Lesson on the phenomenon of self-induction. Lesson topic: “The phenomenon of self-induction

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, and determine that self-induction is a special case of electromagnetic induction. At the end of the lesson, we will introduce a physical quantity showing the dependence of the self-inductive emf on the size and shape of the conductor and on the environment in which the conductor is located, i.e. inductance.

Henry invented flat coils made of strip copper, with the help of which he achieved power effects that were more pronounced than when using wire solenoids. The scientist noticed that when there is a powerful coil in the circuit, the current in this circuit reaches its maximum value much more slowly than without the coil.

Rice. 2. Diagram of the experimental setup by D. Henry

In Fig. Figure 2 shows an electrical diagram of the experimental setup, on the basis of which the phenomenon of self-induction can be demonstrated. An electrical circuit consists of two parallel-connected light bulbs connected through a switch to a direct current source. A coil is connected in series with one of the light bulbs. After closing the circuit, it can be seen 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 light bulbs at the moment the circuit is turned on

When the source is turned off, the light bulb connected in series with the coil goes out more slowly than the second light bulb.

Why don't the lights go out at the same time?

When the switch is closed (Fig. 4), due to the occurrence of self-induction emf, the current in the light bulb with the coil increases more slowly, so this light bulb lights up more slowly.

Rice. 4. Key closure

When the switch is opened (Fig. 5), the resulting self-induction EMF prevents the current from decreasing. Therefore, the current continues to flow for some time. For current to exist, a closed circuit is needed. There is such a circuit in the circuit; it contains both light bulbs. Therefore, when the circuit is opened, the light bulbs should glow the same for some time, and the observed delay may be caused by other reasons.

Rice. 5. Key opening

Let us consider the processes occurring in this circuit when the key is closed and opened.

1. Key closure.

There is a current-carrying coil in the circuit. Let the current in this turn flow counterclockwise. Then the magnetic field will be directed upward (Fig. 6).

Thus, the coil ends up in the space of its own magnetic field. As the current increases, the coil will find itself in the space of a changing magnetic field of its 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 should be directed clockwise (Fig. 7), thereby preventing the increase in the turn’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 appears in this circuit, directed in the opposite direction.

2. Opening the key

When the switch is opened, the current in the circuit decreases, which leads to a decrease in the magnetic flux through the plane of the coil. A decrease in magnetic flux leads to the appearance of induced emf and induced current. In this case, the induced current is directed in the same direction as the coil’s own current. This leads to a slower decrease in the intrinsic current.

Conclusion: when the current in a conductor changes, electromagnetic induction occurs in the same conductor, which generates an induced current directed in such a way as to prevent any change in its own 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 magnetic induction; - magnetic constant; - current strength; - distance from the conductor to the point.

The flux of magnetic induction through the area is equal to:

where is the surface area that is penetrated by the magnetic flux.

Thus, the flux of magnetic induction is proportional to the magnitude of the current in the conductor.

For a coil in which is the number of turns and is the length, the magnetic field induction is determined by the following relationship:

Magnetic flux created by a coil with the number of turns N, is equal to:

Substituting the formula for magnetic field induction into this expression, we obtain:

The ratio of the number of turns to the length of the coil is denoted by the number:

We obtain the final expression for the magnetic flux:

From the resulting relationship it is clear that the flux value depends on the current value and on the geometry of the coil (radius, length, number of turns). A value equal to is called inductance:

The unit of inductance is henry:

Therefore, the flux of magnetic induction caused by the current in the coil is equal to:

Taking into account the formula for induced emf, we find that self-induction emf is equal to the product of the rate of change of current and inductance, taken with the “-” sign:

Self-induction- this is the phenomenon of the occurrence of electromagnetic induction in a conductor when the strength of the current flowing through this conductor changes.

Electromotive force of self-induction is directly proportional to the rate of change of current flowing through the conductor, taken with a minus sign. The proportionality factor is called inductance, which depends on the geometric parameters of the conductor.

A conductor has an inductance equal to 1 H if, at a rate of change of current in the conductor equal to 1 A per second, a self-inductive electromotive force equal to 1 V arises in this conductor.

People encounter the phenomenon of self-induction every day. Every time we turn on or off the light, we thereby close or open the circuit, thereby 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 11th grade general education institutions. - M.: Education, 2010.
Kasyanov V.A. Physics. 11th grade: Educational. for general education institutions. - M.: Bustard, 2005.
Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.

