Dependence of self-induction emf on the rate of change of current and conductor inductance, Lenz’s rule. Topic: “Self-induction

Repeat the theory:

1. Self-induction is ____________________________________________________________

____________________________________________________________________________________________________________________________________________________________________________.

2. Inductance - ______________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

[L] = ______.

3. Self-induction emf : ______________, Where L- ______________________________, -_______________________Δ I - _______________________________.

4.Lenz's rule: ______________________________________________________________________________

5.Lenz's rule: ______________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

6. The induced current arising in a closed circuit has a direction in which the own magnetic flux created by it through the area limited by the circuit tends to __________________ the change in the external magnetic flux that caused this current.

7. Magnetic flux passing through the solenoid Ф=________________.

8. Induction current is _______________________________________________________________________

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

9. Magnetic field energy W m =______________

10. Volumetric magnetic field energy density ω=__________________________.

Solve problems:

1. What is the inductance of the circuit if, at a current strength of 5A, a magnetic flux of 0.5 mWb appears in it?

Given: SI: Solution:


2. When the current in the coil decreases uniformly over 0.1 s from 10 A to zero, a self-inductive emf of 60 V arises in it. Determine the inductance of the coil.

Given: Solution:


3. Using a rheostat, the current in the coil is uniformly increased at a speed of 2 A/s. Coil inductance 200 mH. What is the self-induced emf in the coil?

Given: SI: Solution:


4. In a coil with an inductance of 0.6 H, the current is 20 A. What is the energy of the coil's magnetic field? How will the field energy change if the current strength is halved?

Given: Solution:


Answer: the magnetic field energy _____________ __________ times when the current is halved.



5. What should be the current strength in the winding of a choke with an inductance of 0.5 H so that the field energy turns out to be equal to 1 J?

Given: Solution:


6. What is the energy of the magnetic field of the solenoid, in which a magnetic flux of 0.3 Wb appears at a current strength of 1A?

Given: Solution:


Test yourself:

1. What magnetic flux occurs in a circuit with an inductance of 0.2 mH at a current of 10 A?

Given: SI: Solution:


2. Find the inductance of the conductor in which a uniform change in current strength by 2A for 0.25 s excites a self-inductive emf of 20 mV.

Given: SI: Solution:


3. Find the energy of the magnetic field of the solenoid, in which a magnetic flux of 0.5 Wb appears at a current strength of 10A.

Given: Solution:


4. Coil inductance 0.1 mH. At what current strength will the magnetic field energy be equal to 0.2 mJ?

Given: SI: Solution:


Date “___” _________20____

Task 35

Independent work on topic

"Magnetic field. Electromagnetic induction"

OPTION 1

1. A magnetic field is created

1) electric charges 2) magnetic charges

3) moving electric charges 4) any body

2. Magnetic induction lines around a current-carrying conductor are correctly shown in the case.

1) A 2) B 3) C 4) D


3. A straight conductor with current / is located between the poles of the magnet (the conductor is located perpendicular to the plane of the sheet, the current flows to the reader). The Ampere force acting on a conductor is directed

1) right → 2) left ← 3) up 4) down ↓

4. Flight trajectory of an electron flying into a uniform magnetic field at an angle of 60°

5. Which of the following processes is explained by the phenomenon of electromagnetic induction?



1) interaction of conductors with current.

2) deflection of a magnetic needle when an electric current passes through a wire.

3) the occurrence of an electric current in a closed coil when the current strength in the coil located next to it increases.

4) the occurrence of a force acting on a straight conductor carrying current.

6. A light wire ring suspended by a thread. When a magnet is pushed into the ring with the north pole, it will be:

1) repelled by a magnet 2) attracted to a magnet 3) stationary 4) first repelled, then attracted

7. The figure shows a graph of the current in the inductor versus time. The self-induction EMF module adopts highest value in the interim

1) from 0 s to 1 s 2) from 1 s to 5 s 3) from 5 s to 6 s 4) from 6 s to 8 s

8. Match technical devices from the left column of the table with the physical phenomena used in them in the right column.

