Algorithm for applying the laziness rule. The phenomenon of electromagnetic induction

Induction electricity in a conductor, which occurs when the magnetic flux changes, is directed in such a way that its magnetic field counteracts the change in the magnetic flux.

In 1831, English physicist Michael Faraday discovered what is now called Faraday's law of electromagnetic induction, according to which a change in magnetic flux within a conducting circuit excites an electric current in that circuit even when there is no power source in the circuit. Left by Faraday open question The direction of the induction current was soon decided by the Russian physicist Emilius Christianovich Lenz.

Imagine a closed circular current-carrying circuit without a connected battery or other power source, into which a magnet begins to be inserted with the north pole. This will increase the magnetic flux passing through the loop, and, according to Faraday's law, an induced current will appear in the loop. This current, in turn, according to the Biot-Savart law, will generate a magnetic field, the properties of which are no different from the properties of the field of an ordinary magnet with north and south poles. Lenz just managed to find out that the induced current will be directed in such a way that the north pole of the generated current magnetic field will be oriented to the side north pole push-in magnet. Since mutual repulsion forces act between the two north poles of the magnets, the induction current induced in the circuit will flow in precisely the direction that will counteract the introduction of the magnet into the circuit. And this is only a special case, but in a generalized formulation, Lenz’s rule states that the induced current is always directed in such a way as to counteract the root cause that caused it.

Today they are trying to use Lenz’s rule in intercity passenger transport. Prototypes of trains on the so-called magnetic levitation have already been built and are being tested. Powerful magnets are mounted under the bottom of the car of such a train, located a few centimeters from the steel sheet. When the train moves, the magnetic flux passing through the contour of the track is constantly changing, and strong induction currents arise in it, creating a powerful magnetic field that repels the magnetic suspension of the train (similar to how repulsive forces arise between the contour and the magnet in the experiment described above). This force is so great that, having gained some speed, the train literally lifts off the track by 10-15 centimeters and, in fact, flies through the air. Magnetic levitation trains can reach speeds of over 500 km/h, making them ideal for medium-distance intercity transport.

See also:

Lesson on the topic “Lenz's rule. The phenomenon of self-induction. Magnetic field energy".

The purpose of the lesson : learn to determine the direction of the induction current; Using the example of Lenz’s rule, formulate an idea of ​​the fundamental nature of the ESA; explain the essence of the phenomenon of self-induction; derive a formula for calculating the energy of the magnetic field, find out the physical meaning of this formula.

Lesson plan:

Examination homework.

Presentation of new material.

Consolidation.

Homework.

Checking homework.

Plan for presenting new material:

1. Direction of induction current.
2. Lenz's rule and ZSE.
3. The phenomenon of self-induction.
4. EMF of self-induction.
5. Inductance.
6. Application and accounting of self-induction in technology.
7. Energy of the magnetic field of current.

Direction of induction current.

Questions for students to update previous knowledge:

Name two series of experiments by Faraday to study the phenomenon of electromagnetic induction (the occurrence of an induction current in a coil when a magnet or coil with current is moved in and out; the occurrence of an induction current in one coil when the current changes in another by closing or opening a circuit or using a rheostat).

Does the direction of deflection of the galvanometer needle depend on the direction of movement of the magnet relative to the coil? (depends: when the magnet approaches the coil, the arrow deviates in one direction, when the magnet is removed, in the other).

How does (judging by the readings of the galvanometer) the induced current that arises in the coil when the magnet approaches, differ from the current that arises when the magnet moves away (at the same speed of the magnet)? (current differs in direction).

Thus, when the magnet moves relative to the coil, the direction of deflection of the galvanometer needle (and, therefore, the direction of the current) can be different (slide 5).

Using Lenz’s experiment, let us formulate the rule for finding the direction of the induction current (video “Demonstration of the phenomenon of electromagnetic induction”). Explanation of Lenz's experiment (slide 6): If you bring a magnet closer to a conducting ring, it will begin to be repelled from the magnet. This repulsion can only be explained by the fact that an induced current arises in the ring, caused by an increase in the magnetic flux through the ring, and the ring with the current interacts with the magnet.

Lenz's rule and the law of conservation of energy (slide 7).

