In 1831, Michael Faraday discovered that in a closed conducting loop, when the magnetic field changes, an electric current arises, called induction.
An induced current in a coil of metal wire occurs when a magnet is pushed into the coil and when a magnet is pulled out of the coil, as well as when the current strength changes in the second coil, the magnetic field of which penetrates the first coil.
The phenomenon of the occurrence of electric current in a closed conducting circuit when the magnetic field penetrating the circuit changes is called electromagnetic induction. The appearance of an electric current in a closed circuit with changes in the magnetic field penetrating the circuit indicates the action of external forces of a non-electric nature in the circuit or the emergence of induced emf.
The direction of the induction current in the circuit depends on whether the magnetic flux passing through the circuit increases or decreases, as well as on the direction of the magnetic field induction vector relative to the circuit. The general rule for determining the direction of the induction current in a circuit was established in 1833 by E.H. Lenz.
Lenz's rule can be clearly demonstrated using a lightweight aluminum ring (Fig. 11.1). Experience shows that when a permanent magnet is introduced, the ring is repelled from it, and when removed, it is attracted to the magnet. The result of the experiments does not depend on the polarity of the magnet.
The repulsion and attraction of a solid ring is explained by the occurrence of an induction current in the ring when the magnetic flux through the ring changes and the effect of a magnetic field on the induction current. When a magnet is pushed into the ring, the induction current in it has such a direction that the magnetic field created by this current counteracts the external magnetic field, and when the magnet is pulled out, the induction current in it has such a direction that the induction vector of its magnetic field coincides in direction with the induction vector of the external field .
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.
Law of electromagnetic induction: The induced emf in a closed loop is equal to the modulus of the rate of change of the magnetic flux through the surface bounded by the loop:
Taking into account Lenz's rule, the law of electromagnetic induction is written as follows:
If identical changes in magnetic flux occur in series-connected circuits, then the induced emf in them is equal to the sum of the induced emf in each of the circuits. Therefore, when the magnetic flux changes in a coil consisting of n identical turns of wire, the total induced emf in n times the induced emf in a single circuit:
The occurrence of an electric current in a closed circuit indicates that when the magnetic flux penetrating the circuit changes, forces act on the free electric charges in the circuit. The circuit wire is motionless; the free electric charges in it can be considered motionless. Stationary electric charges can only be affected by an electric field. Consequently, with any change in the magnetic field in the surrounding space, an electric field appears. This electric field sets in motion free electric charges in the circuit, creating an inductive electric current. The electric field that arises when the magnetic field changes is called vortex electric field.
The work of the forces of the vortex electric field to move electric charges is the work of external forces, the source of induced emf.
The vortex electric field differs from the electrostatic one in that it is not associated with electric charges; its lines of tension are closed lines. The work done by the forces of a vortex electric field when an electric charge moves along a closed line can be different from zero.
Magnetic flux Ф= BS cos. A change in the magnetic flux through the circuit can occur: 1) in the case of a stationary conducting circuit placed in a time-varying field; 2) in the case of a conductor moving in a magnetic field, which may not change over time. The value of the induced emf in both cases is determined by the law of electromagnetic induction, but the origin of this emf is different.
Let us first consider the first case of the occurrence of an induction current. Let's place a circular wire coil of radius r in a time-varying uniform magnetic field (Fig. 2.8).
Let the magnetic field induction increase, then the magnetic flux through the surface limited by the coil will increase with time. According to the law of electromagnetic induction, an induced current will appear in the coil. When the magnetic field induction changes according to a linear law, the induction current will be constant.
What forces make the charges in the coil move? The magnetic field itself, penetrating the coil, cannot do this, since the magnetic field acts exclusively on moving charges (this is how it differs from the electric one), and the conductor with the electrons in it is motionless.
In addition to the magnetic field, charges, both moving and stationary, are also affected by an electric field. But those fields that have been discussed so far (electrostatic or stationary) are created by electric charges, and the induced current appears as a result of the action of a changing magnetic field. Therefore, we can assume that electrons in a stationary conductor are driven by an electric field, and this field is directly generated by a changing magnetic field. This establishes a new fundamental property of the field: changing over time, the magnetic field generates an electric field. This conclusion was first reached by J. Maxwell.
