Lenz's rule. Vortex field
In this lesson, the topic of which is: “Lenz’s rule. The Law of Electromagnetic Induction,” we learn a general rule that allows us to determine the direction of the induced current in a circuit, established in 1833 by E.X. Lenz. We will also consider the experiment with aluminum rings, which clearly demonstrates this rule, and formulate the law of electromagnetic induction
By bringing the magnet closer to or moving away from the solid ring, we change the magnetic flux that penetrates the area of the ring. According to the theory of the phenomenon of electromagnetic induction, an inductive electric current should arise in the ring. From Ampere's experiments it is known that where the current passes, a magnetic field arises. Consequently, the closed ring begins to behave like a magnet. That is, there is an interaction between two magnets (a permanent magnet that we move, and a closed circuit with current).
Since the system did not react to the approach of the magnet to the ring with the cut, we can conclude that the induced current does not arise in the open circuit.
Reasons for repulsion or attraction of a ring to a magnet
1. When a magnet approaches
As the pole of the magnet approaches, the ring is repelled from it. That is, it behaves like a magnet, which on our side has the same pole as the approaching magnet. If we bring the north pole of the magnet closer, then the magnetic induction vector of the ring with the induced current is directed in the opposite direction relative to the magnetic induction vector of the north pole of the magnet (see Fig. 2).
Rice. 2. Approaching the magnet to the ring
2. When removing the magnet from the ring
When the magnet is removed, the ring is pulled behind it. Consequently, on the side of the receding magnet, an opposite pole is formed at the ring. The magnetic induction vector of the current-carrying ring is directed in the same direction as the magnetic induction vector of the receding magnet (see Fig. 3).
Rice. 3. Removing the magnet from the ring
From this experiment we can conclude that when the magnet moves, the ring also behaves like a magnet, the polarity of which depends on whether the magnetic flux penetrating the ring area increases or decreases. If the flux increases, then the magnetic induction vectors of the ring and magnet are opposite in direction. If the magnetic flux through the ring decreases with time, then the induction vector of the magnetic field of the ring coincides in direction with the induction vector of the magnet.
The direction of the induced current in the ring can be determined by the right-hand rule. If you point the thumb of your right hand in the direction of the magnetic induction vector, then the four bent fingers will indicate the direction of the current in the ring (see Fig. 4).
Rice. 4. Right hand rule
When the magnetic flux penetrating the circuit changes, an induced current appears in the circuit in such a direction that its magnetic flux compensates for the change in the external magnetic flux.
If the external magnetic flux increases, then the induced current, with its magnetic field, tends to slow down this increase. If the magnetic flux decreases, then the induced current with its magnetic field tends to slow down this decrease.
This feature of electromagnetic induction is expressed by the minus sign in the induced emf formula.
Law of Electromagnetic Induction
When the external magnetic flux penetrating the circuit changes, an induced current appears in the circuit. In this case, the value of the electromotive force is numerically equal to the rate of change of the magnetic flux, taken with the “-” sign.
Lenz's rule is a consequence of the law of conservation of energy in electromagnetic phenomena.
Bibliography
- Myakishev G.Ya. Physics: Textbook. for 11th grade general education institutions. - M.: Education, 2010.
- Kasyanov V.A. Physics. 11th grade: Educational. for general education institutions. - M.: Bustard, 2005.
- Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
Homework
- Questions at the end of paragraph 10 (p. 33) - Myakishev G.Ya. Physics 11 (see list of recommended readings)
- How is the law of electromagnetic induction formulated?
- Why is there a “-” sign in the formula for the law of electromagnetic induction?
- Internet portal Festival.1september.ru ().
- Internet portal Physics.kgsu.ru ().
- Internet portal Youtube.com ().
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 the surface limited by the contour, extraneous forces appear in the circuit, the action of which is characterized by the 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 the chemical elements, the transition elements Fe, Co and Ni have ferromagnetic properties (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.
An oscillatory circuit is the 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 electric charges. Oscillations of electric charges are accompanied by electromagnetic radiation having a frequency equal to the frequency of charge oscillations.
>> Direction of induction current. Lenz's rule
By connecting the coil in which the induced current occurs to a galvanometer, you can find that the direction of this current depends on whether the magnet is approaching the coil (for example, with the north pole) or moving away from it (see Fig. 2.2, b).