If the magnetic flux through the circuit increases, then the direction of the induced current in the circuit is such that the magnetic induction vector of the field created by this current is directed opposite to the magnetic induction vector of the external magnetic field.

If the magnetic flux through the circuit decreases, then the direction of the induced current is such that the vector of the magnetic induction of the field created by this current is codirectional to the vector of the magnetic induction of the external field.

Formulation of Lenz's rule (slide 8): the induced current has such a direction that the magnetic flux created by it always tends to compensate for the change in magnetic flux that caused this current.

Lenz's rule is a consequence of the law of conservation of energy.

Let's consider an example of the manifestation of Lenz's rule in life (slide 9) - a magnet floating above a superconducting bowl. You can briefly explain what is happening like this: the magnet falls; an alternating magnetic field arises; a vortex electric field arises; undamped ring currents arise in the superconductor; according to Lenz's rule, the direction of these currents is such that the magnet is repelled from the superconductor; the magnet “floats” above the bowl.

The phenomenon of self-induction.

Before considering the phenomenon of self-induction, let us remember what the essence of the phenomenon of electromagnetic induction is - the occurrence of an induced current in a closed circuit when the magnetic flux passing through this circuit changes. Let's consider one of the variants of Faraday's experiments (slide 10): If the current strength is changed in a circuit containing a closed circuit (coil), then an induced current will also arise in the circuit itself. This current will also obey Lenz's rule.

Let's consider an experiment on closing a circuit containing a coil (slide 11). When the circuit with the coil is closed, a certain current value is established only after some time.

Definition of self-induction (slide 12): SELF-INDUCTION – the appearance of a vortex electric field in a conducting circuit when the current strength in it changes; a special case of electromagnetic induction.
Due to self-induction, a closed circuit has “inertia”: the current strength in the circuit containing the coil cannot be changed instantly.

Self-induction EMF (slide 13). What is the formula for the law of electromagnetic induction?

(ℰ i= -). If the magnetic field is created by a current, then it can be argued that Ф ~ В ~I, i.e. F~ I or Ф= LI, Where L– circuit inductance (or self-inductance coefficient). Then the law of electromagnetic induction in the case of self-induction will take the form:ℰ si= - = - or ℰ si = - L(formula for calculating self-induction emf).

Inductance (slide 14).

If from the formula for calculating the self-induction emf we express the proportionality coefficientL, we get: L= ℰ si/ . Then we equate to unity the values ​​of quantities that we can directly set - the rate of change of current strength is 1 ampere per second. We obtain a formula reflecting the physical meaning of the coefficient of self-induction (inductance): the inductance of the circuit is numerically equal to the EMF of self-induction that occurs when the current changes by 1 A in 1 s.

SI units of inductance: = 1 = 1 H (henry).

Application and accounting of self-induction in technology (slide 15).

Due to the phenomenon of self-induction, when circuits containing coils with steel cores (electromagnets, motors, transformers) are opened, a significant self-induction emf is created and sparking or even an arc discharge may occur. As homework, I suggest (if desired) prepare a presentation on the topic “How to eliminate unwanted self-induction when opening a circuit?”

Magnetic field energy (slide 16):

Let us recall the experiment confirming the existence of the phenomenon of self-induction: when the circuit was closed, the light bulb did not flash immediately, but when the circuit with the coil was opened, the light bulb, instead of going out, flashed for a short time. Obviously, it takes energy to flash a light bulb. And this energy is stored in the coil in the form of magnetic field energy. To derive the energy of the magnetic field, we use an analogy between the establishment of an electric current in a circuit of magnitude I and the process of the body gaining speed V.

1. The establishment of current I in the circuit occurs gradually.

1. The body reaches speed V gradually.

2. To achieve current strength I, work must be done.

2. To achieve speed V, work must be done.

3. The larger L, the slower I grows.

3. The larger m, the slower V grows.

4. W m =

4. E to =

Consolidation (slide 17) - questions 1 - 8 on page 113 of the textbook.

Homework (slide 18) - § 15

Electromagnetic induction is a physical phenomenon consisting of the appearance of an electric current in a closed circuit when the flux of magnetic induction changes through the surface limited by this circuit.

2. A change in what physical quantities can lead to a change in magnetic flux?

A change in magnetic flux can result from a change over time in the surface area that is limited by the contour; magnetic induction vector module; the angle formed by the induction vector with the area vector of this surface.