Now the phenomenon of electromagnetic induction appears before us in a new light. The main thing in it is the process of generating an electric field by a magnetic field. In this case, the presence of a conducting circuit, for example a coil, does not change the essence of the process. A conductor with a supply of free electrons (or other particles) plays the role of a device: it only allows one to detect the emerging electric field.
The field sets electrons in motion in the conductor and thereby reveals itself. The essence of the phenomenon of electromagnetic induction in a stationary conductor is not so much the appearance of an induction current, but rather the appearance of an electric field that sets electric charges in motion.
The electric field that arises when the magnetic field changes has a completely different nature than the electrostatic one.
It is not directly connected with electric charges, and its lines of tension cannot begin and end on them. They do not begin or end anywhere at all, but are closed lines, similar to magnetic field induction lines. This is the so called vortex electric field(Fig. 2.9).
The faster the magnetic induction changes, the greater the electric field strength. According to Lenz's rule, with increasing magnetic induction, the direction of the electric field intensity vector forms a left screw with the direction of the vector. This means that when a screw with a left-hand thread rotates in the direction of the electric field strength lines, the translational movement of the screw coincides with the direction of the magnetic induction vector. On the contrary, when the magnetic induction decreases, the direction of the intensity vector forms a right screw with the direction of the vector.
The direction of the tension lines coincides with the direction of the induction current. The force acting from the vortex electric field on the charge q (external force) is still equal to = q. But in contrast to the case of a stationary electric field, the work of the vortex field in moving the charge q along a closed path is not zero. Indeed, when a charge moves along a closed line of electric field strength, the work on all sections of the path has the same sign, since the force and movement coincide in direction. The work of a vortex electric field when moving a single positive charge along a closed stationary conductor is numerically equal to the induced emf in this conductor.
Induction currents in massive conductors. Induction currents reach a particularly large numerical value in massive conductors, due to the fact that their resistance is low.
Such currents, called Foucault currents after the French physicist who studied them, can be used to heat conductors. The design of induction furnaces, such as microwave ovens used in everyday life, is based on this principle. This principle is also used for melting metals. In addition, the phenomenon of electromagnetic induction is used in metal detectors installed at the entrances to airport terminal buildings, theaters, etc.
However, in many devices the occurrence of Foucault currents leads to useless and even unwanted energy losses due to heat generation. Therefore, the iron cores of transformers, electric motors, generators, etc. are not made solid, but consist of separate plates isolated from each other. The surfaces of the plates must be perpendicular to the direction of the vortex electric field strength vector. The resistance to electric current of the plates will be maximum, and the heat generation will be minimal.
Application of ferrites. Electronic equipment operates in the region of very high frequencies (millions of vibrations per second). Here, the use of coil cores from separate plates no longer gives the desired effect, since large Foucault currents arise in each plate.
During magnetization reversal, eddy currents do not arise in ferrites. As a result, energy losses due to heat generation in them are minimized. Therefore, cores of high-frequency transformers, magnetic antennas of transistors, etc. are made from ferrites. Ferrite cores are made from a mixture of powders of starting substances. The mixture is pressed and subjected to significant heat treatment.
With a rapid change in the magnetic field in an ordinary ferromagnet, induction currents arise, the magnetic field of which, in accordance with Lenz's rule, prevents a change in the magnetic flux in the coil core. Because of this, the flux of magnetic induction practically does not change and the core does not remagnetize. In ferrites, eddy currents are very small, so they can be quickly remagnetized.
Along with the potential Coulomb electric field, there is a vortex electric field. The intensity lines of this field are closed. The vortex field is generated by a changing magnetic field.
How does electromotive force arise in a conductor that is in an alternating magnetic field? What is a vortex electric field, its nature and causes of its occurrence? What are the main properties of this field? Today's lesson will answer all these and many other questions.
Topic: Electromagnetic induction
Lesson:Vortex electric field
Let us remember that Lenz's rule allows us to determine the direction of the induced current in a circuit located in an external magnetic field with an alternating flux. Based on this rule, it was possible to formulate the law of electromagnetic induction.
