Physics lesson in 11th grade on the topic:
"Electromagnetic induction. Lenz's rule"
The purpose of the lesson:
educational: introduce students to the phenomenon of electromagnetic induction, reproduce Faraday’s experiments, show that the induced current appears when the magnetic flux passing through the circuit changes; derive the formula and understand the physical meaning of the law of electromagnetic induction; formulate Lenz's rule.
educational: to develop teamwork skills in combination with student independence, to cultivate cognitive needs and interest in the subject;
developing: develop the ability to quickly perceive information and perform practical tasks; develop logical thinking and attention, the ability to analyze, compare the results obtained, and draw appropriate conclusions.
Lesson plan:
Induction current.
Electromagnetic induction in modern technology
Reinforcing the topic: Laboratory work “Electromagnetic induction”
Summing up the lesson I . Setting a learning task.
We have covered the topic “Magnetic Field”. Today we have to find out how you learned this material. We will generalize our knowledge about the magnetic field and continue to improve our skills in explaining magnetic phenomena.
II. Implementation of reference knowledge.
To do this, we need to answer some questions.
What is electric current?
What is necessary for electric current to exist?
What creates a magnetic field?
How can a magnetic field be detected?
What value characterizes the magnetic field at each point?
In what units is magnetic induction measured?
What is 1T equal to?
What value characterizes the magnetic field in a certain region of space?
In what units is magnetic flux measured?
What is 1 Wb equal to?
What determines the magnetic flux that penetrates the area of a flat circuit placed in a uniform magnetic field?
Complete the following definitions:
A) The Lorentz force is...
B) Ampere force is..
B) The Curie temperature is...
D) Magnetic permeability of the medium characterizes..
13. Write formulas for calculations:
A) Lorentz forces
B) Ampere forces
B) Magnetic induction vector module
D) Magnetic flux
D) magnetic permeability of the medium
14. Ampere force is applied..
15. The Lorentz force is used..
III. Learning new material
So, after summarizing the knowledge about the magnetic field, we will continue to improve our skills in explaining magnetic phenomena.
Today in the lesson we will discover a new phenomenon, which is one of the most remarkable scientific achievements of the first half of the 19th century, which caused the emergence and rapid development of electrical and radio engineering. So, go ahead for knowledge!
The topic of the lesson is “Electromagnetic induction. Lenz's rule"
Sequence of presentation of new material
The history of the discovery of the phenomenon of electromagnetic induction.
Demonstration of Faraday's experiments on electromagnetic induction.
Induction current.
Causes of induction current.
Direction of induction current. Lenz's rule
Law of electromagnetic induction.
Laboratory work “Electromagnetic induction”
Previously, in electrodynamics, phenomena related to or caused by the existence of time-constant (static and stationary) electric and magnetic fields were studied. Do new phenomena appear in the presence of variable fields?
The history of the discovery of the phenomenon of electromagnetic induction.
On the screen is a portrait of M. Faraday (1791 - 1867).
Bibliographic information: M. Faraday
Demonstration of Faraday's experiments on electromagnetic induction, analysis of experiments
Experience 1. Insertion (removal) of a strip magnet from a closed circuit connected to a galvanometer.
Experience 2. When the key is closed (opened) or the rheostat motor is moved, the magnetic field penetrating the coil changes and a current arises in it.
The current that occurs in a coil when a permanent magnet moves relative to it is called induction. This current in the coil is induced, that is, induced by a moving magnet. .A magnetic field that does not change does not create an induction current .
Experience 3. Rotate the frame in a magnetic field.
An induced current in a circuit occurs if and only if the conductor crosses the magnetic field lines.
Induction current.
We looked at ways to obtain induction current:
movement of the magnet relative to the coil;
movement of the coil relative to the magnet;
circuit closing and opening;
rotation of the frame inside the magnet;
moving the rheostat slider;
movement of one coil relative to another.
Causes of induction current:
only when the magnetic flux piercing the area covered by the conductor changes (when the magnet and coil move relative to each other);
due to changes in current strength in the circuit (when closing and opening the circuit);
due to changing the orientation of the circuit relative to the lines of magnetic induction.
