Lenz's rule. The phenomenon of electromagnetic induction

It always has such a direction that it weakens the action of the cause that excites this current.

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

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Lesson 281. Electromagnetic induction. Magnetic flux. Lenz's rule

Lenz's rule. Physics

Subtitles

The physical essence of the rule

E i n d = − d Φ d t (\displaystyle (\mathcal (E))^(ind)=-(\frac (d\Phi )(dt)))

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 that appears 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.

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

The physical essence of the rule

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.

Notes

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See what the “Lenz Rule” is in other dictionaries:

LENZ'S RULE- LENZ'S RULE, an electromagnetic law derived by Russian physicist Heinrich Lenz (1804 65) in 1834. The law states that an induced electric current flows in the direction opposite to the charge that produced the current. see also INDUCTION... Scientific and technical encyclopedic dictionary

Lenz's rule- - [Ya.N.Luginsky, M.S.Fezi Zhilinskaya, Yu.S.Kabirov. English-Russian dictionary of electrical engineering and power engineering, Moscow, 1999] Topics of electrical engineering, basic concepts EN law of induced current Lenz s law Lenz s rule ... Technical Translator's Guide

Lenz's rule- a rule that determines the direction of induction currents (arising during electromagnetic induction); a consequence of the law of conservation of energy. According to Lenz's rule, the induced current arising in a closed circuit is directed so that... ...

Lenz's rule- Lenko taisyklė statusas T sritis fizika atitikmenys: engl. Lenz's law; Lenz's rule vok. Lenzsche Regel, f; Lenzsches Gesetz, n rus. Lenz's law, m; Lenz's rule, n pranc. loi de Lenz, f … Fizikos terminų žodynas

LENZA RULE- determines the direction of the flow. currents arising as a result of electromagnetic induction; is a consequence of the law of conservation of energy. L. p. established (1833) by E. H. Lenz. Induction the current in the circuit is directed so that the flow it creates... ... Physical encyclopedia

RULE- (1) the gimlet determines the direction of the magnetic field strength vector of a straight conductor with direct current. If a gimlet is screwed in in the direction of the current, then the direction of its rotation determines the direction of the magnetic lines of force... ... Big Polytechnic Encyclopedia

Lenz's rule- Lenz's rule, a rule for determining the direction of the induction current: The induction current arising from the relative movement of the conductive circuit and the source of the magnetic field always has a direction such that its own magnetic flux ... ... Wikipedia

right hand rule- an easy-to-memorize rule for determining the direction of the induction current in a conductor moving in a magnetic field: if you position your right palm so that your thumb is aligned with the direction of movement... ... Encyclopedic Dictionary of Metallurgy

phase rule- an equation connecting the number of degrees of freedom (C) of a thermodynamic system with the number of components (K) and the number of equilibrium phases (F): C = K F + 2. If the influence of pressure on phase equilibrium can be neglected, then the phase rule has the form:... ... Encyclopedic Dictionary of Metallurgy

leverage rule- , the rule of segments is one of the manifestations of the law of conservation of mass of a substance, which establishes the relationship between the chemical compositions and masses of two substances and the 3rd substance formed from the first two; serves to determine from the diagram... Encyclopedic Dictionary of Metallurgy

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The inductive electric current 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. The question of the direction of the induction current, left open by Faraday, was soon solved 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 magnetic field generated by the current will be oriented towards the north pole of the driven 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 so 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.

Formulation of Lenz's law

An induced current is always directed in such a way that its effect is opposite to the action of the cause that caused this current.

Lenz's law is applicable when the conductors are moving and the magnetic field is constant and in the case when the conductors are stationary and the magnetic field (current strength) is variable. Induced currents always produce a field that tends to counteract the changes in the external field that caused the currents.

Lenz's law is a consequence of the law of conservation of energy. So, induction currents, like any other currents, do a certain amount of work. This means that when a closed conductor moves in a magnetic field, additional work must be done by external forces. This work appears because induction currents interact with the magnetic field and cause forces that are directed in the direction opposite to the movement (that is, they impede the movement).

If we write the law of electromagnetic induction in Maxwell's formulation:

where is the induced emf, F is the magnetic flux. The minus sign in formula (1) corresponds to Lenz's law.

Let us assume that the positive direction of the normal coincides with the direction of magnetic induction. In this case, the flow through the loop is positive. If the magnetic field, in the case under consideration, increases (that is, title="Rendered by QuickLaTeX.com" height="22" width="54" style="vertical-align: -6px;">), то в соответствии (1), а это значит, что сила тока . Получается, что направление тока индукции является противоположным к избранному нами положительному направлению.!}

The principle of reversibility of electric machines is considered to be a consequence of Lenz’s law:

An electric machine is reversible, that is, it can work both as a generator and as a motor.

Plan for using Lenz's rule

Lenz's rule, for example, can be applied using the following sequence of actions (convenient for a closed loop):

Determine (consider) the direction of the external magnetic field vector.
Determine whether the magnetic flux through the circuit decreases or increases.
Indicate the direction of the magnetic induction vector of the induction current field. In the event that the magnetic flux of the external field decreases, then the magnetic induction vector of the induced current field is codirectional with the external field.
Using the gimlet rule (for circular current) or the right hand rule for direct current, determine the direction of the induction current.

Examples of problem solving

EXAMPLE 1

Exercise	A straight conductor moves parallel to itself in a constant magnetic field (Fig. 1). How will the induced current be directed?
Solution	We will assume that the plane in which the conductor moves is perpendicular to the plane of the drawing, the magnetic field lines lie in the plane of the drawing (Fig. 1). The direction of the induction current and the sign of the EMF are determined using Lenz's law: the current is directed so that the mechanical force that acts on a moving conductor is opposite to the speed of movement, that is, it slows down the conductor. The force that acts on a current-carrying conductor is the Ampere force. Its direction is determined using the rule of the left hand: The magnetic field lines must enter the palm, four fingers are directed along the current, the thumb bent by 900 indicates the direction of the force. In order for the Ampere force to be directed against the speed, the current in the conductor must flow toward us.
Answer	The induction current is directed towards us.

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

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 magnetic field energy, find out the physical meaning of this formula.

Lesson plan:

Checking 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 (optional) preparing 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