by stationary electric charges, the field lines are open - - potential field, the sources of the field are electric charges, the work of field forces to move a test charge along a closed path is 0

Induction electric field (vortex electric field)- caused by changes in the magnetic field, the lines of force are closed (vortex field), the field sources cannot be specified, the work of the field forces to move the test charge along a closed path is equal to the induced emf.

Eddy currents

Induction currents in massive conductors are called Foucault currents. Foucault currents can reach very large values, because The resistance of massive conductors is low. Therefore, transformer cores are made from insulated plates.
In ferrites - magnetic insulators, eddy currents practically do not arise.

Use of eddy currents

Heating and melting of metals in a vacuum, dampers in electrical measuring instruments.

Harmful effects of eddy currents

These are energy losses in the cores of transformers and generators due to the release of large amounts of heat.

Electromagnetic field - Cool physics

For the curious

Click beetle somersault

If you tickle a click beetle lying on its back, it jumps up 25 centimeters, and a loud click is heard. Nonsense, you might say.
But, indeed, the bug, without the help of its legs, makes a push with an initial acceleration of 400 g, and then turns over in the air and lands on its legs. 400 g - amazing!
Even more surprising is that the power developed during the push is one hundred times greater than the power that any of the bug's muscles can provide. How does a bug manage to develop such enormous power?
How often is he able to make his amazing leaps? What is the limitation on the frequency of their repetition?

Turns out...
When the bug is lying upside down, a special protrusion on the front of its body prevents it from straightening up to make a jump. For some time he accumulates muscle tension, then, bending sharply, throws himself up.
Before the bug can jump again, it must slowly "tense" its muscles again.

How does electromotive force arise in a conductor that is in an alternating magnetic field? What is a vortex electric field, its nature and causes of its occurrence? What are the main properties of this field? Today's lesson will answer all these and many other questions.

Topic: Electromagnetic induction

Lesson:Vortex electric field

Let us remember that Lenz's rule allows us to determine the direction of the induced current in a circuit located in an external magnetic field with an alternating flux. Based on this rule, it was possible to formulate the law of electromagnetic induction.

Law of Electromagnetic Induction

When the magnetic flux piercing the area of the circuit changes, an electromotive force appears in this circuit, numerically equal to the rate of change of the magnetic flux, taken with a minus sign.

How does this electromotive force arise? It turns out that the EMF in a conductor that is in an alternating magnetic field is associated with the emergence of a new object - vortex electric field.

Let's consider experience. There is a coil of copper wire in which an iron core is inserted in order to enhance the magnetic field of the coil. The coil is connected through conductors to an alternating current source. There is also a coil of wire placed on a wooden base. An electric light bulb is connected to this coil. The wire material is covered with insulation. The base of the coil is made of wood, i.e., a material that does not conduct electric current. The coil frame is also made of wood. Thus, any possibility of contact of the light bulb with the circuit connected to the current source is eliminated. When the source is closed, the light bulb lights up, therefore, an electric current flows in the coil, which means that external forces do work in this coil. It is necessary to find out where outside forces come from.

A magnetic field penetrating the plane of a coil cannot cause the appearance of an electric field, since the magnetic field acts only on moving charges. According to the electronic theory of conductivity of metals, there are electrons inside them that can move freely within the crystal lattice. However, this movement in the absence of an external electric field is random. Such disorder leads to the fact that the total effect of the magnetic field on a current-carrying conductor is zero. This distinguishes the electromagnetic field from the electrostatic field, which also acts on stationary charges. Thus, the electric field acts on moving and stationary charges. However, the type of electric field that was studied earlier is created only by electric charges. The induced current, in turn, is created by an alternating magnetic field.

Suppose that the electrons in a conductor are set into ordered motion under the influence of some new kind of electric field. And this electric field is generated not by electric charges, but by an alternating magnetic field. Faraday and Maxwell came to a similar idea. The main thing in this idea is that a time-varying magnetic field generates an electric one. A conductor with free electrons in it makes it possible to detect this field. This electric field sets the electrons in the conductor in motion. The phenomenon of electromagnetic induction consists not so much in the appearance of an induction current, but in the appearance of a new type of electric field that sets in motion electric charges in a conductor (Fig. 1).

The vortex field differs from the static one. It is not generated by stationary charges, therefore, the intensity lines of this field cannot begin and end on the charge. According to research, the vortex field strength lines are closed lines similar to the magnetic field induction lines. Consequently, this electric field is a vortex - the same as a magnetic field.

The second property concerns the work of the forces of this new field. By studying the electrostatic field, we found out that the work done by the forces of the electrostatic field along a closed loop is zero. Since when a charge moves in one direction, the displacement and the effective force are co-directed and the work is positive, then when the charge moves in the opposite direction, the displacement and the effective force are oppositely directed and the work is negative, the total work will be zero. In the case of a vortex field, the work along a closed loop will be different from zero. So, when a charge moves along a closed line of an electric field that has a vortex character, the work in different sections will maintain a constant sign, since the force and displacement in different sections of the trajectory will maintain the same direction relative to each other. The work of the vortex electric field forces to move a charge along a closed loop is non-zero, therefore, the vortex electric field can generate an electric current in a closed loop, which coincides with the experimental results. Then we can say that the force acting on the charges from the vortex field is equal to the product of the transferred charge and the strength of this field.