Conclusion: Only an alternating magnetic field can create a current (induction current). The deflection of the galvanometer needle indicates the presence of an induced current in the coil circuit. As soon as the movement stops, the current stops.
What have we learned today? Phenomenon. Which? The phenomenon of the occurrence of induction current in a closed circuit. This is the phenomenon of electromagnetic induction. The condition for its occurrence is a change in the number of magnetic induction lines through the surface bounded by the contour.
In all cases, it can be noted that an electric current arises when the magnetic field changes, that is, when the number of lines of force piercing the coil changes. Switching to the language of physical quantities, the common cause of the occurrence of current can be called a change in the magnetic flux penetrating the circuit. Further quantitative studies confirmed that the phenomenon of electromagnetic induction is the occurrence of current in a closed circuit when the magnetic flux through the circuit changes. The current that arises is called induced current.
Let us explain the reason for the occurrence of induction current
Induction current occurs under the influence of an electric field created by a change in the magnetic field. Like any electric field, it does work to move charge in a circuit. The electric field that arises during the process of changing the magnetic field is not associated with any distribution of electric charges. An alternating magnetic field is inextricably linked with this electric field, and therefore they say that in this case we are dealing with an electromagnetic field. The electric field lines associated with an alternating magnetic field have no beginning and end - they are closed like magnetic field lines. Such a field is called a vortex field. The vortex electric field that arises during the process of electromagnetic induction creates an electric current in a closed conductor, therefore, it is capable of causing the circulation of electric charges. In this regard, there is a need to introduce a special energy characteristic of the vortex electric field: electromotive force of induction (abbreviated as induction emf). The induced emf is denoted by the letter ε i. The electromotive force of induction is the ratio of the work done by the vortex field when moving an electric charge along a closed circuit to the module of the moved charge:
ε i =A vortex /q
Induction emf, like voltage, is expressed in volts. According to Ohm's law for a closed circuit I i = ε i /R
where R is the resistance of the entire closed circuit. Faraday's experiments showed that the strength of the induced current I i in a conducting circuit is directly proportional to the rate of change in the number of magnetic induction lines penetrating the surface bounded by this circuit.
Experience 4: introducing (removing) a magnet into a closed circuit, first with one magnet, then with two magnets.
Conclusion: the magnitude of the current depends on the magnitude of the magnetic induction.
If you introduce the same permanent magnet into a coil (see Fig. 1), but at different speeds, you will notice that when the magnet moves quickly, the current strength is greater than when it moves slowly.
Experience 5: We introduce the magnet first slowly, then quickly.
Conclusion: The magnitude of the current depends on the speed at which the magnet is inserted.
Therefore, the strength of the induction current is proportional to the rate of change of the magnetic flux through the surface limited by the contour: I i ~ ∆Ф /∆ t
Since R does not depend on ∆Ф then the induced emf ε i ~ ∆Ф /∆ t
Thus, we conclude: the induced emf is proportional to the rate of change of the magnetic field penetrating the coil.
Experience 6. Dependence of EMF on the number of turns in the coil.
Conclusion: The strength of the induced current, and therefore the induced emf, is proportional to the number of turns of the secondary coil at the same rate of change of the magnetic field.
ε i ~ N ·∆Ф /∆ t
The induced emf coincides in direction with the induced current.
Thus, from the experiments performed we conclude: the induced emf is proportional to the rate of change of the magnetic field penetrating the coil and the number of turns on it. Faraday's experiments showed that the strength of the induced current I i in a conducting circuit is directly proportional to the rate of change in the number of magnetic induction lines penetrating the surface bounded by this circuit.
Direction of induction current
Experience 7: insertion (removal) of a magnet first with the north pole, then with the south pole.
Conclusion: The direction of the current depends on the direction of the magnetic field.
Experience 8. demonstrate the dependence of the direction of the current on the closure or opening of the primary coil circuit.
Having studied all the most important aspects of electromagnetic induction in 1831, Faraday established several rules for determining the direction of the induction current in various cases, but he was unable to find a general rule. It was established later, in 1834, by St. Petersburg academician Emil Christianovich Lenz and therefore bears his name.
Lenz's rule.