3. In which case is the direction of the induction current considered positive, and in which - negative?

If the selected direction of bypassing the circuit coincides with the direction of the induction current, then it is considered positive. If the selected direction of bypassing the circuit is opposite to the direction of the induction current, then it is considered negative.

4. Formulate the law of electromagnetic induction. Write down its mathematical expression.

The EMF of electromagnetic induction in a closed circuit is equal in magnitude and opposite in sign to the rate of change of magnetic flux through the surface, which is limited by this circuit.

5. Formulate Lenz’s rule. Give examples of its application

The induced current arising in the circuit, with its magnetic field, counteracts the change in the magnetic flux that caused this current. For example, as the magnetic flux through the circuit increases, the magnetic flux of the induced current will be negative, and the resulting flux, equal to their sum, will decrease. And when the magnetic flux through the circuit decreases, the magnetic flux of the induced current will support the resulting flux, preventing it from sharply decreasing.

Lenz's rule determines the direction of the induced current resulting from electromagnetic induction

Animation

Description

“If a metal conductor moves near a galvanic current or near a magnet, then a galvanic current is excited in it in a direction that would cause the stationary wire to move in the direction straight opposite direction movement imposed here on the wire from the outside, on the assumption that a wire at rest can only move in the direction of this last movement or directly opposite." Professor of St. Petersburg University E.H. Lenz, 1833.

Lenz's rule is based on a generalization of experiments on electromagnetic induction.

In a condensed form, Lenz's rule can be formulated as follows:

the induced current arising in a closed conductor has such a direction as to prevent the change in the flux of magnetic induction that causes it.

That is, the induced current creates, through the area limited by the contour, its own flux of magnetic induction, compensating for the change in the flux of magnetic induction that causes it:

dФ = (B, d S) Yu dФ = B Х dS Х cos a,

where a is the angle between the magnetic induction vector of the external field and the normal to the plane of the solenoid turns.

Let's look at some examples.

1. Take a solenoid (coil) C, closed through a galvanometer G (Fig. 1).

The appearance of an induction current in a solenoid when a permanent magnet approaches it

Rice. 1

We will bring a permanent magnet closer to one of its ends, for example, with the north pole. An electric current will arise in the solenoid, which will be detected by the deflection of the galvanometer needle. The induction current is directed counterclockwise when looking at the solenoid from the magnet side.

As the magnet approaches the solenoid, the flux of the magnetic induction vector penetrating the turns of the solenoid increases, as the magnetic induction of the magnet's field increases. The magnetic field of the induced current in the solenoid is directed outward from the solenoid (gimlet rule), that is, it compensates for the increase in the magnet field. Corresponds to Lenz's rule.

2. Take a solenoid C, closed through a galvanometer G. We will remove a permanent magnet from one of its ends (Fig. 2).

The appearance of an induction current in a solenoid when a permanent magnet moves away from it

Rice. 2.

As the magnet moves away from the solenoid, the flux of the magnetic induction vector penetrating the turns of the solenoid decreases, since the magnetic induction of the magnet's field decreases. The magnetic field of the induced current in the solenoid is directed inside the solenoid (gimlet rule), that is, it compensates for the decrease in the magnet field. Corresponds to Lenz's rule.

Obviously, the result of the experiments will not change if the magnet is stationary and the solenoid moves.

Analyzing the results of these two experiments, one more conclusion can be drawn: when the north pole of the magnet approaches the solenoid, the induction current creates a magnetic field, the induction of which is directed towards the induction of the magnetic field of the magnet, and, therefore, the magnet and the solenoid repel, that is, a counteracting force arises between them the movement of a magnet, which causes the occurrence of an induction current. When the magnet is removed, the magnet and the solenoid are attracted, that is, again a force arises between them that counteracts the movement of the magnet.

Lenz's rule is a consequence of the law of conservation of energy. Indeed, induction currents, like any other electric currents, do some work. This means that when a closed conductor (solenoid) moves in a magnetic field, extra work external forces. This is the work that occurs due to the forces that impede the movement of the magnet.