Emerging induced current of one direction or another somehow interacts with a magnet (attracts or repels it). A coil with current passing through it is like a magnet with two poles - north and south. The direction of the induction current determines which end of the coil acts as the north pole (the magnetic induction lines come out of it). Based on the law of conservation of energy, it is possible to predict in which cases the coil will attract a magnet and in which cases it will repel it.
Interaction of induction current with a magnet. If the magnet is brought closer to the coil, then an induced current appears in it in such a direction that the magnet is necessarily repelled. To bring the magnet and coil closer together, positive work must be done. The coil becomes like a magnet, with its pole of the same name facing the magnet approaching it. Poles of the same name repel each other.
When the magnet is removed, on the contrary, a current appears in the coil in such a direction that a force attracting the magnet appears.
What is the difference between the two experiments: bringing a magnet closer to the coil and moving it away? In the first case, the number of lines of magnetic induction penetrating the turns of the coil, or, what is the same, the magnetic flux, increases (Fig. 2.5, a), and in the second case it decreases (Fig. 2.5, b). Moreover, in the first case, the induction lines of the magnetic field created by the induction current that arises in the coil come out of the upper end of the coil, since the coil repels the magnet, and in the second case, on the contrary, they enter this end. These magnetic induction lines are shown in black in Figure 2.5. In case a, the coil with current is similar to a magnet, the north pole of which is located at the top, and in case b, at the bottom.
Similar conclusions can be drawn using the experiment shown in Figure 2.6. At the ends of the rod, which can rotate freely around a vertical axis, two conductive aluminum rings are fixed. One of them has a cut. If you bring a magnet to the ring without a cut, then an induction current will arise in it and it will be directed so that this ring will push away from the magnet and the rod will rotate. If you remove the magnet from the ring, then, on the contrary, it will be attracted to the magnet. The magnet does not interact with the cut ring, since the cut prevents the occurrence of induction current in the ring. Whether a magnet repels or attracts a coil depends on the direction of the induction current in it. Therefore, the law of conservation of energy allows us to formulate a rule that determines the direction of the induction current.
Now we come to the main thing: with an increase in the magnetic flux through the turns of the coil, the induced current has such a direction that the magnetic field it creates prevents the increase in the magnetic flux through the turns of the coil. After all, the induction lines of this field are directed against the induction lines of the field, a change in which generates an electric current. If the magnetic flux through the coil weakens, then the induction
the current creates a magnetic field with induction, increasing the magnetic flux through the turns of the coil.
This is the essence of the general rule for determining the direction of the induction current, which is applicable in all cases. This rule was established by the Russian physicist E. H. Lenz.
According to 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. More briefly, this rule can be formulated as follows: the induced current is directed so as to interfere with the cause that causes it.
To apply Lenz's rule to find the direction of the induction current in the circuit, it is necessary to do this:
1. Determine the direction of the magnetic induction lines of the external magnetic field.
2. Find out whether the flux of the magnetic induction vector of this field through the surface bounded by the contour increases (Ф > 0) or decreases (Ф< 0).
3. Set the direction of the magnetic induction lines of the magnetic field of the induced current. According to Lenz's rule, these lines must be directed opposite to the lines of magnetic induction at Ф > 0 and have the same direction as them at Ф< 0.
4. Knowing the direction of the magnetic induction lines, find the direction of the induction current using the gimlet rule.
The direction of the induction current is determined using the law of conservation of energy. In all cases, the induced current is directed so that its magnetic field prevents the change in the magnetic flux causing the given induced current.
1. How is the direction of the induction current determined?
2. Will an electric field appear in a ring with a cut if you bring a magnet to it?
« Physics - 11th grade"
Direction of induction current
The direction of the induction current arising in the coil depends on whether the magnet is approaching the coil or moving away from it.
The resulting induced current can attract or repel a magnet, because the coil becomes like a magnet with two poles - north and south.
Based on the law of conservation of energy, it is possible to predict in which cases the coil will attract a magnet and in which cases it will repel it.
Interaction of the induction current of the coil with the magnet.
What is the difference between the two experiments: bringing a magnet closer to the coil and moving it away?
If the magnet is brought closer to the coil
The number of lines of magnetic induction piercing the turns of the coil, or, what is the same, magnetic flux, increases.