Investigating the phenomenon of electromagnetic induction, E. H. Lenz in 1833 established a general rule for determining the direction of the induction current: the induction current always has such a direction as to interfere with the cause that caused this current with its magnetic field.
Experience 9. Demonstration of Lenz's experience. In the installation, bring the magnet to the solid ring. They see: the ring is repelled from the pole of the magnet. If you put a ring on a magnet and then pull the magnet out of it, the ring pulls behind the magnet. As can be seen, the current induced in the ring prevents the magnet from approaching in the first case, and its removal in the second.
Based on similar observations, the Russian scientist E. H. Lenz proposed the following rule for determining the direction of the current induced in a conductor: the induced current is always directed in such a way that its magnetic field counteracts the change in the magnetic field that causes this current.
The direction of the induction current is determined by the gimlet rule, by the right hand rule.
Teacher: To determine the direction of the induction current in a closed circuit, it is used Lenz's rule: The induced current has such a direction that the magnetic flux it creates through the surface bounded by the contour prevents the change in the magnetic flux that caused this current.
Experimental task: A closed circuit with a light bulb is inserted into the steel core of a transformer connected to a voltage of 220V (RNSh). Why does the light come on?
6. Law of electromagnetic induction
We have established that the E.M.F. induction in any circuit is directly proportional to the rate of change of magnetic flux ∆ t– time during which the magnetic flux changes. The minus sign shows that when the magnetic flux decreases ( ∆Ф– negative), e.m.f. creates an induction current that increases the magnetic flux and vice versa. The law of electromagnetic induction was established experimentally by M. Faraday. The German physicist and natural scientist G. Helmholtz showed that the basic law of electromagnetic induction ε i = – ∆Ф/∆t is a consequence of the law of conservation of energy. The induced emf in a closed loop is equal to the rate of change of the magnetic flux passing through the loop, taken with the opposite sign.
Expression ε i = – ∆Ф/∆t (1) , called Faraday's law, is universal: it is valid for all cases of electromagnetic induction. For a coil with N, the law of electromagnetic induction has the form:
ε i = – N ∆Ф/∆t, Ф=BS [T m 2 V b], 1 Wb= 1V 1s
The minus sign shows that the induced emf E i is directed so that the magnetic field of the induced current prevents a change in the magnetic induction flux ∆Ф. If the flow increases (∆Ф > 0), then E i< 0 и поле индукционного тока направлено навстречу потоку. Если же поток уменьшается (∆Ф < 0), то Е i >0 and the direction of the flow and the fields of the induced current coincide. Thus electromagnetic phenomenon consists in the appearance (guidance) of an electromotive force in a conducting circuit located in a magnetic field in the event of a change in the magnitude of the magnetic flux passing through the surface bounded by this circuit. Expression ε i = – N ·∆Ф/∆t(1) represents one of the mathematical notations law of electromagnetic induction - The emf induced in the circuit of an electrical circuit is equal to the rate of change of the magnetic flux passing through the surface bounded by this circuit, taken with the opposite sign.
7. Electromagnetic induction in modern technology
The phenomenon of electromagnetic induction underlies the operation of induction electric current generators, which account for almost all the electricity generated in the world.
Examples of the use of the phenomenon of electromagnetic induction in modern technology:
special detectors for detecting metal objects;
magnetic levitation train;
electric furnaces for melting metals
household microwave microwave ovens.
Consolidation of what has been learned: Laboratory work “Study of the phenomenon of electromagnetic induction”
Summing up the lesson
9. Homework: § 8-11.
The phenomenon of electromagnetic induction was discovered by Faraday in 1831. Faraday's experiments showed that in any closed conducting circuit, when the number changes
lines of magnetic induction passing through it, an electric current arises. This current was named induced current. For example, at the moment the magnet is inserted and at the moment it is pulled out of the coil, a deflection of the galvanometer needle is observed. The deflections of the arrow when moving in and out are opposite. The faster the magnet moves, the greater the deviations. If you move the magnet into the coil with the other pole, the needle deflections will be opposite to the original ones.
In another experiment, one of the coils K1 is inside another coil K2. When the current through coil K1 is turned on or off, or when it changes, or when the coils move relative to each other, a deflection of the galvanometer needle is observed if current flows through K1.
