With any change in the current in the coil (or in general in the conductor), EMF of self-induction.
When an EMF is induced in a coil by changing its own magnetic flux, the magnitude of this EMF depends on the rate of change of the current. The greater the rate of current change, the greater the EMF of self-induction.
The value of the EMF of self-induction also depends on the number of turns of the coil, the density of their winding and the size of the coil. The larger the diameter of the coil, the number of its turns and the density of winding, the greater the EMF of self-induction. This dependence of the EMF of self-induction on the rate of change of current in the coil, the number of its turns and dimensions is of great importance in electrical engineering.
The direction of the EMF of self-induction is determined by the Lenz law. The EMF of self-induction always has such a direction in which it prevents a change in the current that caused it.
In other words, a decrease in the current in the coil entails the appearance of an EMF of self-induction directed in the direction of the current, i.e., preventing its decrease. And, conversely, with an increase in current in the coil, an EMF of self-induction arises, directed against the current, i.e., preventing its increase.
It should not be forgotten that if the current in the coil does not change, then no EMF self-induction does not occur. The phenomenon of self-induction is especially pronounced in a circuit containing a coil with an iron core, since iron significantly increases the magnetic flux of the coil, and, consequently, the magnitude of the self-induction EMF when it changes.
Inductance
So, we know that the value of the EMF of self-induction in the coil, in addition to the rate of change of current in it, also depends on the size of the coil and the number of its turns.
Consequently, coils of different design at the same rate of current change are capable of inducing self-induction EMFs of different magnitudes.
In order to distinguish coils among themselves by their ability to induce self-induction EMF in themselves, the concept is introduced coil inductance, or self-induction coefficient.
The inductance of a coil is a value that characterizes the property of the coil to induce an EMF of self-induction in itself.
The inductance of a given coil is a constant value, independent of both the strength of the current passing through it and the rate of its change.
Henry is the inductance of such a coil (or conductor), in which, when the current strength changes by 1 ampere in 1 second, an EMF of self-induction of 1 volt appears.
In practice, sometimes you need a coil (or winding) that does not have inductance. In this case, the wire is wound on a coil, having previously folded it in half. This method of winding is called bifilar.
Mutual induction emf
So, we know that the induction EMF in the coil can be caused without moving the electromagnet in it, but by changing only the current in its winding. But that in order to cause an EMF of induction in one coil by changing the current in another, it is absolutely not necessary to insert one of them inside the other, but you can place them side by side
And in this case, when the current in one coil changes, the resulting alternating magnetic flux will penetrate (cross) the turns of the other coil and cause an EMF in it.
Mutual induction makes it possible to interconnect various electrical circuits by means of a magnetic field. Such a connection is called inductive connection.
The magnitude of the EMF of mutual induction depends primarily on the rate at which the current in the first coil changes. The faster the current changes in it, the greater the EMF of mutual induction is created.
In addition, the magnitude of the EMF of mutual induction depends on the magnitude of the inductance of both coils and on their relative position, as well as on the magnetic permeability of the environment.
Hence, coils different in their inductance and mutual arrangement and in different environments are capable of inducing mutual induction of different EMF values in one another.
In order to be able to distinguish between different pairs of coils by their ability to mutually induce EMF, the concept of mutual inductance or coefficient of mutual induction.
Mutual inductance is denoted by the letter M. Its unit of measurement, as well as inductance, is henry.
Henry is such a mutual inductance of two coils, in which a change in current in one coil by 1 ampere per 1 second causes a mutual inductance EMF equal to 1 volt in the other coil.
The magnitude of the EMF of mutual induction is affected by the magnetic permeability of the environment. The greater the magnetic permeability of the medium through which the alternating magnetic flux connecting the coils closes, the stronger the inductive coupling of the coils and the greater the magnitude of the mutual induction EMF.
The operation of such an important electrical device as a transformer is based on the phenomenon of mutual induction.
