The physical essence of the phenomenon of self-induction. III

We have already studied that a magnetic field arises near a current-carrying conductor. And also studied that a variable magnetic field generates a current (the phenomenon of electromagnetic induction). Consider an electrical circuit. When the current strength changes in this circuit, a change in the magnetic field will occur, as a result of which an additional voltage will appear in the same circuit. induction current. Such a phenomenon is called self-induction, and the resulting current is called self-induction current.

The phenomenon of self-induction- this is the occurrence in a conducting circuit of an EMF created due to a change in the current strength in the circuit itself.

Loop inductance depends on its shape and size, on the magnetic properties of the environment and does not depend on the current strength in the circuit.

EMF of self-induction is determined by the formula:

The phenomenon of self-induction is similar to the phenomenon of inertia. Just as in mechanics it is impossible to instantly stop a moving body, so the current cannot instantly acquire a certain value due to the phenomenon of self-induction. If a coil is connected in series with the second lamp in a circuit consisting of two identical lamps connected in parallel to a current source, then when the circuit is closed, the first lamp lights up almost immediately, and the second with a noticeable delay.

When the circuit is opened, the current strength decreases rapidly, and the resulting self-induction EMF prevents the magnetic flux from decreasing. In this case, the induced current is directed in the same way as the original one. The self-induced emf can be many times greater than the external emf. Therefore, light bulbs very often burn out when the light is turned off.

Being, as it were, a special case of it).

The direction of the EMF of self-induction always turns out to be such that when the current in the circuit increases, the EMF of self-induction prevents this increase (directed against the current), and when the current decreases, it decreases (co-directed with the current). With this property, the EMF of self-induction is similar to the force of inertia.

The value of the EMF of self-induction is proportional to the rate of change of the current:

The proportionality factor is called self-induction coefficient or inductance circuit (coil).

Self-induction and sinusoidal current

In the case of a sinusoidal dependence of the current flowing through the coil on time, the self-induction EMF in the coil lags the current in phase by (that is, by 90 °), and the amplitude of this EMF is proportional to the current amplitude, frequency and inductance (). After all, the rate of change of a function is its first derivative, and .

To calculate more or less complex circuits containing inductive elements, i.e. turns, coils, etc. devices in which self-induction is observed, (especially, completely linear, that is, not containing non-linear elements) in the case of sinusoidal currents and voltages, the method of complex impedances is used or, in simpler cases, a less powerful but more visual version of it is the method of vector diagrams.

Note that everything described is applicable not only directly to sinusoidal currents and voltages, but also practically to arbitrary ones, since the latter can almost always be expanded into a series or Fourier integral and thus reduced to sinusoidal ones.

In more or less direct connection with this, one can mention the use of the phenomenon of self-induction (and, accordingly, inductors) in a variety of oscillatory circuits, filters, delay lines, and various other circuits in electronics and electrical engineering.

Self-induction and current surge

Due to the phenomenon of self-induction in an electric circuit with an EMF source, when the circuit is closed, the current is not established instantly, but after some time. Similar processes also occur when the circuit is opened, while (with a sharp opening) the value of the self-induction emf can at this moment significantly exceed the source emf.

Most often in ordinary life it is used in car ignition coils. Typical ignition voltage at 12V battery voltage is 7-25 kV. However, the excess of the EMF in the output circuit over the EMF of the battery here is due not only to a sharp interruption of the current, but also to the transformation ratio, since most often not a simple inductor coil is used, but a transformer coil, the secondary winding of which, as a rule, has many times more turns ( that is, in most cases, the circuit is somewhat more complex than that which would be fully explained by self-induction; however, the physics of its operation in this version partly coincides with the physics of the circuit with a simple coil).

This phenomenon is also used to ignite fluorescent lamps in a standard traditional circuit (here we are talking about a circuit with a simple inductor - a choke).

In addition, it must always be taken into account when opening contacts, if the current flows through the load with a noticeable inductance: the resulting jump in the EMF can lead to a breakdown of the intercontact gap and / or other undesirable effects, to suppress which in this case, as a rule, it is necessary to take a variety of special measures.

