Self-induction is the appearance in a conductor of an electromotive force (EMF) directed in the opposite direction relative to the voltage of the power source when current flows. Moreover, it occurs at the moment when the current strength in the circuit changes. A changing electric current generates a changing magnetic field, which in turn induces an emf in the conductor.
This is similar to the wording of the law electromagnetic induction Faraday, where it says:
When a magnetic flux passes through a conductor, an emf occurs in the latter. It is proportional to the rate of change of magnetic flux (mathematical derivative with respect to time).
E=dФ/dt,
Where E is the self-inductive emf, measured in volts, F is the magnetic flux, the unit of measurement is Wb (weber, also equal to V/s)
Inductance
We have already said that self-induction is inherent in inductive circuits, so let’s consider the phenomenon of self-induction using the example of an inductor.
An inductor is an element that is a coil of insulated conductor. To increase the inductance, the number of turns is increased or a core made of soft magnetic or other material is placed inside the coil.
The unit of inductance is Henry (H). Inductance measures how strongly a conductor resists electric current. Since a magnetic field is formed around each conductor through which current flows, and if you place a conductor in an alternating field, a current will arise in it. In turn, the magnetic fields of each turn of the coil add up. Then a strong magnetic field will arise around the coil through which the current flows. When its strength in the coil changes, the magnetic flux around it will also change.
According to Faraday's law of electromagnetic induction, if a coil is penetrated by an alternating magnetic flux, then a current and self-induction emf will arise in it. They will impede the current that would flow in the inductance from the power source to the load. They are also called extra-current EMF of self-induction.
The formula for self-induction EMF on inductance has the form:
That is, the greater the inductance, and the more and faster the current has changed, the stronger the EMF surge will be.
As the current in the coil increases, a self-inductive emf appears, which is directed against the voltage of the power source; accordingly, the increase in current will slow down. The same thing happens when decreasing - self-induction will lead to the appearance of an emf, which will maintain the current in the coil in the same direction as before. It follows that the voltage at the coil terminals will be opposite to the polarity of the power source.
In the figure below you can see that when an inductive circuit is turned on/off, the current does not suddenly arise, but changes gradually. The laws of commutation also speak about this.
Another definition of inductance is that magnetic flux is proportional to current, but in its formula inductance acts as a proportionality factor.
Transformer and mutual induction
If you place two coils in close proximity, for example, on the same core, then the phenomenon of mutual induction will be observed. Let's pass alternating current through the first, then its alternating flow will penetrate the turns of the second and an EMF will appear at its terminals.
This EMF will depend on the length of the wire, respectively, the number of turns, as well as on the value of the magnetic permeability of the medium. If they are simply placed next to each other, the EMF will be low, and if we take a core made of soft magnetic steel, the EMF will be much greater. Actually, this is how the transformer is designed.
Interesting: This mutual influence of the coils on each other is called inductive coupling.
Benefits and harms
If you understand theoretical part, it is worth considering where the phenomenon of self-induction is applied in practice. Let's look at examples of what we see in everyday life and technology. One of useful applications– this is a transformer, we have already examined the principle of its operation. Nowadays they are becoming less common, but previously fluorescent tubular lamps were used daily in lamps. The principle of their operation is based on the phenomenon of self-induction. You can see her diagrams below.
After voltage is applied, current flows through the circuit: phase - inductor - spiral - starter - spiral - zero.
Or vice versa (phase and zero). After the starter is triggered, its contacts open, then (the coil with high inductance) tends to maintain the current in the same direction, induces a self-inductive emf of large magnitude and the lamps are ignited.
Similarly, this phenomenon applies to the ignition circuit of a car or motorcycle that runs on gasoline. In them, a mechanical (chopper) or semiconductor switch (transistor in the ECU) is installed in the gap between the inductor and the minus (ground). This key, at the moment when a spark should form in the cylinder to ignite the fuel, breaks the power circuit of the coil. Then the energy stored in the coil core causes an increase in the self-induction emf and the voltage at the spark plug electrode increases until a breakdown of the spark gap occurs, or until the coil burns out.