Law of Electromagnetic Induction
When the magnetic flux piercing the area of the circuit changes, an electromotive force appears in this circuit, numerically equal to the rate of change of the magnetic flux, taken with a minus sign.
How does this electromotive force arise? It turns out that the EMF in a conductor that is in an alternating magnetic field is associated with the emergence of a new object - vortex electric field.
Let's consider experience. There is a coil of copper wire in which an iron core is inserted in order to enhance the magnetic field of the coil. The coil is connected through conductors to an alternating current source. There is also a coil of wire placed on a wooden base. An electric light bulb is connected to this coil. The wire material is covered with insulation. The base of the coil is made of wood, i.e., a material that does not conduct electric current. The coil frame is also made of wood. Thus, any possibility of contact of the light bulb with the circuit connected to the current source is eliminated. When the source is closed, the light bulb lights up, therefore, an electric current flows in the coil, which means that external forces do work in this coil. It is necessary to find out where outside forces come from.
A magnetic field penetrating the plane of a coil cannot cause the appearance of an electric field, since the magnetic field acts only on moving charges. According to the electronic theory of conductivity of metals, there are electrons inside them that can move freely within the crystal lattice. However, this movement in the absence of an external electric field is random. Such disorder leads to the fact that the total effect of the magnetic field on a current-carrying conductor is zero. This distinguishes the electromagnetic field from the electrostatic field, which also acts on stationary charges. Thus, the electric field acts on moving and stationary charges. However, the type of electric field that was studied earlier is created only by electric charges. The induced current, in turn, is created by an alternating magnetic field.
Suppose that the electrons in a conductor are set into ordered motion under the influence of some new kind of electric field. And this electric field is generated not by electric charges, but by an alternating magnetic field. Faraday and Maxwell came to a similar idea. The main thing in this idea is that a time-varying magnetic field generates an electric one. A conductor with free electrons in it makes it possible to detect this field. This electric field sets the electrons in the conductor in motion. The phenomenon of electromagnetic induction consists not so much in the appearance of an induction current, but in the appearance of a new type of electric field that sets in motion electric charges in a conductor (Fig. 1).
The vortex field differs from the static one. It is not generated by stationary charges, therefore, the intensity lines of this field cannot begin and end on the charge. According to research, the vortex field strength lines are closed lines similar to the magnetic field induction lines. Consequently, this electric field is a vortex - the same as a magnetic field.
The second property concerns the work of the forces of this new field. By studying the electrostatic field, we found out that the work done by the forces of the electrostatic field along a closed loop is zero. Since when a charge moves in one direction, the displacement and the effective force are co-directed and the work is positive, then when the charge moves in the opposite direction, the displacement and the effective force are oppositely directed and the work is negative, the total work will be zero. In the case of a vortex field, the work along a closed loop will be different from zero. So, when a charge moves along a closed line of an electric field that has a vortex character, the work in different sections will maintain a constant sign, since the force and displacement in different sections of the trajectory will maintain the same direction relative to each other. The work of the vortex electric field forces to move a charge along a closed loop is non-zero, therefore, the vortex electric field can generate an electric current in a closed loop, which coincides with the experimental results. Then we can say that the force acting on the charges from the vortex field is equal to the product of the transferred charge and the strength of this field.
This force is the external force that does the work. The work done by this force, related to the amount of charge transferred, is the induced emf. The direction of the vortex electric field intensity vector at each point of the intensity lines is determined by Lenz's rule and coincides with the direction of the induction current.
In a stationary circuit located in an alternating magnetic field, an induced electric current arises. The magnetic field itself cannot be a source of external forces, since it can only act on orderly moving electric charges. There cannot be an electrostatic field, since it is generated by stationary charges. After the assumption that a time-varying magnetic field generates an electric field, we learned that this alternating field is of a vortex nature, i.e. its lines are closed. The work of the vortex electric field along a closed loop is different from zero. The force acting on the transferred charge from the vortex electric field is equal to the value of this transferred charge multiplied by the intensity of the vortex electric field. This force is the external force that leads to the occurrence of EMF in the circuit. The electromotive force of induction, i.e. the ratio of the work of external forces to the amount of transferred charge, is equal to the rate of change of magnetic flux taken with a minus sign. The direction of the vortex electric field intensity vector at each point of the intensity lines is determined by Lenz's rule.
- Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 pp.: ill., 8 l. color on
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- How to explain the fact that a lightning strike can melt fuses and damage sensitive electrical appliances and semiconductor devices?
- * When the ring was opened, a self-induction emf of 300 V arose in the coil. What is the intensity of the vortex electric field in the coil turns, if their number is 800, and the radius of the turns is 4 cm?
The phenomenon of electromagnetic induction was discovered by M. Faraday in 1831. The phenomenon can be observed in the following experiments. Let's take a coil with a large number of turns (solenoid), close it with a galvanometer, and move a permanent magnet from one of its ends along the axis. In this case, an electric current will arise in the solenoid, which will be detected by the deflection of the galvanometer needle. This current will stop when the magnet stops moving. If you remove the magnet from the solenoid, a current will again arise in the solenoid, but in the opposite direction. The same phenomenon will occur if the magnet is left stationary and the solenoid is moved. Instead of a magnet, you can take a second solenoid (Fig. 51), through which a direct current flows: formula" src="http://hi-edu.ru/e-books/xbook785/files/I2.gif" border="0" align ="absmiddle" alt=".
The phenomenon of electromagnetic induction is as follows: in any closed conducting circuit, when the flux of magnetic induction changes through the area limited by this circuit, an electric current arises. This current is called induction current.
The appearance of an induced current in a closed circuit is due to the appearance in this circuit under the influence of a time-varying flow of a specific electromotive force, the electromotive force. The magnitude of this EMF was first associated with the rate of change of the magnetic induction flux by Faraday
definition">Faraday's law
The minus sign in the law means that the induced emf always has such a direction that it interferes with the cause that causes it. This rule was established by St. Petersburg professor E.Kh. Lenz.
If we consider the magnetic flux formula" src="http://hi-edu.ru/e-books/xbook785/files/108-2.gif" border="0" align="absmiddle" alt="(Fig. 52, b), or directed opposite to it, if it increases mark "> B. The flux of magnetic induction through the area S, limited by the frame, is equal to
formula" src="http://hi-edu.ru/e-books/xbook785/files/109-1.gif" border="0" align="absmiddle" alt="the angle between the normal to the frame and vector B changes
formula" src="http://hi-edu.ru/e-books/xbook785/files/109-3.gif" border="0" align="absmiddle" alt="According to Faraday's law (12.1), with a changing flow through the frame, an induced current appears in it, which will change over time with a frequency equal to the speed of rotation of the frame formula" src="http://hi-edu.ru/e-books/xbook785 /files/109-4.gif" border="0" align="absmiddle" alt="
As you can see, the induced emf changes according to a harmonic law with frequency formula" src="http://hi-edu.ru/e-books/xbook785/files/109-5.gif" border="0" align="absmiddle" alt="Obtaining an EMF when a coil rotates in a magnetic field is the basis for the operation of an alternating current generator.
Mechanism of occurrence induced current in a moving conductor can be explained using the Lorentz force F = qvB.
Under the influence of the Lorentz force, charges are separated: positive charges accumulate at one end of the conductor, negative ones at the other (Fig. 53). These charges create an electrostatic Coulomb field inside the conductor. If the conductor is open, then the movement of charges under the influence of the Lorentz force will occur until the electric force balances the Lorentz force. The action of the Lorentz force is similar to the action of some electric field; this field is third-party field.
The occurrence of induced emf is also possible in a stationary circuit located in an alternating magnetic field. What is the nature of external forces (non-electrostatic origin) in this case?
Maxwell hypothesized that any alternating magnetic field excites an electric field in the surrounding space, which is the cause of the appearance of induced current in the circuit. This field is characterized by intensity (the index indicates the reason for the occurrence of this field - the magnetic field).
The circulation of this electric field marked ">L is not equal to zero:
formula" src="http://hi-edu.ru/e-books/xbook785/files/111-1.gif" border="0" align="absmiddle" alt="
formula" src="http://hi-edu.ru/e-books/xbook785/files/111-2.gif" border="0" align="absmiddle" alt="
formula" src="http://hi-edu.ru/e-books/xbook785/files/111-5.gif" border="0" align="absmiddle" alt="- partial derivative of induction B with respect to time.