A change in the flux through the turns of solenoid C is also observed when considering the relative movement of the magnet with the south pole to the solenoid C, the replacement of the magnet with a solenoid or turn with current, the closing and opening of the circuit of such a solenoid (or turn), as well as the mutual rotations of the solenoid C and the element creating the magnetic field .

Timing characteristics

Initiation time (log to -10 to 2);

Lifetime (log tc from 15 to 15);

Keywords

• magnetic induction
• electromagnetic induction
• magnetic flux
• magnetic induction vector flux
• closed loop
• closed conductor
• magnet
• a magnetic field
• electricity
• induced current
• solenoid
• turn
• Lenz's rule
• Lenz's law
• coil

Sections of natural sciences:

The induced current arising in a closed circuit with its magnetic field counteracts the change in the magnetic flux that causes it.

Application of Lenz's rule

1. show the direction of vector B of the external magnetic field; 2. determine whether the magnetic flux through the circuit is increasing or decreasing; 3. show the direction of the vector Bi of the magnetic field of the induction current (when the magnetic flux of the vector B of the external m.field and Bi of the magnetic field of the induction current decreases, they should be directed in the same way, and when the magnetic flux increases, B and Bi should be directed in the opposite direction); 4. Using the gimlet rule, determine the direction of the induction current in the circuit.

LAW OF ELECTROMAGNETIC INDUCTION

Email current in a circuit is possible if external forces act on the free charges of the conductor. The work done by these forces to move a single positive charge along a closed loop is called emf. When the magnetic flux changes through a surface bounded by a contour, extraneous forces appear in the circuit, the action of which is characterized by induced emf. Considering the direction of the induction current, according to Lenz's rule:

The induced emf in a closed loop is equal to the rate of change of the magnetic flux through the surface bounded by the loop, taken with the opposite sign.

Why "-" ? - because the induced current counteracts the change in the magnetic flux, the induced emf and the rate of change of the magnetic flux have different signs.

If we consider not a single circuit, but a coil, where N is the number of turns in the coil:

Where R is the conductor resistance.

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, and a vortex electric field appears, directed against the current, i.e. A self-induction emf arises in the coil, preventing the increase in current in the circuit (the vortex field inhibits the 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 when turned off flashes brightly. Conclusion in electrical engineering, the phenomenon of self-induction manifests itself when the circuit is closed (the electric current increases gradually) and when the circuit is opened (the electric current does not disappear immediately).

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. a value numerically equal to the self-inductive emf that occurs in the 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.

Ferromagnets- substances (usually in a solid crystalline or amorphous state) in which, below a certain critical temperature (Curie point), a long-range ferromagnetic order is established in the magnetic moments of atoms or ions (in non-metallic crystals) or the moments of itinerant electrons (in metallic crystals). In other words, a ferromagnet is a substance that, at a temperature below the Curie point, is capable of magnetization in the absence of an external magnetic field.

Among chemical elements have ferromagnetic properties transition elements Fe, Co and Ni (3 d-metals) and rare earth metals Gd, Tb, Dy, Ho, Er

Magnetic hysteresis- the phenomenon of dependence of the magnetization vector and the magnetic field strength vector in a substance not only on the applied external field, but also on the prehistory of a given sample. Magnetic hysteresis usually manifests itself in ferromagnets - Fe, Co, Ni and alloys based on them. It is magnetic hysteresis that explains the existence of permanent magnets.

Oscillatory circuit- an oscillator, which is an electrical circuit containing a connected inductor and capacitor. In such a circuit, current (and voltage) fluctuations can be excited.

Oscillatory circuit - simplest system, in which free electromagnetic oscillations can occur

The resonant frequency of the circuit is determined by the so-called Thomson formula:

ELECTROMAGNETIC WAVES

This is an electromagnetic field propagating in space at a finite speed, depending on the properties of the medium.

Properties of electromagnetic waves: - propagate not only in matter, but also in vacuum; - propagate in vacuum at the speed of light (C = 300,000 km/s); - these are transverse waves; - these are traveling waves (transfer energy).

The source of electromagnetic waves are accelerated moving electrical charges. Oscillations electric charges are accompanied by electromagnetic radiation having a frequency equal to the frequency of charge oscillations.

