In this lesson, we will learn how and by whom the phenomenon of self-induction was discovered, consider the experience with which we will demonstrate this phenomenon, define that self-induction is a special case electromagnetic induction... At the end of the lesson, we will introduce a physical quantity showing the dependence of the EMF of self-induction on the size and shape of the conductor and on the environment in which the conductor is located, i.e. inductance.
Henry invented flat copper strip coils with which he achieved power effects that were more pronounced than with wire solenoids. The scientist noticed that when a powerful coil is in the circuit, the current in this circuit reaches its maximum value much slower than without a coil.
Rice. 2. Scheme of the experimental setup D. Henry
In fig. 2 depicts electrical circuit experimental setup, on the basis of which it is possible to demonstrate the phenomenon of self-induction. The electrical circuit consists of two parallel-connected light bulbs, connected through a key to a direct current source. A coil is connected in series with one of the lamps. After closing the circuit, you can see that the light bulb, which is connected in series with the coil, lights up more slowly than the second light bulb (Fig. 3).
Rice. 3. Different incandescence of bulbs at the moment of switching on the circuit
When the source is disconnected, the lamp connected in series with the coil goes out more slowly than the second lamp.
Why the lights don't go out at the same time
When the key is closed (Fig. 4), due to the occurrence of EMF of self-induction, the current in the lamp with the coil grows more slowly, therefore this lamp lights up more slowly.
Rice. 4. Closing the key
When the key is opened (Fig. 5), the emerging EMF of self-induction prevents the current from decreasing. Therefore, the current continues to flow for some time. For the existence of a current, a closed loop is needed. There is such a circuit in the circuit, it contains both bulbs. Therefore, when the circuit is opened, the lamps should glow the same for some time, and the observed delay may be caused by other reasons.
Rice. 5. Opening the key
Consider the processes occurring in this circuit when the key is closed and opened.
1. Closing the key.
There is a conductive coil in the circuit. Let the current in this loop flow counterclockwise. Then the magnetic field will be directed upward (Fig. 6).
Thus, the loop turns out to be in the space of its own magnetic field... As the current increases, the loop will find itself in the space of a changing magnetic field own current... If the current increases, then the magnetic flux created by this current also increases. As is known, with an increase in the magnetic flux penetrating the plane of the circuit, an electromotive force of induction arises in this circuit and, as a consequence, an induction current. According to Lenz's rule, this current will be directed in such a way that its magnetic field prevents a change in the magnetic flux penetrating the plane of the circuit.
That is, for the one considered in Fig. 6 turns, the induction current must be directed clockwise (Fig. 7), thereby preventing the growth of the coil's own current. Consequently, when the key is closed, the current in the circuit does not increase instantly due to the fact that a braking induction current arises in this circuit, directed in the opposite direction.
2. Opening the key
When the key is opened, the current in the circuit decreases, which leads to a decrease in the magnetic flux through the plane of the loop. A decrease in the magnetic flux leads to the appearance of an EMF of induction and induction current. In this case, the induction current is directed in the same direction as the coil's own current. This leads to a slowdown in the decay of the self-current.
Output: when the current in the conductor changes, electromagnetic induction occurs in the same conductor, which generates an induction current directed in such a way as to prevent any change in the intrinsic current in the conductor (Fig. 8). This is the essence of the phenomenon of self-induction. Self-induction is a special case of electromagnetic induction.
Rice. 8. The moment of switching on and off the circuit
Formula for finding the magnetic induction of a straight conductor with current:
where is the magnetic induction; - magnetic constant; - current strength; - the distance from the conductor to the point.
The flux of magnetic induction through the pad is:
where is the surface area that is pierced magnetic flux.
Thus, the flux of magnetic induction is proportional to the amount of current in the conductor.
For a coil in which is the number of turns, and is the length, the magnetic induction is determined by the following relationship:
Magnetic flux generated by a coil with a number of turns N, is equal to:
Substituting in given expression the formula for the induction of the magnetic field, we get:
The ratio of the number of turns to the length of the coil is denoted by the number:
We get the final expression for the magnetic flux:
It can be seen from the obtained relation that the value of the flux depends on the magnitude of the current and on the geometry of the coil (radius, length, number of turns). A value equal to is called inductance:
The unit of measure for inductance is henry:
Therefore, the flux of magnetic induction caused by the current in the coil is:
Taking into account the formula for the EMF of induction, we find that the EMF of self-induction is equal to the product of the rate of change of the current by the inductance, taken with the "-" sign:
Self-induction- this is the phenomenon of the occurrence of electromagnetic induction in a conductor when the current flowing through this conductor changes.