The principle of operation of the transformer
The principle of operation of the transformer is based on and is as follows. Two windings are wound on an iron core, one of them is connected to an alternating current source, and the other to a current consumer (resistance).
A winding connected to an alternating current source creates an alternating magnetic flux in the core, which induces an emf in the other winding.
The winding connected to the AC source is called primary, and the winding to which the consumer is connected is called secondary. But since a variable magnetic flux permeates both windings simultaneously, variable EMF is induced in each of them.
The value of the EMF of each turn, as well as the EMF of the entire winding, depends on the magnitude of the magnetic flux penetrating the turn, and the rate of its change. The rate of change of magnetic flux depends solely on the frequency of the alternating current, which is constant for a given current. The magnitude of the magnetic flux is also constant for a given transformer. Therefore, in the considered transformer, the EMF in each winding depends only on the number of turns in it.
The ratio of the primary voltage to the secondary voltage is equal to the ratio of the number of turns of the primary and secondary windings. This relationship is called.
If mains voltage is applied to one of the transformer windings, then voltage will be removed from the other winding, more or less than the mains voltage as many times as the number of turns of the secondary winding is more or less.
If a voltage greater than that applied to the primary winding is removed from the secondary winding, then such a transformer is called a step-up transformer. On the contrary, if a voltage is removed from the secondary winding, less than the primary one, then such a transformer is called a step-down transformer. Each transformer can be used as a step-up or step-down.
The transformation ratio is usually indicated in the transformer passport as the ratio of the highest voltage to the lowest, that is, it is always greater than one.
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 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"
Wikimedia Foundation. 2010 .
- Bourdon, Robert Gregory
- Juan Amar
See what "Self-induction" is in other dictionaries:
self-induction- self-induction ... Spelling Dictionary
SELF-INDUCTION- the occurrence of induction emf 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
SELF-INDUCTION- excitation of the electromotive force of induction (emf) in an electric 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, self-induction, for women. (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- (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
SELF-INDUCTION- 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
self-induction- noun, number of synonyms: 1 electromotive force excitation (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:
SELF-INDUCTION
Each conductor through which electricity flows. current is in its own magnetic field.
When the current strength changes in the conductor, the m.field changes, i.e. the magnetic flux created by this current changes. A change in the magnetic flux leads to the emergence of a vortex el. field and induction emf appears in the circuit. 
This phenomenon is called self-induction.
Self-induction - the phenomenon of the occurrence of EMF induction in email. circuit as a result of a change in current strength.
The resulting emf is called EMF self-induction
Closing the circuit 
When closing in el. the current increases in the circuit, which causes an increase in the magnetic flux in the coil, a vortex electric arises. field directed against the current, i.e. an EMF of self-induction occurs in the coil, which prevents the current from rising in the circuit (the vortex field slows down the electrons).
As a result L1 lights up later, than L2.
Open circuit 
When the electric circuit is opened, the current decreases, there is a decrease in the m.flow in the coil, a vortex electric field appears, directed like a current (tending to maintain the same current strength), i.e. A self-inductive emf appears in the coil, which maintains the current in the circuit.
As a result, L when turned off flashes brightly.
Conclusion
in electrical engineering, the phenomenon of self-induction manifests itself when the circuit is closed (the electric current increases gradually) and when the circuit is opened (the electric current does not disappear immediately).
What does the EMF of self-induction depend on?
Email current creates its own magnetic field. The magnetic flux through the circuit is proportional to the magnetic field induction (Ф ~ B), the induction is proportional to the current strength in the conductor
(B ~ I), therefore the magnetic flux is proportional to the current strength (Ф ~ I).
The EMF of self-induction depends on the rate of change in the current strength in the email. circuits, from the properties of the conductor
(size and shape) and on the relative magnetic permeability of the medium in which the conductor is located.