Induction emf. Direction of induction current

The cause of the electromotive force can be a change in the magnetic field in the surrounding space. This phenomenon is called electromagnetic induction. The magnitude of the induced emf in the circuit is determined by the expression

where is the magnetic field flux through a closed surface bounded by a contour. The “−” sign before the expression shows that the induced current created by the induced emf prevents a change in the magnetic flux in the circuit

Induction current- electric current that arises in a closed conductive circuit when the flux of magnetic induction passing through this circuit changes. The magnitude and direction of the induction current are determined by the law of electromagnetic induction and Lenz's rule.

Lenz's rule determines the direction of the induction current and states:

The induced current always has such a direction that it weakens the effect of the cause that excites this current.

The rule was formulated in 1833 by E. H. Lenz. Later it was generalized to all physical phenomena in the works of Le Chatelier (1884) and Brown (1887), this generalization is known as the Le Chatelier-Brown principle.

A spectacular demonstration of Lenz's rule is the experiment of Elihu Thomson.

The physical essence of the rule

According to Faraday's law of electromagnetic induction, when the magnetic flux passing through an electrical circuit changes, a current called induction is excited in it. The magnitude of the electromotive force responsible for this current is determined by the equation:

where the minus sign means that the induced emf acts in such a way that the induced current prevents a change in flux. This fact is reflected in Lenz's rule.

Lenz's rule is general in nature and is valid in various physical situations, which may differ in the specific physical mechanism for excitation of the induction current. So, if a change in magnetic flux is caused by a change in the area of ​​the circuit (for example, due to the movement of one of the sides of a rectangular circuit), then the induced current is excited by the Lorentz force acting on the electrons of a moving conductor in a constant magnetic field. If the change in magnetic flux is associated with a change in the magnitude of the external magnetic field, then the induction current is excited by an eddy electric field, appearing when the magnetic field changes. However, in both cases, the induced current is directed so as to compensate for the change in the magnetic field flux through the circuit.

If an external magnetic field penetrating a stationary electric circuit is created by a current flowing in another circuit, then the induced current can be directed either in the same direction as the external one or in the opposite direction: this depends on whether the external current decreases or increases. If the external current increases, then the magnetic field it creates and its flux increase, which leads to the appearance of an induction current that reduces this increase. In this case, the induction current is directed in the direction opposite to the main one. In the opposite case, when the external current decreases with time, the decrease in magnetic flux leads to the excitation of an induced current, tending to increase the flux, and this current is directed in the same direction as the external current.

Lenz's rule is:

Lenz's rule determines the direction of induction currents, i.e. currents arising as a result of electromagnetic induction (See Electromagnetic induction) ; is a consequence of the law of conservation of energy. L.P. was established in 1833 by E. H. Lenz. According to magnetic induction, the induced current arising in a closed circuit is directed in such a way that the magnetic induction flux it creates through the area limited by the circuit tends to prevent the change in flux that the current causes. So, for example, the induced current in a coil placed in a magnetic field B, which is directed perpendicular to the plane of the coil ( rice .) from the observer (i.e., beyond the drawing plane), directed counterclockwise if the field increases with time (a), and clockwise if the field decreases (b).

Great Soviet Encyclopedia. - M.: Soviet encyclopedia. 1969-1978.

To find the direction of the induced current in a circuit with a known direction of its magnetic field, use

a) right hand rule
b) Lenz's rule
c) gimlet rule

DIRECTION OF INDUCTION CURRENT
1. Straight conductor

The direction of the induction current is determined by the right-hand rule:
If you place your right hand so that the magnetic induction vector enters the palm, the thumb set at 90 degrees indicates the direction of the velocity vector, then straightened 4 fingers will show the direction of the induction current in the conductor.
2. Closed loop
The direction of the induction current in a closed loop is determined by Lenz's rule.

Lenz's rule:
The induced current arising in a closed circuit with its magnetic field counteracts the change in the magnetic flux that causes it.
Application of Lenz's rule:
show the direction of vector B of the external magnetic field;
determine whether the magnetic flux through the circuit is increasing or decreasing;
show the direction of the vector Bi of the magnetic field of the induction current;
(with a decrease in the magnetic flux of the vector B of the external m. field and Bi of the magnetic field of the induction current should be directed equally, and with an increase in the magnetic flux B and Bi should be directed in the opposite direction);
Using the gimlet rule, determine the direction of the induction current in the circuit.