Electromotive force of self-induction is directly proportional to the rate of change of the current flowing through the conductor, taken with a minus sign. The aspect ratio is called inductance, which depends on the geometric parameters of the conductor.
A conductor has an inductance of 1 H if, at a rate of change in the current in the conductor of 1 A per second, an electromotive self-induction force of 1 V arises in this conductor.
A person encounters the phenomenon of self-induction every day. Each time, turning on or off the light, we thereby close or open the circuit, while exciting induction currents. Sometimes these currents can reach such high values that a spark jumps inside the switch, which we can see.
Bibliography
- Myakishev G.Ya. Physics: Textbook. for 11 cl. general education. institutions. - M .: Education, 2010.
- Kasyanov V.A. Physics. 11th grade: Textbook. for general education. institutions. - M .: Bustard, 2005.
- Gendenshtein L.E., Dick Yu.I., Physics 11. - M .: Mnemosyne.
- Internet portal Myshared.ru ().
- Internet portal Physics.ru ().
- Festival.1september.ru Internet portal ().
Homework
- Questions at the end of paragraph 15 (p. 45) - Myakishev G.Ya. Physics 11 (see the list of recommended reading)
- Which conductor has an inductance of 1 Henry?
What is the EMF of self-induction?
According to Faraday's law ℰ is= -. If Ф = LI, then ℰ is= = -. Provided that the inductance of the circuit does not change during the current change (i.e., the geometric dimensions of the circuit and the magnetic properties of the medium do not change), then
ℰ is = – . (13.2)
It can be seen from this formula that if the inductance of the coil L is large enough, and the time of the current change is small, then the quantity ℰ is can reach a large value and exceed the EMF of the current source when the circuit is opened. It is this effect that we observed in experiment 1.
From formula (13.2) we can express L:
L = – ℰ is/ (D I/ D t),
those. inductance has another physical meaning: it is numerically equal to the EMF of self-induction at a rate of change of current through the circuit 1 A in 1 s.
Reader: But then it turns out that the dimension of the inductance
[L] = Gn =.
STOP! Decide for yourself: A3, A4, B3 – B5, C1, C2.
Task 13.2. What is the inductance of an iron core coil if in time D t= 0.50 s the current in the circuit has changed from I 1 = = 10.0 A to I 2 = 5.0 A, and the resulting EMF of self-induction modulo | ℰ is| = 25 V?
Answer: L = ℰ is"2.5 G.
STOP! Decide for yourself: A5, A6, B6.
Reader: And what is the meaning of the minus sign in formula (13.2)?
 Rice. 13.6 |
author: Consider a conductive circuit through which current flows. Let's choose bypass direction contour - clockwise or counterclockwise (Fig. 13.6). Recall: if the direction of the current coincides with the selected direction of the bypass, then the current is considered positive, and if not, negative.
Change in current D I = I con - I nach is also an algebraic quantity (negative or positive). EMF of self-induction is the work done by the vortex field when moving a single positive charge along the contour along the direction of traversing the contour... If the intensity of the vortex field is directed along the direction of bypassing the contour, then this work is positive, and if against, it is negative. Thus, the minus sign in formula (13.2) shows that the quantities D I and ℰ is always have different signs.
Let's show this with examples (Fig.13.7):
a) I> 0 and D I> 0, hence ℰ is < 0, т.е. ЭДС самоиндукции «включена» навстречу направлению обхода;
b) I> 0 and D I < 0, значит, ℰis >
v) I < 0, а D|I |> 0, i.e. the modulus of the current increases, and the current itself becomes more and more negative. Hence D I < 0, тогда ℰis> 0, i.e. EMF of self-induction is "on" along the bypass direction;
G) I < 0, а D|I | < 0, т.е. модуль тока уменьшается, а сам ток становится все «менее отрицательным». Значит, DI> 0, then ℰ is < 0, т.е. ЭДС самоиндукции «включена» навстречу направлению обхода.
In tasks, if possible, you should choose such a bypass direction so that the current is positive.