The total number of lines of magnetic induction through the area of the circuit is magnetic flux. Thus, The cause of the induced current is a change in the magnetic flux through the circuit . If the circuit is located in a uniform magnetic field, the induction of which is equal to B, then the magnetic flux through the circuit, the area of which is S
:Φ = B·Scosα (3.10)
Where α angle between vector IN and normal n to the contour surface.
Magnetic flux is a scalar quantity. If the vector lines IN exit the platform, the magnetic flux is considered positive, if they enter it, the magnetic flux is considered negative. The SI unit of magnetic flux is the weber (Wb).
One weber is a magnetic flux created by a uniform magnetic field of induction 1 T through an area of 1 m² perpendicular to the induction lines. 1Wb = 1T m².
The occurrence of an induced current means that when the magnetic flux Φ changes in the circuit, an induced emf occurs. It is determined by the rate of change of the magnetic flux, i.e.
e = – ΔΦ / Δt (3.11)
Formula (3.11) expresses Faraday's law. The minus sign is a mathematical expression of Lenz's rule, which states that induced current is always directed so as to counteract the cause that causes it .
In other words:
The induced current creates a magnetic flux that prevents the change in magnetic flux that causes induced emf .
Note 28. Electromagnetic induction (EMI).
5. The phenomenon of electromagnetic induction
Definition.Magnetic flux– a quantity characterizing the number of magnetic induction lines that pass through a flat surface with a given area (circuit).
– external magnetic flux through the circuit, Wb
Where S– contour area, m²
α
– angle between and perpendicular to the contour, degrees or rads
The phenomenon of electromagnetic induction– the phenomenon of the appearance of an induction current in a closed conductor (circuit), through which the magnetic flux changes.
The mechanism of occurrence of induction current:
1) A change in magnetic flux leads to the appearance of a vortex electric field;
2) The vortex (induction) electric field acts on free charges in the circuit and separates them;
3) Charge separation is characterized by the induced emf that occurs in the circuit;
4) When the circuit is closed, an induction current arises as a consequence.
– law of electromagnetic induction (induction emf in the circuit), V
Where ∆t– time interval, s
– induced emf in a coil of N turns, V
– induction current strength in a closed circuit, A
Where R– circuit resistance, Ohm 
– induced emf in a straight conductor moving in the MF, V
Where l– conductor length, m
υ
– speed of conductor movement, m/s
α
– angle between and , degrees or rads
Options for the occurrence of induced emf:
1) Changing the magnetic induction vector. 
2) Changing the contour area ∆S: 
3) Changing the angle α (rotating the contour): 
Comment. The principle of operation of an electric generator is based on the idea of rotating a frame in a magnetic field.
Lenz's rule (determining the direction of induction current). When the magnetic flux changes, a current arises in the circuit, which prevents the change in this magnetic flux.
Algorithm for determining the direction of induction current:
1) Set the direction of the magnetic induction lines of the external MF;
2) Find out whether the flow of external MP through the surface increases or decreases;
3) Set the direction of the magnetic lines of the induction current according to Lenz’s rule: opposite to the lines of the external field when the external magnetic flux increases and in the same direction when the external magnetic flux decreases;
4) Determine the direction of the induction current using the right-hand rule.
6. The phenomenon of self-induction
Self-induction phenomenon– the phenomenon of the occurrence of induced emf and induced current in a conductor when the current in it changes.
Explanation of the manifestation of self-induction:
1) When the circuit is opened, the main current in the conductor decreases, and according to Lenz’s rule, a self-induction emf and a self-induction current arise, which prevents the change in the magnetic flux in the circuit. As a result, the self-induction current supports the main current, i.e. The self-induction current and the main current are co-directed;
2) When the circuit is closed, according to similar reasoning, the self-induction current is directed oppositely to the main current.
Comment. The phenomenon of self-induction is a special case of the manifestation of electromagnetic induction.
– EMF of self-induction, V
Where ∆I– change in current strength in the circuit, A
Definition. Inductance (L,
) – a quantity characterizing the magnetic properties of a conductor (coil).