In power supplies and audio equipment, there is often a need to remove unnecessary ripples, noise or frequencies from a signal. For this, filters of different configurations are used. One of the options is LC, LR filters. By inhibiting current growth and alternating current resistance, respectively, it is possible to achieve the desired goals.
The EMF of self-induction causes harm to the contacts of switches, knife switches, sockets, automatic machines and other things. You may have noticed that when you pull out the plug of a running vacuum cleaner from the socket, a flash inside it is very often noticeable. This is the resistance to the change in current in the coil (motor winding in in this case).
In semiconductor switches the situation is more critical - even a small inductance in the circuit can lead to their breakdown when peak values of Uke or Usi are reached. To protect them, snubber circuits are installed, on which the energy of inductive bursts is dissipated.
Conclusion
Let's summarize. The conditions for the occurrence of self-inductive emf are: the presence of inductance in the circuit and a change in the current in the load. This can happen both during work, when changing modes or disturbing influences, and when switching devices. This phenomenon can harm the contacts of relays and starters, as it leads to the opening of inductive circuits, for example, electric motors. To reduce Negative influence most of switching equipment is equipped with arc suppression chambers.
The EMF phenomenon is used quite often for useful purposes, from a filter to smooth out current ripples and a frequency filter in audio equipment, to transformers and high-voltage ignition coils in cars.
We hope you now understand what self-induction is, how it manifests itself and where it can be used. If you have any questions, ask them in the comments below the article!
Materials
Relationship between electric and magnetic fields
Electrical and magnetic phenomena have been studied for a long time, but it never occurred to anyone to somehow connect these studies with each other. It was only in 1820 that it was discovered that a current-carrying conductor acts on a compass needle. This discovery belonged to the Danish physicist Hans Christian Oersted. Subsequently, the unit of tension measurement was named after him magnetic field in the GHS system: Russian designation E (Ørsted), English - Oe. This is the magnetic field strength in a vacuum with an induction of 1 Gauss.
This discovery suggested that a magnetic field could be generated from an electric current. But at the same time, thoughts also arose about the reverse transformation, namely, how to obtain an electric current from a magnetic field. After all, many processes in nature are reversible: water produces ice, which can be melted back into water.
It took twenty-two years to study this now obvious law of physics after Oersted’s discovery. The English scientist Michael Faraday was involved in generating electricity from a magnetic field. Done various shapes and sizes of conductors and magnets, options for their relative arrangement were sought. And only, apparently, by accident did the scientist discover that in order to obtain an EMF at the ends of the conductor, one more term is necessary - the movement of the magnet, i.e. The magnetic field must be variable.
Now this no longer surprises anyone. This is exactly how all electric generators work - as long as it is rotated by something, electricity is generated and the light bulb shines. They stopped, stopped rotating, and the light went out.
Electromagnetic induction
Thus, EMF at the ends of the conductor occurs only if it is moved in a certain way in a magnetic field. Or, more precisely, the magnetic field must necessarily change, be variable. This phenomenon is called electromagnetic induction, in Russian electromagnetic induction: in this case they say that an EMF is induced in the conductor. If a load is connected to such an EMF source, current will flow in the circuit.
The magnitude of the induced EMF depends on several factors: the length of the conductor, the induction of the magnetic field B, and, to a large extent, the speed of movement of the conductor in the magnetic field. The faster the generator rotor is rotated, the higher the voltage at its output.
Note: electromagnetic induction (the phenomenon of the occurrence of EMF at the ends of a conductor in an alternating magnetic field) should not be confused with magnetic induction - a vector physical quantity characterizing the magnetic field itself.
Induction
This method has been reviewed. It is enough to move the conductor in a magnetic field permanent magnet, or vice versa, move (almost always by rotation) the magnet near the conductor. Both options will definitely allow you to obtain an alternating magnetic field. In this case, the method of producing EMF is called induction. It is induction that is used to produce EMF in various generators. In Faraday's experiments in 1831, a magnet moved progressively inside a coil of wire.