Task 13.3. In the circuit in fig. 13.8, a L 1 = 0.02 H and L 2 = 0.005 H. At some point, the current I 1 = 0.1 A and increases at a rate of 10 A / s, and the current I 2 = 0.2 A and increases at a rate of 20 A / s. Find resistance R.
  a b Rice. 13.8 Solution. Since both currents increase, EMF of self-induction appears in both coils ℰ is 1
|
|
| L 1 = 0.02 Gn L 2 = 0.005 H I 1 = 0.1 A I 2 = 0.2 A D I 1 / D t= 10 A / s D I 2 / D t= 20 A / s | |
| R = ? | |
and ℰ is 2 switched on opposite currents I 1 and I 2 (fig.13.8, b), where
|ℰ is 1 | =; | ℰ is 2 | = .
Let's choose the direction of bypass clockwise (see fig.13.8, b) and apply the second Kirchhoff rule
–|ℰ is 1 | + | ℰ is 2 | = I 1 R - I 2 R ,
R = |ℰ is 2 | - | ℰ is 1 | / (I 1 - I 2) = 
=
1 ohm.
Answer: R = »1 Ohm.
STOP! Decide for yourself: B7, B8, C3.
Task 13.4. Resistance coil R= 20 Ohm and inductance L= 0.010 H is in an alternating magnetic field. When the magnetic flux created by this field increased by DF = 0.001 Vb, the current in the coil increased by D I = 0.050 A. What charge passed through the coil during this time?
| Rice. 13.9 |
ductions |ℰ is| =. And ℰ is"Turned on" towards ℰ i, as the current in the circuit increased (Fig.13.9).
Take the clockwise direction of traversing the contour. Then, according to the second rule of Kirchhoff, we get:
|ℰ i| – |ℰ is| = IR ,
I = (|ℰ i| – |ℰ is|)/R = 
.
Charge q passed along the coil in time D t, is equal to
q = I D t = 
Answer: 
25 μC.
STOP! Decide for yourself: B9, B10, C4.
Task 13.5. Coil with inductor L and electrical resistance R connected through a key to a current source with EMF ℰ . In the moment t= 0 the key is closed. How the current strength changes over time I in the circuit immediately after the key is closed? Across long time after closing? Estimate the characteristic time t of current rise in such a circuit. The internal resistance of the current source can be neglected.
Rice. 13.10
 Rice. 13.11 |
Immediately after closing the key I= 0, so we can assume »ℰ / L, i.e. current increases with constant speed (I = (ℰ / L)t;rice. 13.11).
When the switch is closed, an electric current will appear in the circuit shown in Figure 1, the direction of which is shown by single arrows. With the appearance of a current, a magnetic field arises, the induction lines of which cross the conductor and induce an electromotive force (EMF) in it. As indicated in the article "The Phenomenon of Electromagnetic Induction", this EMF is called the EMF of self-induction. Since any induced EMF according to Lenz's rule is directed against the cause that caused it, and this cause will be the EMF of the battery of cells, the EMF of the self-induction of the coil will be directed against the EMF of the battery. The direction of the self-induction EMF in Figure 1 is shown by double arrows.
Thus, the current is not established in the circuit immediately. Only when the magnetic flux is established, the crossing of the conductor magnetic lines will stop and the EMF of self-induction will disappear. Then a direct current will flow in the circuit.
Figure 2 shows a graphical representation of a direct current. The horizontal axis is time, the vertical axis is current. It can be seen from the figure that if at the first moment of time the current is 6 A, then at the third, seventh and so on moments in time it will also be equal to 6 A.
Figure 3 shows how the current in the circuit is established after switching on. EMF of self-induction, directed at the moment of switching on against the EMF of the battery of cells, weakens the current in the circuit, and therefore at the moment of switching on the current is zero... Further, at the first moment of time, the current is 2 A, at the second moment of time - 4 A, at the third - 5 A, and only after a while the current of 6 A is established in the circuit.
 |  |
| Figure 3. Graph of the current rise in the circuit, taking into account the EMF of self-induction | Figure 4. The EMF of self-induction at the moment of opening the circuit is directed in the same way as the EMF of the voltage source |
When the circuit is opened (Figure 4), the disappearing current, the direction of which is shown by a single arrow, will decrease its magnetic field. This field, decreasing from a certain value to zero, will again cross the conductor and induce the EMF of self-induction in it.