Notes

Links

About self-induction and mutual induction from the "School for an Electrician"

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See what "Self-induction" is in other dictionaries:

Self-induction ... Spelling Dictionary

The occurrence of an emf of induction in a conducting circuit when the current strength changes in it; special cases of electromagnetic induction. When the current in the circuit changes, the magnetic flux changes. induction through the surface bounded by this contour, resulting in ... Physical Encyclopedia

The excitation of the electromotive force of induction (emf) in an electrical circuit when the electric current in this circuit changes; special case of electromagnetic induction. The electromotive force of self-induction is directly proportional to the rate of change of current; ... ... Big Encyclopedic Dictionary

SELF-INDUCTION, self-induction, wives. (physical). 1. only units The phenomenon that when a current changes in a conductor, an electromotive force appears in it, preventing this change. Self-induction coil. 2. A device that has ... ... Explanatory Dictionary of Ushakov

- (Self induction) 1. A device with inductive resistance. 2. The phenomenon consisting in the fact that when an electric current changes in magnitude and direction in a conductor, an electromotive force arises in it that prevents this ... ... Marine Dictionary

Guidance of the electromotive force in the wires, as well as in the windings of electr. machines, transformers, apparatus and instruments when changing the magnitude or direction of the electric current flowing through them. current. The current flowing through the wires and windings creates around them ... ... Technical railway dictionary

self induction- electromagnetic induction caused by a change in the magnetic flux interlocking with the circuit, due to the electric current in this circuit ... Source: ELEKTROTEHNIKA. TERMS AND DEFINITIONS OF BASIC CONCEPTS. GOST R 52002 2003 (approved ... ... Official terminology

Exist., number of synonyms: 1 excitation of electromotive force (1) ASIS synonym dictionary. V.N. Trishin. 2013 ... Synonym dictionary

self-induction- Electromagnetic induction, caused by a change in the magnetic flux interlocking with the circuit, due to the electric current in this circuit. [GOST R 52002 2003] EN self induction electromagnetic induction in a tube of current due to variations… … Technical Translator's Handbook

SELF-INDUCTION- a special case of electromagnetic induction (see (2)), consisting in the occurrence of an induced (induced) EMF in a circuit and due to changes in time of the magnetic field created by a varying current flowing in the same circuit. ... ... Great Polytechnic Encyclopedia

Books

Induction, mutual induction, self-induction - it's simple. Theory of absoluteness, Gurevich Harold Stanislavovich, Kanevsky Samuil Naumovich, The process of interaction of electrons of a changing electromagnetic field with the electrons of conductors located in this electromagnet field is called electromagnetic induction. As a result… Category: Physics Series: Nature of the Far East Publisher: At the Nikitsky Gate, Manufacturer:

The term induction in electrical engineering means the occurrence of current in an electrical closed circuit if it is in a changing state. It was discovered only two hundred years ago by Michael Faraday. Much earlier, this could have been done by André Ampère, who conducted similar experiments. He inserted a metal rod into the coil, and then, bad luck, went into another room to look at the galvanometer needle - and suddenly it would move. And the arrow regularly did its job - it deviated, but while Ampere wandered around the rooms - it returned to zero. This is how the phenomenon of self-induction waited for another ten years, until the coil, the device and the researcher were at the same time in the right place.

The main point of this experiment was that the induction emf occurs only when the magnetic field passing through the closed circuit changes. But you can change it as you like - either change the value of the magnetic field itself, or simply move the source of the field relative to the same closed loop. The emf, which arises in this case, was called the “emf of mutual induction”. But this was only the beginning of discoveries in the field of induction. Even more surprising was the phenomenon of self-induction, which he discovered at about the same time. In his experiments, it was found that the coil not only induced a current in another coil, but also when the current in this coil changed, it induced an additional EMF in it. So it was called the EMF of self-induction. Of great interest is the direction of the current. It turned out that in the case of the EMF of self-induction, its current is directed against its “parent” - the current due to the main EMF.

Is it possible to observe the phenomenon of self-induction? As they say, nothing is easier. We will assemble the first two - a series-connected inductor and a light bulb, and the second - only a light bulb. Connect them to the battery through a common switch. When turned on, you can see that the light in the circuit with the coil lights up “reluctantly”, and the second light, faster “to rise”, turns on instantly. What's happening? In both circuits, after switching on, the current begins to flow, and it changes from zero to its maximum, and it is just the change in current that the inductor coil waits for, which generates the self-induction EMF. There is an EMF and a closed circuit, which means that there is also its current, but it is directed opposite to the main current of the circuit, which, in the end, will reach the maximum value determined by the parameters of the circuit and stop growing, and since there is no change in current, there is no self-induction EMF. Everything is simple. A similar picture, but with “exactly the opposite”, is observed when the current is turned off. True to its “bad habit” of resisting any change in current, the self-inductive EMF keeps it flowing in the circuit after the power is turned off.

Immediately the question arose - what is the phenomenon of self-induction? It was found that the EMF of self-induction is affected by the rate of change of current in the conductor, and we can write:

From this it can be seen that the EMF of self-induction E is directly proportional to the rate of change of the current dI / dt and the coefficient of proportionality L, called inductance. For his contribution to the study of the question of what the phenomenon of self-induction consists of, George Henry was rewarded by the fact that the unit of inductance, the henry (H), bears his name. It is the inductance of the current flow circuit that determines the phenomenon of self-induction. It can be imagined that inductance is a kind of “storage” of magnetic energy. In the case of an increase in current in the circuit, the electrical energy is converted into magnetic energy, which delays the increase in current, and when the current decreases, the magnetic energy of the coil is converted into electrical energy and maintains the current in the circuit.