Mutual induction
This name suggests that two conductors take part in this phenomenon. A changing current flows in one of them, which creates an alternating magnetic field around it. If there is another conductor nearby, then an alternating EMF appears at its ends.
This method of producing EMF is called mutual induction. It is on the principle of mutual induction that all transformers operate, only their conductors are made in the form of coils, and cores made of ferromagnetic materials are used to enhance magnetic induction.
If the current in the first conductor stops (circuit break), or becomes, even very strong, but constant (no changes), then no EMF will be obtained at the ends of the second conductor. This is why transformers operate only on alternating current: if you connect a galvanic battery to the primary winding, then there will definitely be no voltage at the output of the secondary winding.
EMF in the secondary winding is induced only when the magnetic field changes. Moreover, the stronger the rate of change, namely the speed, and not the absolute value, the greater the induced emf will be.
Self-induction
If you remove the second conductor, then the magnetic field in the first conductor will penetrate not only the surrounding space, but also the conductor itself. Thus, under the influence of its field, an emf is induced in the conductor, which is called self-induction emf.
The phenomenon of self-induction was studied by the Russian scientist Lenz in 1833. Based on these experiments, it was possible to find out an interesting pattern: the self-induction EMF always counteracts and compensates for the external alternating magnetic field that causes this EMF. This dependence is called Lenz's rule (not to be confused with the Joule-Lenz law).
The minus sign in the formula just speaks of the counteraction of the self-induction EMF to the causes that gave rise to it. If the coil is connected to a constant current source, the current will increase quite slowly. This is very noticeable when “testing” the primary winding of a transformer with a dial ohmmeter: the speed of the needle moving towards the zero scale division is noticeably less than when checking resistors.
When the coil is disconnected from the current source, the self-induction emf causes sparking of the relay contacts. In the case when the coil is controlled by a transistor, for example a relay coil, then a diode is placed parallel to it in the opposite direction with respect to the power source. This is done in order to protect semiconductor elements from the effects of self-induction emf, which can be tens or even hundreds of times higher than the voltage of the power source.
To conduct experiments, Lenz designed an interesting device. Two aluminum rings are fixed at the ends of the aluminum rocker arm. One ring is solid, but the other has a cut. The rocker rotated freely on the needle.
When a permanent magnet was inserted into a solid ring, it “ran away” from the magnet, and when the magnet was removed, it rushed after it. The same actions with a cut ring did not cause any movement. This is explained by the fact that in a solid ring, under the influence of an alternating magnetic field, a current arises, which creates a magnetic field. But in an open ring there is no current, therefore there is no magnetic field.
An important detail of this experiment is that if a magnet is inserted into the ring and remains motionless, then no reaction of the aluminum ring to the presence of the magnet is observed. This once again confirms that induced emf occurs only when the magnetic field changes, and the magnitude of the emf depends on the rate of change. In this case, it simply depends on the speed of movement of the magnet.
The same can be said about mutual induction and self-induction, only the change in the magnetic field strength, or rather the rate of its change, depends on the rate of change of the current. To illustrate this phenomenon, the following example can be given.
Let large currents pass through two fairly large identical coils: through the first coil 10A, and through the second as much as 1000, and in both coils the currents increase linearly. Let's assume that in one second the current in the first coil changed from 10 to 15A, and in the second from 1000 to 1001A, which caused the appearance of a self-induced emf in both coils.
But despite this great value current in the second coil, the self-induction EMF will be greater in the first, since there the rate of change of current is 5A/sec, and in the second it is only 1A/sec. After all, the self-induction emf depends on the rate of increase of the current (read magnetic field), and not on its absolute value.
Inductance
The magnetic properties of a current-carrying coil depend on the number of turns and geometric dimensions. A significant increase in the magnetic field can be achieved by introducing a ferromagnetic core into the coil. ABOUT magnetic properties coils can be judged with sufficient accuracy by the magnitude of the induced emf, mutual induction or self-induction. All these phenomena have been discussed above.