For electrostatic field mark">Q) circulation along any closed contour is zero:
define-e">potential.
The electric field is defined as a vortex, for which circulation along a closed loop L is not equal to zero:
mark">I(t), then it creates a magnetic field with induction B(t), and therefore the flux formula" src="http://hi-edu.ru/e-books/xbook785/files/112. gif" border="0" align="absmiddle" alt="
The phenomenon of electromagnetic induction caused by a change in current in the circuit itself is called self-induction. Its root cause is a change in current in the circuit, which is easier to measure than a change in magnetic flux.
At any point on the surface stretched over the circuit, the induction dB is proportional to the current in the circuit. If it is integrated over the entire surface, then the total magnetic flux is marked ">I
mark ">L - circuit inductance, proportionality coefficient, depending on the circuit configuration.
Inductance shows how much magnetic flux penetrates the surface covered by the circuit when the current in it is 1 A. Its unit is Wb/A, which is called henry (H).
If the circuit has a complex shape, for example, contains several turns, then instead of defining "flux linkage, the formula" src="http://hi-edu.ru/e-books/xbook785/files/112-4.gif" border ="0" align="absmiddle" alt="
the expression is valid for L = const.
This implies another definition of L (more important in practice): inductance shows what self-inductive emf occurs in the circuit if the rate of change of current in it is 1 A/s.
For a solenoid, the magnetic flux through one turn is marked ">N turns of the solenoid (flux linkage),
mark">V =Sl - solenoid volume.
Comparing this expression with (12.4), we get
formula" src="http://hi-edu.ru/e-books/xbook785/files/mu.gif" border="0" align="absmiddle" alt=".
Magnetic flux through the surface covered by circuit 2 can be created by current illustration" src="http://hi-edu.ru/e-books/xbook785/files/ris54.gif" border="0">
Let us denote the formula" src="http://hi-edu.ru/e-books/xbook785/files/113.gif" border="0" align="absmiddle" alt="
formula" src="http://hi-edu.ru/e-books/xbook785/files/I1.gif" border="0" align="absmiddle" alt="changes, then in circuit 2 it is induced mutual induction emf
formula" src="http://hi-edu.ru/e-books/xbook785/files/I2.gif" border="0" align="absmiddle" alt="EMF of mutual induction occurs
formula" src="http://hi-edu.ru/e-books/xbook785/files/113-3.gif" border="0" align="absmiddle" alt=" - mutual inductances of the circuits, they depend on the geometric shape, size, relative position of the contours and magnetic permeability of the medium.
Let's calculate the mutual inductance of two coils wound on a common toroidal core(Fig. 55). Foucault currents, or eddy currents.
A heavy metal plate oscillating between the poles of an electromagnet stops if the direct current feeding the electromagnet is turned on. All its energy turns into heat generated by Foucault currents. There are no currents in a stationary plate.
Eddy currents can be significantly weakened if cuts are made in the plate to increase its resistance. In the solid cores of transformers and electric motors operating on alternating current, Foucault currents would generate a significant amount of heat. Therefore, the cores are made as composites, consisting of thin plates separated by a dielectric layer.
The phenomenon of the occurrence of Foucault induction currents underlies the operation of induction furnaces, which allow heating metals to the melting point.
Foucault currents obey Lenz's rule: their magnetic field is directed so as to counteract the change in magnetic flux that induces eddy currents. This fact is used to calm the moving parts of various devices (damping).
Eddy currents also occur in wires through which alternating electric current flows. The direction of eddy currents is such that they counteract the change in the primary current in the conductor. Thus, the alternating current turns out to be distributed unevenly over the cross-section of the wire; it is, as it were, forced out onto the surface of the conductor. At the surface of the wire, the current density is maximum, and deep into the conductor it decreases and reaches its lowest value on its axis. This phenomenon is called the skin effect (skin). The current is concentrated in the “skin” of the conductor. Therefore, at high frequencies there is no need for conductors with a large cross-section: anyway, the current will flow only in the surface layer.