This force is the external force that does the work. The work done by this force, related to the amount of charge transferred, is the induced emf. The direction of the vortex electric field intensity vector at each point of the intensity lines is determined by Lenz's rule and coincides with the direction of the induction current.

In a stationary circuit located in an alternating magnetic field, an induced electric current arises. The magnetic field itself cannot be a source of external forces, since it can only act on orderly moving electric charges. There cannot be an electrostatic field, since it is generated by stationary charges. After the assumption that a time-varying magnetic field generates an electric field, we learned that this alternating field is of a vortex nature, i.e. its lines are closed. The work of the vortex electric field along a closed loop is different from zero. The force acting on the transferred charge from the vortex electric field is equal to the value of this transferred charge multiplied by the intensity of the vortex electric field. This force is the external force that leads to the occurrence of EMF in the circuit. The electromotive force of induction, i.e. the ratio of the work of external forces to the amount of transferred charge, is equal to the rate of change of magnetic flux taken with a minus sign. The direction of the vortex electric field intensity vector at each point of the intensity lines is determined by Lenz's rule.

Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 pp.: ill., 8 l. color on
Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
Tikhomirova S.A., Yarovsky B.M., Physics 11. - M.: Mnemosyne.

Electronic physics textbook ().
Cool physics ().
Xvatit.com ().

How to explain the fact that a lightning strike can melt fuses and damage sensitive electrical appliances and semiconductor devices?
* When the ring was opened, a self-induction emf of 300 V arose in the coil. What is the intensity of the vortex electric field in the coil turns, if their number is 800, and the radius of the turns is 4 cm?

The phenomenon of electromagnetic induction was discovered by M. Faraday in 1831. The phenomenon can be observed in the following experiments. Let's take a coil with a large number of turns (solenoid), close it with a galvanometer, and move a permanent magnet from one of its ends along the axis. In this case, an electric current will arise in the solenoid, which will be detected by the deflection of the galvanometer needle. This current will stop when the magnet stops moving. If you remove the magnet from the solenoid, a current will again arise in the solenoid, but in the opposite direction. The same phenomenon will occur if the magnet is left stationary and the solenoid is moved. Instead of a magnet, you can take a second solenoid (Fig. 51), through which a direct current flows: formula" src="http://hi-edu.ru/e-books/xbook785/files/I2.gif" border="0" align ="absmiddle" alt=".

The phenomenon of electromagnetic induction is as follows: in any closed conducting circuit, when the flux of magnetic induction changes through the area limited by this circuit, an electric current arises. This current is called induction current.

The appearance of an induced current in a closed circuit is due to the appearance in this circuit under the influence of a time-varying flow of a specific electromotive force, the electromotive force. The magnitude of this EMF was first associated with the rate of change of the magnetic induction flux by Faraday

definition">Faraday's law

The minus sign in the law means that the induced emf always has such a direction that it interferes with the cause that causes it. This rule was established by St. Petersburg professor E.Kh. Lenz.

If we consider the magnetic flux formula" src="http://hi-edu.ru/e-books/xbook785/files/108-2.gif" border="0" align="absmiddle" alt="(Fig. 52, b), or directed opposite to it, if it increases the mark "> B. The flux of magnetic induction through the area S, limited by the frame, is equal to

formula" src="http://hi-edu.ru/e-books/xbook785/files/109-1.gif" border="0" align="absmiddle" alt="the angle between the normal to the frame and vector B changes

formula" src="http://hi-edu.ru/e-books/xbook785/files/109-3.gif" border="0" align="absmiddle" alt="According to Faraday's law (12.1), with a changing flow through the frame, an induced current appears in it, which will change over time with a frequency equal to the speed of rotation of the frame formula" src="http://hi-edu.ru/e-books/xbook785 /files/109-4.gif" border="0" align="absmiddle" alt="

As you can see, the induced emf changes according to a harmonic law with frequency formula" src="http://hi-edu.ru/e-books/xbook785/files/109-5.gif" border="0" align="absmiddle" alt="Obtaining an EMF when a coil rotates in a magnetic field is the basis for the operation of an alternating current generator.

Mechanism of occurrence induced current in a moving conductor can be explained using the Lorentz force F = qvB.

Under the influence of the Lorentz force, charges are separated: positive charges accumulate at one end of the conductor, negative ones at the other (Fig. 53). These charges create an electrostatic Coulomb field inside the conductor. If the conductor is open, then the movement of charges under the influence of the Lorentz force will occur until the electric force balances the Lorentz force. The action of the Lorentz force is similar to the action of some electric field; this field is third-party field.

The occurrence of induced emf is also possible in a stationary circuit located in an alternating magnetic field. What is the nature of external forces (non-electrostatic origin) in this case?

Maxwell hypothesized that any alternating magnetic field excites an electric field in the surrounding space, which is the cause of the appearance of induced current in the circuit. This field is characterized by intensity (the index indicates the reason for the occurrence of this field - the magnetic field).