The characteristic of the coil that tells about this is called the coefficient of inductance (self-inductance) or simply inductance. In formulas, inductance is denoted by the letter L, and in diagrams, inductors are denoted by the same letter.
The unit of inductance is henry (H). A coil has an inductance of 1H, in which, when the current changes by 1A per second, an emf of 1V is generated. This value is quite large: the network windings of fairly powerful transformers have an inductance of one or more Gn.
Therefore, values of a lower order are often used, namely milli and micro Henry (mH and μH). Such coils are used in electronic circuits. One of the applications of coils is oscillating circuits in radio devices.
Coils are also used as chokes, the main purpose of which is to pass direct current without loss while weakening alternating current (filters). As a general rule, the higher the operating frequency, the less inductance the coils require.
Inductive reactance
If you take a sufficiently powerful mains transformer and the resistance of the primary winding, it turns out that it is only a few ohms, and even close to zero. It turns out that the current through such a winding will be very large, and even tend to infinity. It seems that a short circuit is simply inevitable! So why isn't it there?
One of the main properties of inductor coils is inductive reactance, which depends on the inductance and the frequency of the alternating current supplied to the coil.
It is easy to see that with increasing frequency and inductance, the inductive reactance increases, and at direct current it generally becomes zero. Therefore, when measuring the resistance of coils with a multimeter, only active resistance wires.
The design of inductors is very diverse and depends on the frequencies at which the coil operates. For example, to operate in the decimeter range of radio waves, printed circuit coils are often used. For mass production, this method is very convenient.
The inductance of the coil depends on its geometric dimensions, core, number of layers and shape. Currently, a sufficient number of standard inductors similar to conventional resistors with leads are produced. Such coils are marked with colored rings. There are also surface mount coils used as chokes. The inductance of such coils is several millihenries.
Self-induction
Each conductor through which electric current flows 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 magnetic flux leads to the emergence of a vortex electric field and an induced emf appears in the circuit.
This phenomenon is called self-induction.
Self-induction is the phenomenon of the occurrence of induced emf in an electrical circuit as a result of a change in current strength.
The resulting emf is called self-induced emf
Manifestation of the phenomenon of self-induction
Circuit closure
When there is a short circuit in the electrical circuit, the current increases, which causes an increase in the magnetic flux in the coil, an eddy electric field appears directed against the current, i.e., a self-inductive emf appears in the coil, which prevents the increase in current in the circuit (the vortex field inhibits electrons).
As a result, L1 lights up later than L2.
Open circuit
When the electrical circuit is opened, the current decreases, a decrease in the flux in the coil occurs, and a vortex electrical field appears, directed like a current (trying to maintain the same current strength), i.e. A self-induced emf arises in the coil, maintaining the current in the circuit.
As a result, L flashes brightly when turned off.
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).
INDUCTANCE
What does self-induced emf depend on?
Electric 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 self-induction emf depends on the rate of change of current in the electrical circuit, on 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 quantity, numerically equal to emf self-induction that occurs in a circuit when the current changes by 1 Ampere in 1 second.
Inductance can also be calculated using the formula:
where Ф is the magnetic flux through the circuit, I is the current strength in the circuit.
SI units of inductance:
The inductance of the coil depends on:
the number of turns, the size and shape of the coil and the relative magnetic permeability of the medium (possibly a core).
SELF-INDUCTION EMF
The self-inductive emf prevents the current from increasing when the circuit is turned on and the current from decreasing when the circuit is opened.
ENERGY OF THE MAGNETIC FIELD OF CURRENT
Around a current-carrying conductor there is a magnetic field that has energy.
Where does it come from? The current source included in the electrical circuit has a reserve of energy.
At the moment of closing the electrical circuit, the current source spends part of its energy to overcome the effect of the self-inductive emf that arises. This part of the energy, called the current’s own energy, goes to the formation of a magnetic field.
The energy of the magnetic field is equal to the intrinsic energy of the current.
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.