When the electric circuit with inductance is turned off, the EMF of self-induction will be directed in the same direction as the EMF of the voltage source. The direction of the EMF of self-induction is shown in Figure 4 with a double arrow. As a result of the action of the EMF of self-induction, the current in the circuit does not disappear immediately.
Thus, the EMF of self-induction is always directed against the cause that caused it. Noting this property of it, they say that the EMF of self-induction is reactive in nature.
Graphically, the change in the current in our circuit, taking into account the EMF of self-induction when it is closed and with its subsequent opening at the eighth point in time, is shown in Figure 5.
 |  |
| Figure 5. Graph of the rise and fall of the current in the circuit, taking into account the EMF of self-induction | Figure 6. Induction currents when opening the circuit |
When opening circuits containing a large number of turns and massive steel cores or, as they say, having a high inductance, the EMF of self-induction can be many times greater than the EMF of the voltage source. Then, at the moment of opening, the air gap between the knife and the fixed clamp of the knife switch will be broken and the resulting electric arc will melt the copper parts of the switch switch, and in the absence of a casing on the switch switch, it can burn a person's hands (Figure 6).
In the circuit itself, the EMF of self-induction can break through the insulation of the turns of coils, electromagnets, and so on. To avoid this, in some switching devices, they arrange protection against EMF of self-induction in the form of a special contact that short-circuits the winding of the electromagnet when it is turned off.
It should be borne in mind that the EMF of self-induction manifests itself not only at the moments of switching on and off the circuit, but also with any changes in the current.
The magnitude of the EMF of self-induction depends on the rate of change of the current in the circuit. So, for example, if for the same circuit in one case within 1 second the current in the circuit changed from 50 to 40 A (that is, by 10 A), and in another case from 50 to 20 A (that is, by 30 A ), then in the second case, a three times greater EMF of self-induction will be induced in the circuit.
The magnitude of the EMF of self-induction depends on the inductance of the circuit itself. High inductance circuits are windings of generators, electric motors, transformers and induction coils with steel cores. Straight conductors have less inductance. Short rectilinear conductors, incandescent lamps and electric heating devices (stoves, stoves) practically do not have inductance and the appearance of EMF of self-induction in them is almost not observed.
The magnetic flux penetrating the circuit and inducing EMF of self-induction in it is proportional to the current flowing along the circuit:
Ф = L × I ,
where L- coefficient of proportionality. It is called inductance. Let's define the dimension of inductance:
Ohm × sec is otherwise called henry (Hn).
1 henry = 10 3; millihenry (mH) = 10 6 microhenry (μH).
Inductance, except for henry, is measured in centimeters:
1 henry = 10 9 cm.
So, for example, 1 km of a telegraph line has an inductance of 0.002 H. The inductance of the windings of large electromagnets reaches several hundred henries.
If the current in the circuit has changed by Δ i, then the magnetic flux will change by the value Δ Ф:
Δ Ф = L × Δ i .
The value of the EMF of self-induction that appears in the circuit will be equal to ( EMF formula self-induction):
With a uniform change in current over time, the expression will be constant and it can be replaced by the expression. Then absolute value The self-induction EMF arising in the circuit can be found as follows:
Based on the last formula, we can define the unit of inductance - henry:
A conductor has an inductance of 1 H if, with a uniform change in current by 1 A in 1 second, an EMF of self-induction of 1 V is induced in it.
As we have seen above, the EMF of self-induction arises in the DC circuit only at the moments of its switching on, off and at any change in it. If the magnitude of the current in the circuit is unchanged, then the magnetic flux of the conductor is constant and the EMF of self-induction cannot arise (since. At the moments of current change in the circuit, the EMF of self-induction interferes with changes in the current, that is, it has a kind of resistance to it.
Often, in practice, there are cases when it is necessary to make a coil that does not have inductance (additional resistances to electrical measuring instruments, resistances of plug-in rheostats, and the like). In this case, a bifilar winding of the coil is used (Figure 7)
Self-induction phenomenon
If the reel goes alternating current, 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.
In self-induction, the conducting circuit plays a double role: a current flows through it, causing induction, and the EMF of induction appears in it. The changing magnetic field induces an EMF in the very conductor through which the current flows, which creates this field.
At the moment of current increase, the intensity of the vortex electric field in accordance with the Lenz rule, it is directed against the current. Consequently, at this moment, the vortex field prevents the growth of the current. On the contrary, at the moment of decreasing the current, the vortex field maintains it.