Internet portal Myshared.ru ().
Internet portal Physics.ru ().
Internet portal Festival.1september.ru ().

Homework

Questions at the end of paragraph 15 (p. 45) - Myakishev G.Ya. Physics 11 (see list of recommended readings)
The inductance of which conductor is 1 Henry?

The phenomenon of self-induction.
E.m.f. self-induction.
Magnetic field energy.

Target:
Educational:
1. Ensure assimilation (repetition, consolidation) and study during the lesson
the following basic concepts, laws, theories, scientific facts: what is
self-induction, e.m.f. self-induction, finding magnetic field energy, graph
dependence of magnetic flux on current strength.
2. Check the degree of knowledge acquisition.
Educational:
1.
2. Study the position, principles.
Development objectives:
1.
Cognitiveness of the world and its patterns
To develop in students the ability to highlight the main, essential things in what they have learned
material, compare, generalize, logically express your thoughts.
2. Develop the ability to analyze acquired knowledge and professional skills.

Lesson plan.
1. The phenomenon of self-induction. Definition of self-induction. E.m.f. self-induction.
2. Magnetic field energy. Graph of magnetic flux versus current.
Self-induction
1. Self-induction
R
Consider a circuit consisting of a battery, a rheostat R, an inductor L,
galvanometer G and key K.
If the circuit is closed, then through the galvanometer G and the inductance coil L flows
electricity. At the moment the circuit opens, the galvanometer needle sharply
deviates in the opposite direction. This happens because when the circuit opens
The magnetic flux in the coil decreases, causing e.g. d.s. self-induction. Current
self-induction
, in accordance with Lenz's law, prevents the decrease
cI
magnetic flux, i.e. it is directed in the coil in the same way as the decreasing current
2I
the current passes entirely through the galvanometer; but its direction is opposite
direction
. The phenomenon of the occurrence of induced current in a circuit as a result
. This
1I
changes in current in this circuit are called self
by induction.

Self-induction is a special case of the phenomena of electromagnetic induction.

Let's find out what e depends on. d.s. self-induction. Induction B is proportional
current in the coil, therefore the magnetic FLUX arising in the coil also
proportional to the current:
Ф=LI.
The proportionality coefficient L is called the circuit inductance.
When changing your own; magnetic flux in the circuit, according to the law
electromagnetic induction, e.g. d.s. self-induction

si

F

t
Substituting into expression
formula Ф=LI, we find; that e. d.s.

si

F

t
self-induction is proportional to the rate of change of current:

si
L

I

t
2. Magnetic field energy
Current magnetic field energy
Consider the circuit
, consisting of battery B, resistor
R, solenoid L, key K. If the key is in position 1, then through the solenoid
a current I0 constant in value and direction flows. Any electric current
always surrounded by a magnetic field. The question arises: where is our own
current energy - inside the wires along which they drift or in a magnetic field, i.e. V
environment surrounding currents? To answer this question, consider what will happen
occur if the key is opened and moved to position 2. In this case, after
resistor R will flow for some time, decreasing to zero current, maintained
the resulting self-induction current, and the conversion of magnetic energy occurs
current fields mainly into the energy of molecular thermal motion - heating
resistance. This means that the decrease in magnetic field energy can be calculated as
work of this current:
W = A. Since the own magnetic flux Ф = LI,

penetrating solenoid is proportional to the current strength, then the dependence of Ф on I can be
depicted in the form shown in Fig.

Area of a shaded narrow strip with a base
I matches

basic work
A, carried out by the current, when its value changes by

The total work A performed by the current is equal to the sum of the elementary works
A and numerically
I.


equal to the area of triangle OAB:
A 
00IF
2
Considering that
, formula
F 
0
LI
0
A 
can be rewritten in the form
A 
.
2
0LI
2
00IF
2
In the process of performing this work, the energy of the magnetic field decreases to
zero (since the current decreases from the value to zero). Since there are no
no changes occur in the bodies surrounding the electrical circuit, the following conclusion follows:
The magnetic field is a carrier of energy.
So, the self-energy of the current is equal to the energy of the magnetic field:

2LI
2
is valid for any contour, it characterizes
Wm 
Formula
Wm 
2LI
2
dependence of the energy of the magnetic field of the current on the current strength in the circuit and its inductance.