Where does the magnetic field energy go after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)
QUESTIONS FOR TEST PAPER
on the topic "Electromagnetic induction"
1. List 6 ways to obtain induction current.
2. The phenomenon of electromagnetic induction (definition).
3. Lenz's rule.
4. Magnetic flux (definition, drawing, formula, input quantities, their units of measurement).
5. The law of electromagnetic induction (definition, formula).
6. Properties of the vortex electric field.
7. Induction emf of a conductor moving in a uniform magnetic field (reason for appearance, drawing, formula, input quantities, their units of measurement).
8. Self-induction (brief manifestation in electrical engineering, definition).
9. EMF of self-induction (its action and formula).
10. Inductance (definition, formulas, units of measurement).
11. Energy of the magnetic field of the current (the formula where the energy of the magnetic field of the current comes from, where it disappears when the current stops).
9.4. The phenomenon of electromagnetic induction
9.4.3. Average value electromotive force self-induction
When the flux associated with a closed conductive circuit changes through the area limited by this circuit, a vortex electric field appears in it and an induction current flows - the phenomenon of electromagnetic self-induction.
Module average self-induction emf for a certain period of time is calculated using the formula
〈 | ℰ i s | 〉 = | Δ Ф s | Δt,
where ΔФ s is the change in the magnetic flux coupled to the circuit during the time Δt.
If the current strength in the circuit changes over time I = I (t), then
∆Ф s = L ∆I,
where L is the inductance of the circuit; ΔI - change in current strength in the circuit over time Δt;
〈 | ℰ i s | 〉 = L | ΔI | Δt,
where ΔI /Δt is the rate of change of current in the circuit.
If loop inductance changes over time L = L (t), then
- the change in flow coupled to the contour is determined by the formula
∆Ф s = ∆LI,
where ΔL is the change in circuit inductance over time Δt; I - current strength in the circuit;
- the module of the average self-induction emf for a certain period of time is calculated by the formula
〈 | ℰ i s | 〉 = I | Δ L | Δt.
Example 16. In a closed conducting circuit with an inductance of 20 mH, a current of 1.4 A flows. Find the average value of the self-induction emf that occurs in the circuit when the current in it is uniformly reduced by 20% in 80 ms.
Solution . The appearance of self-induction emf in a circuit is caused by a change in the flux coupled to the circuit when the current strength in it changes.
The flow associated with the circuit is determined by the formulas:
- at current strength I 1
Ф s 1 = LI 1,
where L is the circuit inductance, L = 20 mH; I 1 - initial current in the circuit, I 1 = 1.4 A;
- at current strength I 2
Ф s 2 = LI 2,
where I 2 is the final current strength in the circuit.
The change in the flow coupled to the circuit is determined by the difference:
Δ Ф s = Ф s 2 − Ф s 1 = L I 2 − L I 1 = L (I 2 − I 1) ,
where I 2 = 0.8I 1.
The average value of the self-induction emf that occurs in the circuit when the current strength changes in it:
〈 ℰ s i 〉 = | Δ Ф s Δ t | = | L (I 2 − I 1) Δ t | = | − 0.2 L I 1 Δ t | = 0.2 L I 1 Δ t,
where ∆t is the time interval during which the current decreases, ∆t = 80 ms.
The calculation gives the value:
〈 ℰ s i 〉 = 0.2 ⋅ 20 ⋅ 10 − 3 ⋅ 1.4 80 ⋅ 10 − 3 = 70 ⋅ 10 − 3 s = 70 mV.
When the current in the circuit changes, a self-inductive emf appears in it, the average value of which is 70 mV.
When the current in the circuit changes, the flux of magnetic induction through the surface limited by this circuit changes; the change in the flux of magnetic induction leads to the excitation of the self-induction emf. The direction of the emf turns out to be such that when the current in the circuit increases, the emf prevents the current from increasing, and when the current decreases, it prevents it from decreasing.
The magnitude of the EMF is proportional to the rate of change of current I and loop inductance L :
.Due to the phenomenon of self-induction in electrical 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, and the value of the self-induction emf can significantly exceed the source emf. Most often in ordinary life it is used in automobile ignition coils. The typical self-induction voltage with a supply voltage of 12V is 7-25kV.
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