Phenomenon electromagnetic induction was discovered by Michael Faraday in 1831. He experimentally established that when the magnetic field changes inside a closed circuit, an electric current arises in it, which is called induction current. Faraday's experiments can be reproduced as follows: when a magnet is introduced or removed into a coil closed to a galvanometer, an induction current appears in the coil (Fig. 24). If two coils are placed side by side (for example, on a common core or one coil inside another) and one coil is connected to a current source through a key, then when the key is closed or opened in the circuit of the first coil, an induction current will appear in the second coil (Fig. 25). The explanation for this phenomenon was given by Maxwell. Any alternating magnetic field always generates an alternating electric field.
For quantitative characteristics the process of changing the magnetic field through a closed circuit, a physical quantity called magnetic flux is introduced. magnetic flux through a closed loop with an area S is called a physical quantity equal to the product of the modulus of the magnetic induction vector AT to the contour area S and by the cosine of the angle a between the direction of the magnetic induction vector and the normal to the contour area. F = BS cosα (Fig. 26).
Empirically, the basic law of electromagnetic induction was established: the EMF of induction in a closed circuit is equal in magnitude to the rate of change of the magnetic flux through the circuit. ξ = ΔФ/t..
Considering a coil containing P turns, then the formula of the basic law of electromagnetic induction will look like this: ξ \u003d n ΔФ / t.
The unit of measurement of the magnetic flux is F - weber (Wb): 1V6 \u003d 1Β s.
The meaning of the dimension follows from the basic law ΔФ =ξ t: 1 Weber is the value of such a magnetic flux, which, decreasing to zero in one second, induces an induction EMF of 1 V through a closed circuit.
A classic demonstration of the basic law of electromagnetic induction is Faraday's first experiment: the faster you move a magnet through the turns of a coil, the more induction current appears in it, and hence the induction EMF.
The dependence of the direction of the induction current on the nature of the change in the magnetic field through a closed circuit in 1833 was experimentally established by the Russian scientist Lenz. He formulated the rule that bears his name. The induction current has a direction in which its magnetic field tends to compensate for the change in the external magnetic flux through the circuit. Lenz designed a device that consists of two aluminum rings, solid and cut, mounted on an aluminum crossbar and having the ability to rotate around an axis, like a rocker. (Fig. 27). When a magnet was introduced into a solid ring, it began to "run away" from the magnet, turning the rocker accordingly. When the magnet was taken out of the ring, the ring tried to "catch up" with the magnet. When the magnet moved inside the cut ring, no effect occurred. Lenz explained the experiment by the fact that the magnetic field of the induction current sought to compensate for the change in the external magnetic flux.
Empirically, M. Faraday showed that the strength of the induction current in a conducting circuit is directly proportional to the rate of change in the number of magnetic induction lines that pass through the surface limited by the circuit in question. The modern formulation of the law of electromagnetic induction, using the concept of magnetic flux, was given by Maxwell. The magnetic flux (Ф) through the surface S is a value equal to:
where is the modulus of the magnetic induction vector; - the angle between the magnetic induction vector and the normal to the contour plane. The magnetic flux is interpreted as a quantity that is proportional to the number of magnetic induction lines passing through the considered surface area S.
The appearance of an induction current indicates that a certain electromotive force (EMF) arises in the conductor. The reason for the appearance of EMF induction is a change in the magnetic flux. In the system of international units (SI), the law of electromagnetic induction is written as follows:
where is the rate of change of the magnetic flux through the area that the contour limits.
The sign of the magnetic flux depends on the choice of the positive normal to the contour plane. In this case, the direction of the normal is determined using the rule of the right screw, connecting it with the positive direction of the current in the circuit. So, the positive direction of the normal is arbitrarily assigned, the positive direction of the current and the EMF of induction in the circuit are determined. The minus sign in the basic law of electromagnetic induction corresponds to Lenz's rule.
Figure 1 shows a closed loop. Assume that the positive direction of the contour traversal is counterclockwise, then the normal to the contour () is the right screw in the direction of traversal of the contour. If the magnetic induction vector of the external field is co-directed with the normal and its modulus increases with time, then we get:
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In this case, the induction current will create a magnetic flux (F '), which will be less than zero. The lines of magnetic induction of the magnetic field of the induction current () are shown in fig. 1 dotted line. The induction current will be directed clockwise. The induction emf will be less than zero.
Formula (2) is a record of the law of electromagnetic induction in the most general form. It can be applied to fixed circuits and conductors moving in a magnetic field. The derivative, which is included in expression (2), generally consists of two parts: one depends on the change in the magnetic flux over time, the other is associated with the movement (deformations) of the conductor in a magnetic field.