Probably, everyone had to see a spark when the plug was turned off from the socket - this is the most common variant of the manifestation of self-induction EMF in real life. But in everyday life, currents of a maximum of 10-20 A are opened, and the opening time is about 20 ms. With an inductance of the order of 1 H, the EMF of self-induction in this case will be equal to 500 V. It would seem that the question of what the phenomenon of self-induction consists of is not so complicated. But in fact, self-induction EMF is a big technical problem. The bottom line is that when the circuit breaks, when the contacts have already dispersed, self-induction maintains the flow of current, and this leads to burnout of the contacts, because. in technology, circuits with currents of hundreds and even thousands of amperes are switched. Here we are often talking about the self-induction EMF of tens of thousands of volts, and this requires an additional solution of technical issues related to overvoltages in electrical circuits.

But not everything is so gloomy. It happens that this harmful EMF is very useful, for example, in ICE ignition systems. Such a system consists of an inductor in the form of an autotransformer and a chopper. A current is passed through the primary winding, which is turned off by a breaker. As a result of an open circuit, an EMF of self-induction of hundreds of volts occurs (while the battery gives only 12V). Further, this voltage is additionally transformed, and a pulse of more than 10 kV is supplied to the spark plugs.

The phenomenon of self-induction- this is the occurrence in a conducting circuit of an EMF created due to a change in the current strength in the circuit itself.

Loop inductance depends on its shape and size, on the magnetic properties of the environment and does not depend on the current strength in the circuit.

EMF of self-induction is determined by the formula:

Magnetic field energy

The energy of the magnetic field of the circuit with current.

Topics of the USE codifier: self-induction, inductance, magnetic field energy.

Self-induction is a special case of electromagnetic induction. It turns out that the electric current in the circuit, which changes with time, acts on itself in a certain way.

Situation 1.Suppose that the current in the circuit increases. Let the current flow counterclockwise; then the magnetic field of this current is directed upwards and increases (Fig. 1).

Rice. 1. The vortex field prevents the increase in current

Thus, our circuit is in an alternating magnetic field of its own current. The magnetic field in this case increases (together with the current) and therefore generates a vortex electric field, the lines of which are directed clockwise in accordance with the Lenz rule.

As you can see, the vortex electric field is directed against the current, preventing its increase; it kind of "slows down" the current. Therefore, when any circuit is closed, the current is not established instantly - it takes some time to overcome the inhibitory effect of the emerging vortex electric field.

Situation 2. Let us now assume that the current in the circuit decreases. The magnetic field of the current also decreases and generates a vortex electric field directed counterclockwise (Fig. 2).

Rice. 2. Vortex field supports decreasing current

Now the vortex electric field is directed in the same direction as the current; it maintains the current, preventing it from decreasing.

As we know, the work of a vortex electric field to move a single positive charge around the circuit is the induction EMF. Therefore, we can give such a definition.

The phenomenon of self-induction is that when the current strength changes in the circuit, an induction emf arises in the same circuit.

As the current strength increases (in situation 1), the vortex electric field does negative work, slowing down the free charges. Therefore, the induction emf in this case is negative.

When the current strength decreases (in situation 2), the vortex electric field does positive work, “pushing” the free charges and preventing the current from decreasing. The induction EMF in this case is also positive (it is easy to verify that the sign of the induction EMF, defined in this way, is consistent with the sign selection rule for the induction EMF formulated in the Electromagnetic Induction sheet).

Inductance

We know that the magnetic flux penetrating the circuit is proportional to the magnetic field induction: . In addition, experience shows that the value of the magnetic field induction of the circuit with current is proportional to the strength of the current: . Therefore, the magnetic flux through the surface of the circuit, created by the magnetic field of the current in this very circuit, is proportional to the current strength: .

The proportionality factor is denoted and called inductance contour:

(1)

The inductance depends on the geometric properties of the circuit (shape and dimensions), as well as on the magnetic properties of the medium in which the circuit is placed (Do you catch the analogy? The capacitance of a capacitor depends on its geometric characteristics, as well as on the dielectric constant of the medium between the capacitor plates). The unit of measure for inductance is Henry(GN).

Let us assume that the shape of the contour, its dimensions and the magnetic properties of the medium remain constant (for example, our circuit is a coil into which no core is inserted); the change in magnetic flux through the circuit is caused only by a change in current strength. Then , and Faraday's law takes the form:

(2)

Due to the minus sign in (2), the induction EMF turns out to be negative with increasing current and positive with decreasing current, which we saw above.

Consider two experiments demonstrating the phenomenon of self-induction when closing and opening a circuit.