A physical quantity showing the dependence of the self-induction EMF on the size and shape of the conductor and on the environment in which the conductor is located is called the self-induction coefficient or inductance. 
Inductance - physical. a value numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 ampere in 1 second.
Also, the inductance can be calculated by the formula:
where F is the magnetic flux through the circuit, I is the current strength in the circuit.
Inductance units in the SI system:
The inductance of a coil depends on:
the number of turns, the size and shape of the coil, and the relative magnetic permeability of the medium
(possible core).
EMF of self-induction prevents the increase in current strength when the circuit is turned on and the decrease in current strength when the circuit is opened.
Around a conductor with current there is a magnetic field that has energy.
Where does it come from? Current source included in el. chain, has a store of energy.
At the time of closing email. In the circuit, the current source expends part of its energy to overcome the action of the emerging EMF of self-induction. This part of the energy, called the self-energy of the current, goes to the formation of a magnetic field.
The magnetic field energy is own current energy.
The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction EMF in order to create a current in the circuit.
The energy of the magnetic field created by the current is directly proportional to the square of the current strength.
Where does the energy of the magnetic field disappear after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)
QUESTIONS FOR THE VERIFICATION WORK
on the topic "Electromagnetic induction"
|
1. List 6 ways to obtain an induction current. |
The magnetic field of the circuit, in which the current strength changes, induces a current not only in other circuits, but also in itself. This phenomenon is called self-induction.
It has been experimentally established that the magnetic flux of the magnetic induction vector of the field created by the current flowing in the circuit is proportional to the strength of this current:
where L is the loop inductance. A constant characteristic of the circuit, which depends on its shape and size, as well as on the magnetic permeability of the medium in which the circuit is located. [L] = Hn (Henry,
1H = Wb / A).
If during the time dt the current in the circuit changes by dI, then the magnetic flux associated with this current will change by dФ \u003d LdI, as a result of which an EMF of self-induction will appear in this circuit:
The minus sign shows that the EMF of self-induction (and, consequently, the self-induction current) always prevents a change in the current strength that caused self-induction.
A good example of the phenomenon of self-induction is the extra currents of closing and opening that occur when turning on and off electrical circuits with significant inductance.
Magnetic field energy
The magnetic field has potential energy, which at the moment of its formation (or change) is replenished due to the energy of the current in the circuit, which in this case does work against the self-induction EMF arising from a change in the field.
Work dA for an infinitely small period of time dt, during which the self-induction EMF 
and current I can be considered constant, equals:
.
(5)
The minus sign indicates that the elementary work is done by the current against the EMF of self-induction. To determine the work when the current changes from 0 to I, we integrate the right side, we get:
.
(6)
This work is numerically equal to the increase in potential energy ΔW p of the magnetic field associated with this circuit, i.e. A= -ΔW p.
Let us express the energy of the magnetic field in terms of its characteristics using the example of a solenoid. We will assume that the magnetic field of the solenoid is homogeneous and is mainly located inside it. Let us substitute in (5) the value of the inductance of the solenoid, expressed through its parameters and the value of the current I, expressed from the formula for the induction of the magnetic field of the solenoid:
, (7)
where N is the total number of turns of the solenoid; ℓ is its length; S is the cross-sectional area of the internal channel of the solenoid.
, (8)
After substitution we have:
Dividing both parts by V, we obtain the volumetric field energy density:
(10)
or, given that 
we get 
.
(11)
Alternating current
2.1 Alternating current and its main characteristics
An alternating current is a current that changes over time both in magnitude and direction. An example of alternating current is the consumed industrial current. This current is sinusoidal, i.e. the instantaneous value of its parameters change over time according to the sine (or cosine) law:
i= I 0 sinωt, u = U 0 sin(ωt + φ 0). (12)
P 
Variable sinusoidal current can be obtained by rotating the frame (circuit) at a constant speed
in a uniform magnetic field with induction B(Fig.5). In this case, the magnetic flux penetrating the circuit changes according to the law
where S is the area of the contour, α = ωt is the angle of rotation of the frame in time t. Flux change leads to induction EMF
, (17)
whose direction is determined by the Lenz rule.