In the event that the magnetic flux changes in equal time intervals by the same amount, then the law of electromagnetic induction is written as:
If a circuit consisting of N turns is considered in an alternating magnetic field, then the law of electromagnetic induction will take the form:
where the quantity is called flux linkage.
Examples of problem solving
EXAMPLE 1
| Exercise | What is the rate of change of the magnetic flux in the solenoid, which has N = 1000 turns, if an induction EMF equal to 200 V is excited in it? |
| Decision | The basis for solving this problem is the law of electromagnetic induction in the form:
where is the rate of change of the magnetic flux in the solenoid. Therefore, we find the desired value as:
Let's do the calculations:
|
| Answer |
EXAMPLE 2
| Exercise | A square conducting frame is in a magnetic field that changes according to the law: (where and are constants). The normal to the frame makes an angle with the direction of the field magnetic induction vector. frame wall b. Get an expression for the instantaneous value of the induction emf (). |
| Decision | Let's make a drawing. As a basis for solving the problem, we take the basic law of electromagnetic induction in the form:
|
After it was found that the magnetic field is created by electric currents, scientists tried to solve the inverse problem - using a magnetic field to create electricity. This problem was successfully solved in 1831 by M. Faraday, who discovered the phenomenon of electromagnetic induction. The essence of this phenomenon is that in a closed conducting circuit, with any change in the magnetic flux penetrating this circuit, an electrical current arises, which is called induction. A diagram of some of Faraday's experiments is shown in fig. 3.12.
When the position of the permanent magnet was changed relative to the coil closed to the galvanometer, an electric current arose in the latter, and the direction of the current turned out to be different - depending on the direction of movement of the permanent magnet. A similar result was achieved when moving another coil, through which an electric current flowed. Moreover, a current appeared in the large coil even with the position of the smaller coil unchanged, but with a change in the current in it.
Based on such experiments, M. Faraday came to the conclusion that an electric current always appears in the coil when the magnetic flux coupled to this coil changes. The magnitude of the current depends on the rate of change of the magnetic flux. Now we formulate Faraday's discoveries in the form law of electromagnetic induction: with any change in the magnetic flux coupled to a conducting closed circuit, an EMF of induction arises in this circuit, which is defined as
The “-” sign in expression (3.53) means that with an increase in the magnetic flux, the magnetic field created by the inductive current is directed against the external magnetic field. If the magnetic flux decreases in magnitude, then the magnetic field of the induction current coincides in direction with the external magnetic field. The Russian scientist H. Lenz thus determined the appearance of the minus sign in the expression (3.53) - the induction current in the circuit always has such a direction that the magnetic field created by it has such a direction that it prevents a change in the magnetic flux that caused the induction current to occur.
Let's give another wording. law of electromagnetic induction: The induction emf in a closed conducting circuit is equal to the rate of change of the magnetic flux penetrating this circuit, taken with the opposite sign.
The German physicist Helmholtz showed that the law of electromagnetic induction can be obtained from the law of conservation of energy. In fact, the energy of the EMF source to move the current-carrying conductor in a magnetic field (see Fig. 3.37) will be spent both on the Joule heating of the conductor with resistance R, and on the work of moving the conductor:
Then it immediately follows from equation (3.54) that
The numerator of expression (3.55) is the algebraic sum of the EMF acting in the circuit. Consequently,
What is the physical reason for the occurrence of EMF? The Lorentz force acts on the charges in the conductor AB when the conductor moves along the x axis. Under the action of this force, the positive charges will shift upward, as a result of which the electric field in the conductor will be weakened. In other words, an EMF of induction will appear in the conductor. Therefore, in the case considered by us, the physical cause of the emf is the Lorentz force. However, as we have already noted, an EMF of induction may appear in a stationary closed circuit if the magnetic field penetrating this circuit changes.
In this case, the charges can be considered fixed, and the Lorentz force does not act on fixed charges. To explain the occurrence of EMF in this case, Maxwell suggested that any changing magnetic field generates a changing electric field in the conductor, which is the cause of the induction EMF. The circulation of the voltage vector acting in this circuit will thus be equal to the induction EMF acting in the circuit:
. (3.56)
The phenomenon of electromagnetic induction is used to convert mechanical rotational energy into electrical energy - in electric current generators. The reverse process - the conversion of electrical energy into mechanical energy, based on the torque acting on the frame with current in a magnetic field, is used in electric motors.
Consider the principle of operation of the electric current generator (Fig. 3.13). Let us have a conducting frame rotate between the poles of a magnet (it can be an electromagnet) with a frequency w. Then the angle between the normal to the plane of the frame and the direction of the magnetic field changes according to the law a = wt. In this case, the magnetic flux coupled to the frame will change in accordance with the formula
where S is the area of the contour. In accordance with the law of electromagnetic induction, an EMF will be induced in the frame
With e max = BSw. Thus, if a conducting frame rotates at a constant angular velocity in a magnetic field, then an EMF will be induced in it, changing according to a harmonic law. In real generators, many turns connected in series are rotated, and in electromagnets, to increase the magnetic induction, cores with high magnetic permeability are used. m..