Phenomena Devices

A. electric motor 1) the action of a magnetic field on a permanent magnet

B. compass 2) the effect of a magnetic field on a moving electric charge

B. Galvanometer 3) the effect of a magnetic field on a current-carrying conductor

G. MHD - generator PART C

Solve the problem.

11. A conductor 1 m long slides along horizontal rails located in a vertical magnetic field with an induction of 0.01 T at a constant speed of 10 m/s. The ends of the rails are connected to a resistor with a resistance of 2 ohms. Find the amount of heat released in the resistor in 4 s. Neglect the resistance of the rails and conductor.

Given: SI: Solution


Rating _____ teacher signature ________________/L.S. Tishkina/

OPTION 2

PART A Choose one correct answer

1. A moving electric charge creates

1) only electric field 2) only magnetic field

3) both electric and magnetic fields 4) only gravitational field

2. The figure shows a cylindrical conductor through which electric current flows. The direction of the current is indicated by the arrow. What is the direction of the magnetic induction vector at point C?


1) in the drawing plane up

2) in the drawing plane down

3) from us perpendicular to the drawing plane

4) to us perpendicular to the drawing plane

3. A current-carrying conductor introduced into a magnetic field is acted upon by a force directed

A change in the current strength in the circuit is prevented by the self-inductive emf, equal to the product of the inductance of the circuit and the rate of change in the current strength.

An electric current creates a magnetic field around itself, and part of the magnetic induction lines of this field always passes through the circuit through which the current flows (Fig. 6a). If the current through a circuit changes over time (alternating current), then the magnetic flux through this circuit also changes, which means an induced emf arises, which prevents a change in the magnetic flux (Lenz's rule). However, when the current changes in any circuit, an induced emf occurs, which prevents these changes. This phenomenon is called self-induction, and the corresponding emf is self-induction emf, Eis.

The phenomenon of self-induction is demonstrated in Fig. 6b, which shows how the current strength through the coil changes when a current source is connected and disconnected. It can be seen that when the circuit is closed, the current through the coil reaches a value corresponding to the resistance of the coil, not instantly, but gradually. The reason for this slowdown in the growth of current strength is the self-induced emf, directed against the emf of the current source. When the circuit is opened, a self-induction EMF appears in the coil, trying to maintain the current strength that was before the switch was opened, as a result of which the current strength through the coil does not drop instantly, but gradually. The energy required for current to flow through the coil after the current source has been disconnected (Fig. 6b) is the energy of the coil's magnetic field.

To quantitatively describe the phenomenon of self-induction, we find the dependence of the magnetic flux F through the circuit on the current strength I in this circuit. Obviously, the magnetic flux through a loop is proportional to the magnetic induction within the loop, and the magnetic induction is proportional to the current in the conductor. For this reason, the magnetic flux must be proportional to the current strength:

Ф = L.I, (6.1)

where L is a proportionality coefficient called the circuit inductance. A circuit with inductance is indicated in the diagram by the corresponding icon (see Fig. 6b). Using (6.1), the law of electromagnetic induction (5.2), and also assuming that the inductance of the circuit does not change when the current strength in it changes, one can find the self-inductive emf Eis :

The SI unit of inductance is the henry (H). From (6.2) it follows that the inductance of the circuit depends on the shape and size of this circuit. Thus, the inductance of a flat circuit is greater, the larger its surface area, and the inductance of a coil is proportional to its diameter and the number of turns in it. At the same time, the inductance

The strength of the coil increases when there is a core made of iron or an alloy capable of magnetization inside it.

The phenomenon of self-induction resembles the phenomenon of inertia in mechanics. The inertia of a body, measured by its mass m, slows down the body’s reaction to a force applied to it. The same thing happens in a circuit when they want to change the current strength in it. In this case, as follows from (6.2), the measure of “inertia” of the circuit is its inductance. The analogy between electromagnetic and mechanical phenomena allows us to assume that the current in the circuit plays the same role as the speed of the body v, and the emf is similar to the force acting on the body. Continuing this analogy, we can derive a formula for the energy of the magnetic field of the coil, based on the fact that the kinetic energy of the body is equal. Replacing m with L, and v with I, we obtain the following expression for the energy WМ of the magnetic field of a circuit with inductance L and current strength I:

Calculations show that expression (6.3) is indeed correct, proving the correctness of the analogies between mechanical and electromagnetic phenomena.