E 
If the circuit is closed (Fig. 5), then current flows through it:
.
(18)
Graph of change in electromotive force 
and induction current i shown in Fig.6.
Alternating current is characterized by period T, frequency ν = 1/T, cyclic frequency 
and phase φ \u003d (ωt + φ 0) Graphically, the values \u200b\u200bof the voltage and the strength of the alternating current in the circuit section will be represented by two sinusoids, generally shifted in phase by φ.
To characterize alternating current, the concepts of the effective (effective) value of current and voltage are introduced. The effective value of the alternating current strength is the strength of such a direct current that releases in a given conductor as much heat during one period as it releases heat and a given alternating current.
,
. (13)
Instruments included in the alternating current circuit (ammeter, voltmeter) show the effective values of current and voltage.
The phenomenon of self-induction
If an alternating current flows through the coil, then the magnetic flux penetrating the coil changes. Therefore, an EMF of induction occurs in the same conductor through which the alternating current flows. This phenomenon is called self-induction.
With self-induction, the conducting circuit plays a dual role: a current flows through it, causing induction, and an EMF of induction 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 rise, the intensity of the eddy electric field, in accordance with the Lenz rule, is directed against the current. Therefore, at this moment, the vortex field prevents the current from rising. 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 value of current strength is not set immediately, but gradually over time (Fig. 9). On the other hand, when the source is turned off, the current in closed circuits does not stop instantly. The resulting EMF of self-induction can exceed the EMF of the source, 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 10 shows the parallel connection of two identical lamps. 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-induction emf in the circuit of this lamp is large, and the current strength does not immediately reach its maximum value.
The appearance of an EMF of self-induction upon opening can be observed in an experiment with a circuit shown schematically in Figure 11. When the key is opened in the coil L EMF of self-induction appears, which maintains the initial current. As a result, at the moment of opening, a current flows through the galvanometer (dashed arrow), directed against the initial current before opening (solid arrow). Moreover, the current strength when the circuit is opened exceeds the strength of the current passing through the galvanometer when the key is closed. This means that the EMF of self-induction E is more emf E cell batteries.
Inductance
The magnitude of the magnetic induction B, created by the current in any closed circuit, is proportional to the strength of the current. Since the magnetic flux F proportional AT, then it can be argued that
\(~\Phi = L \cdot I\) ,
where L- coefficient of proportionality between the current in the conductive circuit and the magnetic flux created by it, penetrating this circuit. The value L is called the inductance of the circuit or its coefficient of self-induction.
Using the law of electromagnetic induction, we obtain the equality:
\(~E_(is) = - \frac(\Delta \Phi)(\Delta t) = - L \cdot \frac(\Delta I)(\Delta t)\) ,
From the resulting formula it follows that
inductance- this is a physical quantity numerically equal to the EMF of self-induction that occurs in the circuit when the current changes by 1 A in 1 s.
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. In addition to the geometry of the conductor, the inductance depends on the magnetic properties of the medium in which the conductor is located.
The SI unit of inductance is called the henry (H). The inductance of the conductor is equal to 1 H, if in it, when the current strength changes by 1 A in 1 s, an EMF of self-induction of 1 V occurs:
1 H = 1 V / (1 A/s) = 1 V s/A = 1 Ω s
Magnetic field energy
Find the energy possessed by the electric current in the conductor. According to the law of conservation of energy, the current energy is equal to the energy that the current source (galvanic cell, generator at a power plant, etc.) must expend to create current. When the current is interrupted, this energy is released in one form or another.
The current energy, which will be discussed now, is of a completely different nature than the energy released by direct current in the circuit in the form of heat, the amount of which is determined by the Joule-Lenz law.