Induction currents can also occur in the thickness of conducting bodies placed in an alternating magnetic field. In this case, these currents are called Foucault currents. These currents cause heating of massive conductors. This phenomenon is used in vacuum induction furnaces, where high currents heat the metal to melt. Since the heating of metals occurs in a vacuum, this makes it possible to obtain highly pure materials.
The phenomenon of electromagnetic induction is the occurrence of an electric current in a closed conducting circuit, while the magnetic flux penetrating this circuit changes with time. This phenomenon is based on the law of electromagnetic induction, the formula of which was derived by the English physicist Faraday.
Concepts of electromagnetic induction
One of the main quantities associated with electromagnetic induction is the magnetic flux. To understand him physical meaning, we should consider the formula that determines this value: Φ = B . S. cos a. Here B acts as the modulus of the magnetic induction vector, S is the area of the conducting circuit, α is the angle between the normal to the contour plane and the magnetic induction vector.
With a non-uniform magnetic field and a non-planar contour, the value of the magnetic flux can be generalized. For this, in the SI system there is a designation for the unit of magnetic flux, called Weber. To create 1 Wb, a magnetic field of 1 T is required, which penetrates a flat contour, the area of which is 1 m2. (1 Wb = 1 T. 1 m2)
Faraday discovered the law of electromagnetic induction, the formula of which is expressed in the following terms:
This formula clearly demonstrates that a change in the magnetic flux in the circuit leads to the appearance of an induction emf. The emf, in turn, is equal to the rate at which the magnetic flux changes when passing through the area bounded by the circuit. The entire value of the EMF is taken with a minus sign. That's what it is .
Reasons for changing the magnetic flux
The magnetic flux penetrating a closed loop can change for a number of reasons.
First of all, these changes occur when the circuit moves in a magnetic field that is constant in time. In this case, the conductors, together with free charge carriers, move in a magnetic field. EMF of induction occurs under the influence of external forces that affect the free charges in moving conductors.
Another reason that changes the magnetic flux is the change in time of the magnetic field when the circuit is stationary. In a fixed conductor, electrons can move only under the influence of electric field. This field, in turn, arises from the action of a magnetic field that changes over time.
The work expended on moving one positive charge in a closed circuit is equal to the induction emf for a stationary conductor. Such a field, obtained with the help of a changing magnetic field, is called a vortex electric field.
On this lesson, the theme of which is: “Lenz's rule. The law of electromagnetic induction, we will learn general rule, allowing to determine the direction of the induction current in the circuit, established in 1833 by E.X. Lenz. We will also consider an experiment with aluminum rings, which clearly demonstrates this rule, and formulate the law of electromagnetic induction
By approaching or moving the magnet away from the solid ring, we change the magnetic flux that permeates the area of the ring. According to the theory of the phenomenon of electromagnetic induction, an inductive electric current must occur in the ring. From the experiments of Ampere 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 of two magnets ( permanent magnet, which we move, and a closed loop with current).
Since the system did not respond to the approach of the magnet to the ring with a cut, it can be concluded that the induction current does not occur in an open circuit.
Causes of repulsion or attraction of the ring to the magnet
1. When the magnet approaches
When the pole of the magnet approaches, the ring repels from it. That is, it behaves like a magnet, which has the same pole on our side as the approaching magnet. If we approach the north pole of the magnet, then the magnetic induction vector of the ring with induction 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. Approach of the magnet to the ring
2. When removing the magnet from the ring
When the magnet is removed, the ring trails behind it. Consequently, from the side of the receding magnet, the opposite pole is formed near the ring. The magnetic induction vector of the ring with current 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 the magnet are opposite in direction. If the magnetic flux through the ring decreases with time, then the magnetic field induction vector of the ring coincides in direction with the magnet induction vector.
The direction of the induction current in the ring can be determined by the rule right hand. If sent thumb right hand in the direction of the magnetic induction vector, then 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 induction current arises in the circuit in such a direction as to compensate for the change in the external magnetic flux with its magnetic flux.
If the external magnetic flux increases, then the induction current tends to slow down this increase with its magnetic field. If the magnetic flux decreases, then the inductive current with its magnetic field tends to slow down this decrease.
This feature of electromagnetic induction is expressed by the minus sign in EMF formula induction.
Law of electromagnetic induction
When the external magnetic flux penetrating the circuit changes, an induction 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: Proc. for 11 cells. general education institutions. - M.: Education, 2010.
- Kasyanov V.A. Physics. Grade 11: Proc. 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 reading)
- 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 ().