The coil becomes like a magnet, with its pole of the same name facing the magnet approaching it.
The induction lines of the magnetic field created by the induced current generated in the coil emerge from the upper end of the coil.
An induced current appears in the coil in such a direction that the magnet is necessarily repelled.
To bring the magnet and coil closer together, positive work must be done
![](https://i1.wp.com/class-fizika.ru/images/10_11_class/11-1/11.1-2.jpg)
If the magnet is removed from the coil
The number of lines of magnetic induction piercing the turns of the coil, or, what is the same, magnetic flux, decreases.
The induction lines of the magnetic field created by the induced current generated in the coil enter the upper end of the coil.
The current-carrying coil becomes similar to a magnet, the north pole of which is at the bottom.
A current arises in the coil in such a direction that an attractive force to the magnet appears.
Likewise You can consider an experiment where two conductive aluminum rings (one of them with a cut) are attached to the ends of a rod, which can freely rotate around a vertical axis.
![](https://i0.wp.com/class-fizika.ru/images/10_11_class/11-1/11.2.jpg)
The magnet does not interact with the cut ring, since the cut prevents the occurrence of induction current in the ring.
Whether a magnet repels or attracts another ring depends on the direction of the induction current arising in the ring.
Therefore, the law of conservation of energy allows us to formulate a rule that determines the direction of the induction current.
Lenz's rule
There is a rule that allows you to determine the direction of the induction current, which was established by the Russian physicist E. X. Lenz:
The induced current arising in a closed circuit with its magnetic field counteracts the change in the magnetic flux that causes it.
or more briefly:
The induced current is directed so as to interfere with the cause that causes it.
When the magnetic flux through the turns of the coil increases, the induced current has such a direction that the magnetic field it creates prevents the increase in the magnetic flux through the turns of the coil.
After all, the induction lines of this field are directed against the induction lines of the field, a change in which generates an electric current.
If the magnetic flux through the coil weakens, then the induced current creates a magnetic field with induction “increasing the magnetic flux through the turns of the coil.
Application of Lenz's rule:
1. Determine the direction of the magnetic induction lines of the external magnetic field.
2. Find out whether the flux of the magnetic induction vector of this field through the surface limited by the contour increases (ΔФ > 0), or decreases (ΔФ< 0).
3. Establish the direction of the lines of magnetic induction "of the magnetic field of the induced current. These lines must, according to Lenz's rule, be directed opposite to the lines of magnetic induction B at ΔФ > 0 and have the same direction as them at ΔФ<0.
4. Knowing the direction of the magnetic induction lines, find the direction of the induced current using the gimlet rule.
The phenomenon of electromagnetic induction is that as a result of a change in time of the magnetic flux that penetrates a closed conducting circuit, an electric current arises in the circuit. This phenomenon was discovered by British physicist Max Faraday in 1831.
Let us introduce the notation we need to write the formula. To denote the magnetic flux we use the letter Ф, the contour area - S, the magnitude of the magnetic induction vector - B, α is the angle between the vector B → and the normal n → to the plane of the contour.
The magnetic flux that passes through the area of a closed conducting loop can be given by the following formula:
Φ = B S cos α,
Let's illustrate the formula.
Picture 1 . 20 . 1 . Magnetic flux through a closed loop. The normal direction n → and the selected positive direction l → bypassing the contour are related by the right gimlet rule.
The unit of magnetic flux in SI is taken to be 1 weber (V b). A magnetic flux equal to 1 V b can be created in a flat circuit with an area of 1 m 2 under the influence of a magnetic field with an induction of 1 T l, which penetrates the circuit in the normal direction.
1 V b = 1 T l m 2
Faraday's law
A change in the magnetic flux leads to the appearance of an induced emf δ and n in the conducting circuit. It is equal to the speed at which the magnetic flux changes through the surface limited by the circuit, taken with a minus sign. This was first experimentally established by Max Faraday. He wrote down his observation in the form of the induced emf formula, which is now called Faraday’s Law:
Definition 1
Faraday's Law:
δ and n d = - ∆ Φ ∆ t
Lenz's rule
Definition 2According to experimental results, the induction current that occurs in a closed loop as a result of a change in magnetic flux is always directed in a certain way. The magnetic field created by the induction current prevents the change in the magnetic flux that caused this induction current. Lenz formulated this rule in 1833.