Review questions:

What is the phenomenon of self-induction?

· What is inductance called, and in what units is it measured?

· What is the self-induced emf?

· What is the energy of the magnetic field of the current-carrying circuit?

Rice. 6. (a) – lines of magnetic induction of a coil with current; (b) – graph of the change in current through the coil when the current source is turned on and off.

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“Cosmic velocity” - The movement of a body in a gravitational field. Hyperbola. East. The trajectory of bodies moving at low speed. First escape velocity. Image of a man and a woman. Launched in 1977. Yu.A. Gagarin. Circle. In 1989, the Voyager spacecraft went beyond solar system. Trajectories of bodies.

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“Measuring the speed of light” - The satellite was 22 minutes late to emerge from the shadows, compared to the rocket. Ole Christensen Römer September 25, 1644 – September 19, 1710. C=214300 km/s. Armand Hypollite Louis Fizeau September 23, 1819 – September 18, 1896. Then he reached the mirror, passed between the teeth and entered the eye of the observer. The wheel rotated slowly and the light was visible.

“Lesson Speed ​​time distance” - Speed ​​= Distance: time. A man was walking into the city and on the way he caught up with three of his acquaintances. Warm up. A passenger train covered 75 km in the first hour, 60 km in the second hour and 75 km in the third hour. A freight train traveled 120 km in 3 hours, covering the same distance in each hour. Movement tasks. However, the return flight takes 80 minutes.

Self-induced emf With any change in the current in the coil (or in general in the conductor), a self-inductive emf is induced in it.
The greater the rate of change of current, the greater the self-induction emf.

Any decrease in electric current is accompanied by the appearance of e. d.s. self-induction, which, according to Lenz's rule, tends to maintain a decreasing current. As a result, the voltages on the inductors can increase significantly when the current circuit is broken. Sometimes these voltages are so high that the windings can burn out; to protect the windings, so-called discharge resistors are included in parallel with them.

Proportionality factorLis called inductance.

Inductance is measured in Henry. An inductance of one henry is possessed by a circuit in which, when the current changes uniformly at a rate of one ampere per second, e.g. d.s., equal to one volt.

The inductance of a coil is a quantity that characterizes the property of a coil to induce a self-inductive emf.
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.

The larger the diameter of the coil, the number of its turns and the density of the winding, the greater the inductance and self-inductive emf.
We should not forget that if the current in the coil does not change, then no self-induction emf occurs. 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 therefore the magnitude of the self-induction emf when it changes.

In practice, sometimes a coil (or winding) that does not have inductance is needed. In this case, the wire is wound onto a reel, having previously folded it in half. This winding method is called bifilar.
EMF mutual induction
To cause an induced emf in one coil by changing the current in another, it is not at all 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 connect various electrical circuits with each other through a magnetic field. Such a connection is usually called inductive coupling.
The magnitude of the mutual induction emf depends primarily on the speed at which the current in the first coil changes. The faster the current changes in it, the greater the mutual induction emf is created.
In addition, the magnitude of the mutual inductance emf depends on the inductance of both coils and their relative position, as well as on the magnetic permeability environment.

In order to be able to distinguish between different pairs of coils according to their ability to mutually induce an emf, the concept of mutual inductance or mutual induction coefficient was introduced.
Mutual inductance is designated by the letter M. Its unit of measurement, like inductance, is henry.
Henry is the mutual inductance of two coils such that a change in current in one coil by 1 ampere per second causes an emf of mutual inductance equal to 1 volt in the other coil.
The magnitude of the mutual induction emf 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 is closed, the stronger the inductive coupling of the coils and the greater the value of the mutual induction emf.
The operation of such an important electrical device as a transformer is based on the phenomenon of mutual induction.