Rice. 3. Self-inductance when the circuit is closed

In the first experiment, two bulbs are connected in parallel to the battery, and the second is in series with a coil of a sufficiently large inductance (Fig. 3).

The key is initially open.

When the key is closed, light 1 lights up immediately, and light 2 - gradually. The fact is that an EMF of induction occurs in the coil, which prevents the increase in current. Therefore, the maximum value of the current in the second light bulb is set only some noticeable time after the flashing of the first light bulb.

This delay time is the greater, the greater the inductance of the coil. The explanation is simple: after all, then the intensity of the vortex electric field that arises in the coil will be greater, and therefore the battery will have to do a lot of work to overcome the vortex field that slows down the charged particles.

In the second experiment, a coil and a light bulb are connected in parallel to the battery (Fig. 4). The resistance of the coil is much less than the resistance of the bulb.

Rice. 4. Self-inductance when the circuit is opened

The key is initially closed. The light bulb does not light - the voltage on it is close to zero due to the low resistance of the coil. Almost all of the current flowing in an unbranched circuit passes through the coil.

When the key is opened, the light flashes brightly! Why? The current through the coil begins to decrease sharply, and a significant induction EMF arises, supporting the decreasing current (after all, the induction EMF, as can be seen from (2), is proportional to the rate of current change).

In other words, when the key is opened, a very large vortex electric field appears in the coil, which accelerates free charges. Under the action of this vortex field, a current pulse runs through the light bulb, and we see a bright flash. With a sufficiently large inductance of the coil, the EMF of induction can become significantly larger than the EMF of the battery, and the light bulb will burn out completely.

It may not be a pity for a light bulb, but in industry and energy, this effect is a serious problem. Since when the circuit is opened, the current begins to decrease very quickly, the induction EMF that occurs in the circuit can significantly exceed the rated voltages and reach dangerously large values. Therefore, in units that consume high current, special hardware precautions are provided (for example, oil circuit breakers in power plants) that prevent instantaneous opening of the circuit.

Electromechanical analogy

It is easy to see a certain analogy between inductance in electrodynamics and mass in mechanics.

1. To accelerate the body to a given speed, it takes some time - it is impossible to instantly change the speed of the body. With a constant force applied to the body, this time is the greater, the greater the mass of the body.

It takes some time for the current in the coil to reach its maximum value; instantaneous current is not established. The current establishment time is greater, the greater the inductance of the coil.

2. If a body hits a fixed wall, then the speed of the body decreases very quickly. The wall takes the blow, and its destructive effect is the stronger, the greater the mass of the body.

When the circuit with the coil is opened, the current decreases very quickly. The circuit takes on a "shock" in the form of a vortex electric field generated by a decreasing magnetic field of the current, and this "shock" is the stronger, the greater the inductance of the coil. The induction emf can reach such high values that the breakdown of the air gap will disable the equipment.

Actually these electromechanical analogies extend quite far; they concern not only inductance and mass, but also other quantities, and turn out to be very useful in practice. We will talk more about this in the leaflet on electromagnetic oscillations.

Magnetic field energy

Recall the second experiment with a light bulb that does not light when the key is closed and flashes brightly when the circuit is opened. We directly observe that after opening the key, energy is released in the light bulb. But where does this energy come from?

It is taken, of course, from the coil - nowhere else. But what kind of energy was stored in the coil and how to calculate this energy? To understand this, let's continue our electromechanical analogy between inductance and mass.

To accelerate a body of mass from rest to speed , an external force must do work. The body acquires kinetic energy, which is equal to the work expended:.

In order for the current in the inductor to reach a value after the circuit is closed, the current source must do work to overcome the eddy electric field directed against the current. The work of the source goes to create a current and turns into the energy of the magnetic field of the created current. This energy is stored in the coil; it is this energy that is then released in the light bulb after the key is opened (in the second experiment).

Inductance serves as an analogue of mass; current strength is the obvious analogue of speed. Therefore, it is natural to assume that for the energy of the magnetic field of the coil, a formula similar to the expression for the kinetic energy can take place:

(3)

(especially since the right side of this formula has the dimension of energy - check it out!).

Formula (3) indeed turns out to be valid. It is not necessary to be able to derive it yet, but if you know what an integral is, then it will not be difficult for you to understand the following reasoning.

Let the current through the coil be equal to . Let's take a short period of time. During this interval, the increment in current strength is equal to; the value is considered so small that it is much less than .

In time, a charge passes through the circuit. In this case, the vortex electric field performs negative work:

The current source does the same modulo positive work (recall, we neglect the resistance of the coil, so that all the work of the source is done against the vortex field):

Integrating this from zero to , we find the work of the source, which is spent on creating the current:

This work is converted into the energy of the magnetic field of the created current, and we arrive at formula (3).