Self-test questions.
1. Describe the circuit in which the emf occurs. self-induction.
2. What is called self-induction?
3. Characterize the ratio of the decrease in magnetic field energy to
current work.
4. Draw a work schedule and describe it.
5. Reproduce the formula for finding the magnetic field energy, give it
characteristics.
Self-test tasks.
1) Determine the emf. self-induction, if the change in current is 4.2 A,
the time change is 40 ms, and the loop inductance is 0.37 H.
(Answer: Emf=38.85 V)
2) Determine the inductance of the circuit if it is known that the change in current
is equal to 5.4 A, the time change is 57 ms, and the e.m.f. self-induction is 27 V.
(Answer: L=0.285 Hn)
3) Determine what the magnetic field energy is equal to if the inductance of the circuit
is equal to 0.74 H, and the current is 25 A.
(Answer:
J)
25.231mW

Literature
Dmitrieva V.F. Physics: Textbook. manual for technical schools./ Ed. V.L. Prokofiev,
– 4th ed., erased. – M.: Higher. school, 2001. – 415 p.: ill. ISBN 5060036685

The purpose of the lesson: form the idea that a change in current in a conductor creates a vortex that can either accelerate or slow down moving electrons.

During the classes

Checking homework using individual questioning

1. Obtain a formula for calculating the electromotive force of induction for a conductor moving in a magnetic field.

2. Derive a formula for calculating the electromotive force of induction using the law of electromagnetic induction.

3. Where is an electrodynamic microphone used and how is it designed?

4. Task. The resistance of the wire coil is 0.03 Ohm. The magnetic flux decreases inside the coil by 12 mWb. What electric charge passes through the cross section of the coil?

Solution. ξi=ΔФ/Δt; ξi= Iiʹ·R; Ii =Δq/Δt; ΔФ/Δt = Δq R/Δt; Δq = ΔФΔt/ RΔt; Δq= ΔФ/R;

Learning new material

1. Self-induction.

If an alternating current flows through a conductor, then it creates an induced emf in the same conductor - this is a phenomenon

Self-induction. The conductive circuit plays a dual role: current flows through it, and an induced emf is created in it by this current.

Based on Lenz's rule; when the current increases, the strength of the vortex electric field is directed against the current, i.e. prevents its increase.

As the current decreases, the vortex field maintains it.

Let's look at a diagram that shows that the current strength reaches a certain

values gradually, after some time.

Demonstration of experiments with circuits. Using the first circuit, we will show how the induced emf appears when the circuit is closed.

When the key is closed, the first lamp lights up instantly, the second with a delay, due to the large self-inductance in the circuit created by the coil with the core.

Using the second circuit, we will demonstrate the appearance of induced emf when the circuit is opened.

At the moment of opening, a current will flow through the ammeter, directed against the initial current.

When opening, the current may exceed the original current value. This means that the self-induction emf can be greater than the emf of the current source.

Draw an analogy between inertia and self-induction

Inductance.

Magnetic flux is proportional to the magnitude of magnetic induction and current strength. F~B~I.

Ф= L I; where L is the proportionality coefficient between current and magnetic flux.

This coefficient is often called circuit inductance or self-induction coefficient.

Using the magnitude of inductance, the law of electromagnetic induction can be written as follows:

ξis= – ΔФ/Δt = – L ΔI/Δt

Inductance is a physical quantity numerically equal to the self-inductive emf that occurs in the circuit when the current changes by 1 A in 1 s.

Inductance is measured in henry (H) 1 H = 1 V s/A

On the importance of self-induction in electrical and radio engineering.

Conclusion: when a changing current flows through a conductor, an eddy electric field appears.

The vortex field slows down free electrons when the current increases and maintains it when it decreases.

Consolidation of the studied material.

– How to explain the phenomenon of self-induction?

– Draw an analogy between inertia and self-induction.

– What is circuit inductance, in what units is inductance measured?

- Task. At a current of 5 A, a magnetic flux of 0.5 mWb appears in the circuit. What will be the inductance of the circuit?