This leads to the fact that when a circuit containing a source of constant EMF is closed, a certain value of the current strength is not established 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 the current and its magnetic field when the source is turned off occurs very quickly.
The phenomenon of self-induction can be observed on simple experiments... Figure 10 shows a diagram of 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 EMF of self-induction in the circuit of this lamp is large, and the current strength does not immediately reach its maximum value.
The emergence of EMF of self-induction when opening can be observed experimentally with a circuit schematically shown in Figure 11. When opening the key in the coil L EMF of self-induction arises, 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 battery cells.
Inductance
Magnetic induction value B generated by the current in any closed loop is proportional to the current strength. Since the magnetic flux F proportional V, then it can be argued that
\ (~ \ Phi = L \ cdot I \),
where L- the coefficient of proportionality between the current in the conducting circuit and the magnetic flux created by it, penetrating this circuit. The value of L is called the loop inductance or its self-induction coefficient.
Using the law of electromagnetic induction, we get the equality:
\ (~ E_ (is) = - \ frac (\ Delta \ Phi) (\ Delta t) = - L \ cdot \ frac (\ Delta I) (\ Delta t) \),
It follows from the resulting formula that
inductance- this is physical quantity, numerically equal emf self-induction arising in the circuit when the current strength changes by 1 A for 1 s.
Inductance, like electrical capacity, depends on geometric factors: the size of the conductor and its shape, but does not directly depend on the strength of the current in the conductor. In addition to the geometry of the conductor, the inductance depends on magnetic properties the environment in which the conductor is located.
The SI unit of inductance is called henry (H). The inductance of the conductor is equal to 1 H, if in it, when the current strength changes by 1 A for 1 s, an EMF of self-induction of 1 V occurs:
1 H = 1 V / (1 A / s) = 1 V s / A = 1 Ohm s
Magnetic field energy
Let's find the energy possessed by the electric current in the conductor. According to the law of conservation of energy, the energy of the current is equal to the energy that the current source (galvanic cell, generator at a power plant, etc.) must spend to create a current. When the current stops, this energy is released in one form or another.
The energy of the current, which will now be discussed, 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 driving the electrons of the conductor and the formation of a magnetic field associated with the current, as well as partly on increasing the internal energy of the conductor, i.e. to heat it. After installing constant value current strength, the energy of the source is spent exclusively on the release of heat. In this case, the current energy does not change anymore.
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 appears in the conductor electric field, 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 is used 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 high inductance circuit is opened.
Let us find an expression for the current energy I L.
Work A made by a source with EMF E in a short time Δ t, is equal to:
\ (~ A = E \ cdot I \ cdot \ Delta t \). (1)
According to the law of conservation of energy, 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 in the energy of the current
\ (~ \ 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) \) is the self-induction EMF. 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 complete change in energy with increasing current from zero to I 1 is numerically equal to the area of the triangle OBC with the parties I 1 and L∙I 1 . Hence,
\ (~ W_m = \ frac (L \ cdot I ^ 2_1) (2) \).
Energy current I flowing through the circuit with inductance L, is equal to
\ (~ W_m = \ frac (L \ cdot I ^ 2) (2) \).
The energy of the magnetic field, contained in a unit volume of space occupied by the field, is called volumetric energy density of the magnetic field ω m:
\ (~ \ omega_m = \ frac (W_m) (V) \).
If a magnetic field is created inside a solenoid with a length l and loop area S, then, taking into account that the inductance of the solenoid \ (~ L = \ frac (\ mu_0 \ cdot N ^ 2 \ cdot S) (l) \) and the modulus of the magnetic 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 \).
Because V = S ∙ l, then the energy density of the magnetic field
\ (~ \ omega_m = \ frac (B ^ 2) (2 \ cdot \ mu_0) \).
The magnetic field created electric shock, has energy 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: Textbook. allowance for the 10th grade. general education. shk. from rus. lang. training / V.V. Zhilko, A.V. Lavrinenko, L.G. Markovich. - Mn .: Nar. Asveta, 2001 .-- 319 p.
- Myakishev, G. Ya. Physics: Electrodynamics. 10-11 cl. : textbook. for in-depth study of physics / G.Ya. Myakishev, A. 3. Sinyakov, V.A. Slobodskov. - M .: Bustard, 2005 .-- 476 p.