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 the electrons of the conductor in motion and forming a magnetic field associated with the current, and also partly on increasing the internal energy of the conductor, i.e. for heating it. After a constant value of the current strength is established, the energy of the source is spent exclusively on the release of heat. The current energy does not change.
Let us now find out why it is necessary to expend energy to create a current, i.e. work needs to 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 to become equal I, the current source must do work against the forces of the vortex field. This work goes to increase the energy of the current. The vortex field does negative work.
When the circuit is opened, the current disappears and the vortex field does positive work. The energy stored by the current is released. This is detected by a powerful spark that occurs when a circuit with a large inductance is opened.
Find an expression for the current energy I L.
Work BUT, made by a source with EMF E in a short time Δ t, is equal to:
\(~A = E \cdot I \cdot \Delta t\) . (one)
According to the energy conservation law, this work is equal to the sum of the current energy increment Δ W m and the amount of heat released \(~Q = I^2 \cdot R \cdot \Delta t\):
\(~A = \Delta W_m + Q\) . (2)
Hence the increment of current energy
\(~\Delta W_m = A - Q = I \cdot \Delta t \cdot (E - I \cdot R)\) . (3)
According to Ohm's law for a complete circuit
\(~I \cdot R = E + E_(is)\) . (4)
where \(~E_(is) = - L \cdot \frac(\Delta I)(\Delta t)\) - EMF of self-induction. Replacing in equation (3) the product I∙R its value (4), we get:
\(~\Delta W_m = I \cdot \Delta t \cdot (E - E - E_(is)) = - E_(is) \cdot I \cdot \Delta t = L \cdot I \cdot \Delta I\ ) . (5)
On the dependency graph L∙I from I(Fig. 12) energy increment Δ W m is numerically equal to the area of the rectangle abcd with the parties L∙I and Δ I. The total change in energy as the current increases from zero to I 1 is numerically equal to the area of the triangle OVS with the parties I 1 and L∙I one . Hence,
\(~W_m = \frac(L \cdot I^2_1)(2)\) .
current energy I, flowing through the circuit with inductance L, is equal to
\(~W_m = \frac(L \cdot I^2)(2)\) .
The energy of a magnetic field contained in a unit volume of space occupied by the field is called volume energy density of the magnetic field ω m:
\(~\omega_m = \frac(W_m)(V)\) .
If a magnetic field is created inside a solenoid of length l and coil area S, then, taking into account that the solenoid inductance \(~L = \frac(\mu_0 \cdot N^2 \cdot S)(l)\) and the modulus of the magnetic field induction vector inside the solenoid \(~B = \frac(\mu_0 \cdot N \cdot I)(l)\) , we get
\(~I = \frac(B \cdot l)(\mu_0 \cdot N) ; W_m = \frac(L \cdot I^2)(2) = \frac(1)(2) \cdot \frac( \mu_0 \cdot N^2 \cdot S)(l) \cdot \left (\frac(B \cdot l)(\mu_0 \cdot N) \right)^2 = \frac(B^2)(2 \ cdot \mu_0) \cdot S \cdot l\) .
As V = Sl, then the energy density of the magnetic field
\(~\omega_m = \frac(B^2)(2 \cdot \mu_0)\) .
The magnetic field created by an electric current has an energy that is directly proportional to the square of the current strength. The energy density of the magnetic field is proportional to the square of the magnetic induction.
Literature
- Zhilko V.V. Physics: Proc. allowance for the 10th grade. general education school from Russian lang. training / V.V. Zhilko, A.V. Lavrinenko, L.G. Markovich. - Mn.: Nar. Asveta, 2001. - 319 p.
- Myakishev, G.Ya. Physics: Electrodynamics. 10-11 cells. : studies. for in-depth study of physics / G.Ya. Myakishev, A.3. Sinyakov, V.A. Slobodskov. – M.: Bustard, 2005. – 476 p.