The circulation of this electric field marked ">L is not equal to zero:

formula" src="http://hi-edu.ru/e-books/xbook785/files/111-1.gif" border="0" align="absmiddle" alt="

formula" src="http://hi-edu.ru/e-books/xbook785/files/111-2.gif" border="0" align="absmiddle" alt="

formula" src="http://hi-edu.ru/e-books/xbook785/files/111-5.gif" border="0" align="absmiddle" alt="- partial derivative of induction B with respect to time.

For electrostatic field mark">Q) circulation along any closed contour is zero:

define-e">potential.

The electric field is defined as a vortex, for which circulation along a closed loop L is not equal to zero:

mark">I(t), then it creates a magnetic field with induction B(t), and therefore the flux formula" src="http://hi-edu.ru/e-books/xbook785/files/112. gif" border="0" align="absmiddle" alt="

The phenomenon of electromagnetic induction caused by a change in current in the circuit itself is called self-induction.

At any point on the surface stretched over the circuit, the induction dB is proportional to the current in the circuit. If it is integrated over the entire surface, then the total magnetic flux is marked ">I

mark ">L - circuit inductance, proportionality coefficient, depending on the circuit configuration.

Inductance shows how much magnetic flux penetrates the surface covered by the circuit when the current in it is 1 A. Its unit is Wb/A, which is called henry (H).

If the circuit has a complex shape, for example, contains several turns, then instead of defining "flux linkage, the formula" src="http://hi-edu.ru/e-books/xbook785/files/112-4.gif" border ="0" align="absmiddle" alt="

the expression is valid for L = const.

This implies another definition of L (more important in practice): inductance shows what self-inductive emf occurs in the circuit if the rate of change of current in it is 1 A/s.

For a solenoid, the magnetic flux through one turn is marked ">N turns of the solenoid (flux linkage),

mark">V =Sl - solenoid volume.

Comparing this expression with (12.4), we get

formula" src="http://hi-edu.ru/e-books/xbook785/files/mu.gif" border="0" align="absmiddle" alt=".

Magnetic flux through the surface covered by circuit 2 can be created by current illustration" src="http://hi-edu.ru/e-books/xbook785/files/ris54.gif" border="0">

Let us denote the formula" src="http://hi-edu.ru/e-books/xbook785/files/113.gif" border="0" align="absmiddle" alt="

formula" src="http://hi-edu.ru/e-books/xbook785/files/I1.gif" border="0" align="absmiddle" alt="changes, then in circuit 2 it is induced Mutual induction emf

formula" src="http://hi-edu.ru/e-books/xbook785/files/I2.gif" border="0" align="absmiddle" alt="EMF of mutual induction occurs

formula" src="http://hi-edu.ru/e-books/xbook785/files/113-3.gif" border="0" align="absmiddle" alt=" - mutual inductances of the circuits, they depend on the geometric shape, size, relative position of the contours and magnetic permeability of the medium.

Let's calculate the mutual inductance of two coils wound on a common toroidal core(Fig. 55). Foucault currents, or eddy currents.

A heavy metal plate oscillating between the poles of an electromagnet stops if the direct current feeding the electromagnet is turned on. All its energy turns into heat generated by Foucault currents. There are no currents in a stationary plate.

Eddy currents can be significantly weakened if cuts are made in the plate to increase its resistance. In the solid cores of transformers and electric motors operating on alternating current, Foucault currents would generate a significant amount of heat. Therefore, the cores are made as composites, consisting of thin plates separated by a dielectric layer.

The phenomenon of the occurrence of Foucault induction currents underlies the operation of induction furnaces, which allow heating metals to the melting point.

Foucault currents obey Lenz's rule: their magnetic field is directed so as to counteract the change in magnetic flux that induces eddy currents. This fact is used to calm the moving parts of various devices (damping).

Eddy currents also occur in wires through which alternating electric current flows. The direction of eddy currents is such that they counteract the change in the primary current in the conductor. Thus, the alternating current turns out to be distributed unevenly over the cross-section of the wire; it is, as it were, forced out onto the surface of the conductor. At the surface of the wire, the current density is maximum, and deep into the conductor it decreases and reaches its lowest value on its axis. This phenomenon is called the skin effect (skin). The current is concentrated in the “skin” of the conductor. Therefore, at high frequencies there is no need for conductors with a large cross-section: anyway, the current will flow only in the surface layer.

Topic: Electromagnetic induction

Lesson:Vortex electric field

Law of Electromagnetic Induction

When the magnetic flux piercing the area of the circuit changes, an electromotive force appears in this circuit, numerically equal to the rate of change of the magnetic flux, taken with a minus sign.

Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 pp.: ill., 8 l. color on
Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
Tikhomirova S.A., Yarovsky B.M., Physics 11. - M.: Mnemosyne.

Electronic physics textbook ().
Cool physics ().
Xvatit.com ().

How to explain the fact that a lightning strike can melt fuses and damage sensitive electrical appliances and semiconductor devices?
* When the ring was opened, a self-induction emf of 300 V arose in the coil. What is the intensity of the vortex electric field in the coil turns, if their number is 800, and the radius of the turns is 4 cm?