– own magnetic flux created by a current-carrying conductor, Wb
– magnetic field energy, J
The phenomenon of electromagnetic induction was discovered by the outstanding English physicist M. Faraday in 1831. It consists in the occurrence of an electric current in a closed conducting circuit when the magnetic flux penetrating the circuit changes over time.
The magnetic flux Φ through the area S of the circuit is the quantity
Φ = B S cos α,
Where B is the magnitude of the magnetic induction vector, α is the angle between the vector and the normal to the contour plane (Fig. 4.20.1).
Figure 4.20.1.
Magnetic flux through a closed loop. The normal direction and the selected positive direction of the contour traversal are related by the right gimlet rule.
The definition of magnetic flux is easy to generalize to the case of a non-uniform magnetic field and a non-planar circuit. The SI unit of magnetic flux is called the weber (Wb). A magnetic flux equal to 1 Wb is created by a magnetic field with an induction of 1 T, penetrating in the normal direction a flat contour with an area of 1 m2:
1 Wb = 1 T · 1 m2.
Faraday experimentally established that when the magnetic flux changes in a conducting circuit, an induced emf Eind arises, equal to the rate of change of the magnetic flux through the surface bounded by the circuit, taken with a minus sign:
Experience shows that the induction current excited in a closed loop when the magnetic flux changes is always directed in such a way that the magnetic field it creates prevents the change in the magnetic flux that causes the induction current. This statement is called Lenz's rule (1833).
Rice. 4.20.2 illustrates Lenz’s rule using the example of a stationary conducting circuit that is in a uniform magnetic field, the induction modulus of which increases with time.
Figure 4.20.2.
Illustration of Lenz's rule. In this example, a ind< 0. Индукционный ток Iинд течет навстречу выбранному положительному направлению обхода контура.
Lenz's rule reflects the experimental fact that ind and always have opposite signs (the minus sign in Faraday's formula). Lenz's rule has a deep physical meaning - it expresses the law of conservation of energy.
A change in the magnetic flux penetrating a closed circuit can occur for two reasons.
1. The magnetic flux changes due to the movement of the circuit or its parts in a time-constant magnetic field. This is the case when conductors, and with them free charge carriers, move in a magnetic field. The occurrence of induced emf is explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force plays the role of an external force in this case.
Let us consider, as an example, the occurrence of an induced emf in a rectangular circuit placed in a uniform magnetic field perpendicular to the plane of the circuit. Let one of the sides of a contour of length l slide with speed along the other two sides (Fig. 4.20.3).
Figure 4.20.3.
The occurrence of induced emf in a moving conductor. The component of the Lorentz force acting on a free electron is indicated.
The Lorentz force acts on the free charges in this section of the circuit. One of the components of this force, associated with the transfer speed of charges, is directed along the conductor. This component is shown in Fig. 4.20.3. She plays the role of an outside force. Its module is equal
The work done by the force FL on the path l is equal to
A = FL · l = eυBl.
According to the definition of EMF
In other stationary parts of the circuit, the external force is zero. The ratio for ind can be given the usual form. Over time Δt, the contour area changes by ΔS = lυΔt. The change in magnetic flux during this time is equal to ΔΦ = BlυΔt. Hence,
In order to establish the sign in the formula connecting ind and it is necessary to select the normal direction and the positive direction of traversing the contour that are consistent with each other according to the right gimlet rule, as is done in Fig. 4.20.1 and 4.20.2. If this is done, then it is easy to arrive at Faraday's formula.
If the resistance of the entire circuit is equal to R, then an induction current equal to Iind = ind/R will flow through it. During the time Δt, Joule heat will be released at the resistance R (see § 4.11)
The question arises: where does this energy come from, since the Lorentz force does no work! This paradox arose because we took into account the work of only one component of the Lorentz force. When an induction current flows through a conductor located in a magnetic field, another component of the Lorentz force, associated with the relative speed of movement of the charges along the conductor, acts on the free charges. This component is responsible for the appearance of the Ampere force. For the case shown in Fig. 4.20.3, the ampere force modulus is equal to FA = IBl. Ampere's force is directed towards the movement of the conductor; therefore it does negative mechanical work. During the time Δt this work Amech is equal to
A conductor moving in a magnetic field through which an induced current flows experiences magnetic braking. The total work done by the Lorentz force is zero. Joule heat in the circuit is released either due to the work of an external force, which maintains the speed of the conductor unchanged, or due to a decrease in the kinetic energy of the conductor.