Solution. ΔФ/Δt = – L ΔI/Δt; L = ΔФ/ΔI; L =1 ·10-4H

Let's summarize the lesson

Homework: §15, rep. §13, ex. 2 No. 10

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The purpose of the lesson: to test students’ knowledge on the topic studied, to improve their skills in solving problems of various types. Progress of the lesson Checking homework Students' answers based on what they prepared at home...
The purpose of the lesson: to repeat and summarize knowledge on the topic covered; improve the ability to think logically, generalize, solve qualitative and calculation problems. Progress of the lesson Checking homework 1....
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If the current in the circuit changes, then the magnetic field of this current and the own magnetic flux penetrating the circuit changes. If the current in the circuit changes, then the magnetic field of this current and the own magnetic flux penetrating the circuit changes. An induced emf arises in the circuit, which, according to Lenz’s rule, prevents a change in the current in the circuit. An induced emf arises in the circuit, which, according to Lenz’s rule, prevents a change in the current in the circuit.

SELF-INDUCTION Self-induction is the phenomenon of the occurrence of induced emf in a circuit when the electric current changes in the same circuit. Self-induction is the phenomenon of the occurrence of induced emf in a circuit when the electric current changes in the same circuit. Self-induction is an important special case of electromagnetic induction. Self-induction is an important special case of electromagnetic induction.

INDUCTANCE The self-magnetic flux Φ, penetrating the circuit or coil with current, is proportional to the current strength I. The self-magnetic flux Φ, penetrating the circuit or coil with current, is proportional to the current strength I. The proportionality coefficient L in this formula is called the self-induction coefficient or the inductance of the coil.

INDUCTANCE The SI unit of inductance is called the henry (H). The SI unit of inductance is called the henry (H). The inductance of a circuit or coil is 1 H if, at a direct current of 1 A, its own flux is 1 Wb. The inductance of a circuit or coil is 1 H if, at a direct current of 1 A, its own flux is 1 Wb. 1 H = 1 Wb / 1 A

SELF-INDUCTION The self-induction emf that occurs in a coil with a constant inductance value is equal to the self-induction emf that occurs in a coil with a constant inductance value is equal to the self-induction emf that is directly proportional to the inductance of the coil and the rate of change of the current in it. The self-induction emf is directly proportional to the inductance of the coil and the rate of change of current in it.

Magnetic energy. When the key is opened, the lamp flashes brightly. When the key is opened, the lamp flashes brightly. The current in the circuit arises under the influence of self-induction emf. The source of energy released in the electrical circuit is the magnetic field of the coil.

Magnetic energy. From the law of conservation of energy it follows that all the energy stored in the coil will be released in the form of Joule heat. If we denote the total resistance of the circuit by R, then during the time Δt an amount of heat will be released. From the law of conservation of energy it follows that all the energy stored in the coil will be released in the form of Joule heat. If we denote the total resistance of the circuit by R, then during the time Δt the amount of heat ΔQ = I 2 RΔt will be released
Magnetic energy. Let's plot the dependence of the magnetic flux Φ(I) on the current I. Let's plot the dependence of the magnetic flux Φ(I) on the current I. The total amount of released heat, equal to the initial reserve of magnetic field energy, is determined by the area of the triangle. ФI/2

Subject: Self-induction. Inductance.

The purpose of the lesson : form the idea that a change in current in a conductor creates a vortex that can either accelerate or slow down moving electrons.

During the classes

Checking homework using individual questioning

1. Obtain a formula for calculating the electromotive force of induction for a conductor moving in a magnetic field.

2. Derive a formula for calculating the electromotive force of induction using the law of electromagnetic induction.

3. Where is an electrodynamic microphone used and how is it designed?

4. Task. The resistance of the wire coil is 0.03 Ohm. The magnetic flux decreases inside the turn by 12 mWb. What electric charge passes through the cross section of the coil?

Solution. ξi=ΔФ/Δt; ξi= Iiʹ·R; Ii =Δq/Δt; ΔФ/Δt = Δq R/Δt; Δq = ΔФΔt/ RΔt; Δq= ΔФ/R;

Δq=400 mC

Learning new material

1. Self-induction.

If an alternating current flows through a conductor, then it creates an induced emf in the same conductor - this is the phenomenon of self-induction. The conductive circuit plays a dual role: current flows through it, and an induced emf is created in it by this current.

Based on Lenz's rule; when the current increases, the strength of the vortex electric field is directed against the current, i.e. prevents its increase.

When the current decreases, the vortex field maintains it.

Let's look at a diagram that shows that the current strength reaches a certain

values gradually, over time.

R L1 L

L L2 R A