An alternating magnetic field generates induced electric field. If the magnetic field is constant, then there will be no induced electric field. Hence, the induced electric field is not associated with charges, as is the case in the case of an electrostatic field; its lines of force do not begin or end on charges, but are closed on themselves, similar to magnetic field lines. This means that induced electric field, like magnetic, is a vortex.
If a stationary conductor is placed in an alternating magnetic field, then an e is induced in it. d.s. The electrons are driven in directional motion by an electric field induced by an alternating magnetic field; an induced electric current occurs. In this case, the conductor is only an indicator of the induced electric field. The field sets free electrons in the conductor in motion and thereby reveals itself. Now we can say that even without a conductor this field exists, possessing a reserve of energy.
The essence of the phenomenon of electromagnetic induction lies not so much in the appearance of an induced current, but in the appearance of a vortex electric field.
This fundamental position of electrodynamics was established by Maxwell as a generalization of Faraday's law of electromagnetic induction.
Unlike the electrostatic field, the induced electric field is non-potential, since the work done in the induced electric field when moving a unit positive charge along a closed circuit is equal to e. d.s. induction, not zero.
The direction of the vortex electric field intensity vector is established in accordance with Faraday's law of electromagnetic induction and Lenz's rule. Direction of force lines of vortex electric. field coincides with the direction of the induction current.
Since the vortex electric field exists in the absence of a conductor, it can be used to accelerate charged particles to speeds comparable to the speed of light. It is on the use of this principle that the operation of electron accelerators - betatrons - is based.
An inductive electric field has completely different properties compared to an electrostatic field.
The difference between a vortex electric field and an electrostatic one
1) It is not associated with electric charges;
2) The lines of force of this field are always closed;
3) The work done by the vortex field forces to move charges along a closed trajectory is not zero.
|
electrostatic field |
induction electric field |
| 1. created by stationary electric. charges | 1. caused by changes in the magnetic field |
| 2. field lines are open - potential field | 2. lines of force are closed - vortex field |
| 3. The sources of the field are electric. charges | 3. field sources cannot be specified |
| 4. work done by field forces to move a test charge along a closed path = 0. | 4. work of field forces to move a test charge along a closed path = induced emf |
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 penetrating 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 intensity 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 forces of the vortex electric field 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 results of the experiment. 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 magnitude 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
- Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
- Tikhomirova S.A., Yarovsky B.M., Physics 11. - M.: Mnemosyne.
- Electronic physics textbook ().
- Cool physics ().
- Xvatit.com ().
- 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?
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 penetrating 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 intensity 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 forces of the vortex electric field 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 results of the experiment. 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 magnitude 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
- Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
- Tikhomirova S.A., Yarovsky B.M., Physics 11. - M.: Mnemosyne.
- Electronic physics textbook ().
- Cool physics ().
- Xvatit.com ().
- 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?
« Physics - 11th grade"
Self-induction.
If alternating current flows through the coil, then:
the magnetic flux passing through the coil varies with time,
and an induced emf occurs in the coil.
This phenomenon is called self-induction.
According to Lenz's rule, as the current increases, the intensity of the vortex electric field is directed against the current, i.e. the vortex field prevents the current from increasing.
When the current decreases, the intensity of the vortex electric field and the current are directed in the same way, i.e. the vortex field supports the current.
The phenomenon of self-induction is similar to the phenomenon of inertia in mechanics.
In mechanics:
Inertia causes a body to gradually acquire a certain speed under the influence of force.
The body cannot be instantly slowed down, no matter how great the braking force.
In electrodynamics:
When the circuit is closed due to self-induction, the current strength increases gradually.
When the circuit is opened, self-induction maintains the current for some time, despite the resistance of the circuit.
The phenomenon of self-induction plays a very important role in electrical and radio engineering.
Current magnetic field energy
According to the law of conservation of energy magnetic field energy, created by the current, is equal to the energy that the current source (for example, a galvanic cell) must expend to create the current.
When the circuit is opened, this energy transforms into other types of energy.
When closed circuit current increases.
A vortex electric field appears in the conductor, acting against the electric field created by the current source.
In order for the current strength to become equal to I, the current source must do work against the forces of the vortex field.
This work goes to increase the energy of the magnetic field of the current.
When opening circuit current disappears.
The vortex field does positive work.
The energy stored in the current is released.
This is detected, for example, by a powerful spark that occurs when a circuit with high inductance is opened.
The energy of the magnetic field created by a current passing through a section of a circuit with inductance L is determined by the formula 
The magnetic field created by an electric current has an energy directly proportional to the square of the current.
The energy density of the magnetic field (i.e., the energy per unit volume) is proportional to the square of the magnetic induction: w m ~ V 2,
similar to how the energy density of the electric field is proportional to the square of the electric field strength w e ~ E 2.
Electric 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.
VORTEX ELECTRIC FIELD
The reason for the occurrence of electric current in a stationary conductor is the electric field.
Any change in the magnetic field generates an inductive electric field, regardless of the presence or absence of a closed circuit, and if the conductor is open, then a potential difference arises at its ends; If the conductor is closed, then an induced current is observed in it.
The inductive electric field is vortex.
The direction of the vortex electric field lines coincides with the direction of the induction current
An inductive electric field has completely different properties compared to an electrostatic field.
Electrostatic field- is created by stationary electric charges, the field lines are open - - potential field, the sources of the field are electric charges, the work of field forces to move a test charge along a closed path is 0
Induction electric field (vortex electric field)- caused by changes in the magnetic field, the lines of force are closed (vortex field), the field sources cannot be specified, the work of the field forces to move the test charge along a closed path is equal to the induced emf.
Eddy currents
Induction currents in massive conductors are called Foucault currents. Foucault currents can reach very large values, because The resistance of massive conductors is low. Therefore, transformer cores are made from insulated plates.
In ferrites - magnetic insulators, eddy currents practically do not arise.
Use of eddy currents
Heating and melting of metals in a vacuum, dampers in electrical measuring instruments.
Harmful effects of eddy currents
These are energy losses in the cores of transformers and generators due to the release of large amounts of heat.
Electromagnetic field - Cool physics
For the curious
Click beetle somersault
If you tickle a click beetle lying on its back, it jumps up 25 centimeters, and a loud click is heard. Nonsense, you might say.
But, indeed, the bug, without the help of its legs, makes a push with an initial acceleration of 400 g, and then turns over in the air and lands on its legs. 400 g - amazing!
Even more surprising is that the power developed during the push is one hundred times greater than the power that any of the bug's muscles can provide. How does a bug manage to develop such enormous power?
How often is he able to make his amazing leaps? What is the limitation on the frequency of their repetition?
Turns out...
When the bug is lying upside down, a special protrusion on the front of its body prevents it from straightening up to make a jump. For some time he accumulates muscle tension, then, bending sharply, throws himself up.
Before the bug can jump again, it must slowly "tense" its muscles again.