2. The second reason for the change in the magnetic flux penetrating the circuit is the change in time of the magnetic field when the circuit is stationary. In this case, the occurrence of induced emf can no longer be explained by the action of the Lorentz force. Electrons in a stationary conductor can only be driven by an electric field. This electric field is generated by a time-varying magnetic field. The work of this field when moving a single positive charge along a closed circuit is equal to the induced emf in a stationary conductor. Therefore, the electric field generated by a changing magnetic field is not potential. It is called the vortex electric field. The concept of a vortex electric field was introduced into physics by the great English physicist J. Maxwell (1861).
The phenomenon of electromagnetic induction in stationary conductors, which occurs when the surrounding magnetic field changes, is also described by Faraday's formula. Thus, the phenomena of induction in moving and stationary conductors proceed in the same way, but the physical cause of the occurrence of induced current turns out to be different in these two cases: in the case of moving conductors, the induction emf is due to the Lorentz force; in the case of stationary conductors, the induced emf is a consequence of the action on free charges of the vortex electric field that occurs when the magnetic field changes.
Electromagnetic induction- this is a phenomenon that consists in the occurrence of an electric current in a closed conductor as a result of a change in the magnetic field in which it is located. This phenomenon was discovered by the English physicist M. Faraday in 1831. Its essence can be explained by several simple experiments.
Described in Faraday's experiments principle of obtaining alternating current used in induction generators that generate electrical energy in thermal or hydroelectric power plants. The resistance to rotation of the generator rotor, which arises when the induction current interacts with the magnetic field, is overcome by the operation of a steam or hydraulic turbine that rotates the rotor. Such generators convert mechanical energy into electrical energy .
Eddy currents or Foucault currents
If a massive conductor is placed in an alternating magnetic field, then in this conductor, due to the phenomenon of electromagnetic induction, eddy induced currents arise, called Foucault's currents.
Eddy currents also arise when a massive conductor moves in a constant, but spatially inhomogeneous magnetic field. Foucault currents have such a direction that the force acting on them in a magnetic field inhibits the movement of the conductor. A pendulum in the form of a solid metal plate made of non-magnetic material, oscillating between the poles of an electromagnet, stops abruptly when the magnetic field is turned on.
In many cases, the heating caused by Foucault currents turns out to be harmful and must be dealt with. Transformer cores and electric motor rotors are made from separate iron plates, separated by layers of insulator that prevent the development of large induction currents, and the plates themselves are made from alloys with high resistivity.
Electromagnetic field
The electric field created by stationary charges is static and acts on the charges. Direct current causes the appearance of a time-constant magnetic field acting on moving charges and currents. Electric and magnetic fields exist in this case independently of each other.
Phenomenon electromagnetic induction demonstrates the interaction of these fields observed in substances that have free charges, i.e., in conductors. An alternating magnetic field creates an alternating electric field, which, acting on free charges, creates an electric current. This current, being alternating, in turn generates an alternating magnetic field, which creates an electric field in the same conductor, etc.
The set of alternating electric and alternating magnetic fields that generate each other is called electromagnetic field. It can exist in a medium where there are no free charges, and propagates in space in the form of an electromagnetic wave.
Classical electrodynamics- one of the highest achievements of the human mind. She had a huge influence on the subsequent development of human civilization by predicting the existence of electromagnetic waves. This subsequently led to the creation of radio, television, telecommunication systems, satellite navigation, as well as computers, industrial and household robots and other attributes of modern life.
cornerstone Maxwell's theories It was stated that the source of a magnetic field can only be an alternating electric field, just as the source of an electric field that creates an induction current in a conductor is an alternating magnetic field. The presence of a conductor is not necessary - an electric field also arises in empty space. The alternating electric field lines, similar to the magnetic field lines, are closed. The electric and magnetic fields of an electromagnetic wave are equal.