Let us illustrate Lenz's rule with a drawing that depicts a stationary closed conducting circuit placed in a uniform magnetic field. The induction modulus increases with time.
Example 1
Thanks to Lenz's rule, we can justify the fact that in the formula of electromagnetic induction δ and n d and ∆ Φ ∆ t are opposite in sign.
If you think about the physical meaning of Lenz's rule, then this is a special case of the Law of Conservation of Energy.
There are two reasons why a change in the magnetic flux penetrating a closed circuit may occur:
- Change in magnetic flux due to movement of the entire circuit or its individual parts in a magnetic field that does not change over time;
- Change in magnetic field with a stationary circuit.
Let's move on to consider these cases in more detail.
Moving a circuit or its parts in a constant magnetic field
When conductors and free charge carriers move in a magnetic field, an induced emf occurs. The occurrence of δ and n d can be explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force here is an external force.
Example 2
In the figure we depicted an example of induction when a rectangular contour is placed in a uniform magnetic field B → directed perpendicular to the plane of the contour. One side of the contour moves along the other two sides at a certain speed.
Picture 1 . 20 . 3. The occurrence of induced emf in a moving conductor. The component of the Lorentz force that acts on a free electron is reflected
The free charges of the moving part of the circuit are affected by the Lorentz force. The main component of the Lorentz force in this case is directed along the conductor and is associated with the transfer velocity of charges υ →. The modulus of this external force is equal to:
F L = e υ → B.
The work done by force F L on path l is equal to:
A = F L · l = e υ B l .
According to the definition of EMF:
δ and n d = A e = υ B l .
The value of the external force for the stationary parts of the contour is zero. For the relationship between δ and n d, you can write another version of the formula. The contour area changes over time by Δ S = l υ Δ t. Accordingly, the magnetic flux will also change over time: Δ Φ = B l υ Δ t.
Hence,
δ and n d = ∆ Φ ∆ t.
The signs in the formula that relates δ and ind and ∆ Φ ∆ t can be set depending on which normal and contour directions are chosen. In the case of choosing the normal directions n → and the positive direction of traversing the contour l → consistent with each other according to the right-hand gimlet rule, one can arrive at Faraday’s formula.
Provided that the resistance of the entire circuit is R, then an induction current will flow through it, which is equal to I and n d = δ and n d R. During the time Δt at the resistance R Joule heat will be released:
∆ Q = R I and n d 2 ∆ t = υ 2 B 2 l 2 R ∆ t
There is no paradox here. We simply did not take into account the impact of another force on the system. The explanation is that when an induction current flows through a conductor located in a magnetic field, another component of the Lorentz force acts on the free charges, which is associated with the relative speed of movement of the charges along the conductor. Thanks to this component, the Ampere force F A → appears.
For the example considered above, the modulus of the Ampere force is equal to F A = I B l. The direction of the Ampere force is such that it performs negative mechanical work A me x. This mechanical work over a certain period of time can be calculated using the formula:
A me x = - F υ ∆ t = - I B l υ ∆ t = - υ 2 B 2 l 2 R ∆ t
A conductor moving in a magnetic field experiences magnetic braking. This leads to the fact that the total work done by the Lorentz force is zero. Joule heat can be released either due to a decrease in the kinetic energy of a moving conductor, or due to the energy that maintains the speed of movement of the conductor in space.
Change in magnetic field with a stationary circuit
Definition 3Vortex electric field is an electric field that is caused by a changing magnetic field.
In contrast to the potential electric field, the work of the vortex electric field when moving a single positive charge along a closed conducting circuit is equal to δ and n d in a stationary conductor.
In a stationary conductor, electrons can only be moved by an electric field. And the occurrence of δ and n d cannot be explained by the action of the Lorentz force.
The first to introduce the concept of a vortex electric field was the English physicist John Maxwell. This happened in 1861.
In fact, the phenomena of induction in moving and stationary conductors proceed in the same way. So in this case we can also use Faraday's formula. The differences relate to the physical cause of the occurrence of induced current: in moving conductors δ and n d is determined by the Lorentz force, in stationary ones - by the effect on free charges of the vortex electric field that arises when the magnetic field changes.