Moscow State University of Printing Arts. The law of electromagnetic induction. Vortex electric field. Eddy currents Eddy electric field self-induction inductance
The alternating magnetic field generates induced electric field... If the magnetic field is constant, then the induced electric field will not arise. Consequently, the induced electric field is not related to charges as is the case with an electrostatic field; its lines of force do not begin or end on charges, but are closed on themselves, like the lines of force of a magnetic field. It means that induced electric field like magnetic is vortex.
If a stationary conductor is placed in an alternating magnetic field, then e is induced in it. etc. with. Electrons are set in directed 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 motion in the conductor and thereby reveals itself. Now it can be argued that even without a conductor, this field exists, having a reserve of energy.
The essence of the phenomenon of electromagnetic induction lies not so much in the appearance of an induced current as 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.
In contrast to the electrostatic field, the induced electric field is non-potential, since the work done in the induced electric field, when a single positive charge moves along a closed loop, is equal to e. etc. with. induction, not zero.
The direction of the intensity vector of the vortex electric field is established in accordance with the Faraday law of electromagnetic induction and Lenz's rule. The direction of the lines of force of the vortex el. field coincides with the direction of the induction current.
Since a 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 action of electron accelerators - betatrons is based.
An induction electric field has completely different properties than an electrostatic field.
The difference between a vortex electric field and an electrostatic
1) It is not associated with electrical charges;
2) The lines of force of this field are always closed;
3) The work of the forces of the vortex field on the movement of charges on a closed trajectory is not equal to zero.
|
electrostatic field |
induction electric field |
| 1. created by motionless electr. charges | 1.Caused by changes in the magnetic field |
| 2.the field lines are open - potential field | 2. the lines of force are closed - vortex field |
| 3. The sources of the field are electr. charges | 3.field sources cannot be specified |
| 4. the work of the field forces to move the test charge along a closed path = 0. | 4.the work of the field forces to move the test charge along a closed path = EMF of induction |
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 EMF of induction 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 induction current occurrence. We place a circular wire loop of radius r in a time-varying uniform magnetic field (Fig. 2.8).
Let the induction of the magnetic field increase, then the magnetic flux through the surface bounded by the turn will also increase with time. According to the law of electromagnetic induction, an induction current will appear in the loop. When the magnetic induction changes linearly, the induction current will be constant.
What forces make the charges move in the loop? The magnetic field itself, penetrating the coil, cannot do this, since the magnetic field acts exclusively on moving charges (this is what it differs from the electric one), and the conductor with the electrons in it is motionless.
In addition to the magnetic field, an electric field also acts on charges, both moving and stationary. But the fields that have been discussed so far (electrostatic or stationary) are created by electric charges, and the induction current appears as a result of the action of a changing magnetic field. Therefore, it can be assumed that electrons in a stationary conductor are set in motion by an electric field, and this field is directly generated by a changing magnetic field. Thus, a new fundamental property of the field is affirmed: changing over time, the magnetic field generates an electric field... J. Maxwell first came to this conclusion.
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 you to detect the emerging electric field.
The field sets in motion the electrons and the conductor and thereby reveals itself. The essence of the phenomenon of electromagnetic induction in a fixed conductor consists not so much in the appearance of an induction current, but in the appearance of an electric field, which sets electric charges in motion.
The electric field that occurs when the magnetic field changes is of a completely different nature than the electrostatic one.
It is not directly related to electric charges, and its lines of tension cannot begin and end on them. They generally do not begin or end anywhere, but are closed lines, similar to the lines of induction of a magnetic field. 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 strength vector forms a left screw with the direction of the vector. This means that when the screw with the left 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 tension vector forms a right screw with the direction of the vector.
The direction of the lines of force of force coincides with the direction of the induction current. The force acting from the side of 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 to move the charge q on a closed path is not zero. Indeed, when the 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 a single positive charge moves along a closed fixed conductor is numerically equal to the EMF of induction 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 small.
Such currents, called Foucault currents after the French physicist who studied them, can be used to heat conductors. The device of induction furnaces is based on this principle, for example, microwave ovens used in everyday life. This principle is also used for smelting metals. In addition, the phenomenon of electromagnetic induction is used in metal detectors installed at the entrances to buildings of air terminals, theaters, etc.
However, in many devices, the occurrence of Foucault currents leads to useless and even undesirable losses of energy for the generation of heat. Therefore, the iron cores of transformers, electric motors, generators, etc. are made not solid, but consisting of separate plates, isolated from each other. The surfaces of the plates should be perpendicular to the direction of the vortex electric field strength vector. In this case, the resistance to electric current of the plates will be maximum, and the release of heat will be minimal.
The use of ferrites. Radio-electronic equipment operates at 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.
Eddy currents do not appear in ferrites during magnetization reversal. As a result, the loss of energy for the release of heat in them is minimized. Therefore, the cores of high-frequency transformers, magnetic antennas of transistors, etc. are made of ferrites. Ferrite cores are made from a mixture of powders of the initial 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 re-magnetize. In ferrites, the eddy currents are very small, so they can be quickly re-magnetized.
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.
Electric current in the circuit is possible if external forces act on the free charges of the conductor. The work of these forces to move a single positive charge along a closed loop is called EMF. When the magnetic flux changes through the surface bounded by the contour, external forces appear in the contour, the action of which is characterized by the EMF of induction.
Given the direction of the induction current, according to Lenz's rule:
The EMF of induction 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? - since the induction current counteracts the change in the magnetic flux, the EMF of the induction 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 resistance of the conductor.
VORTEX ELECTRIC FIELD
The reason for the occurrence of an electric current in a fixed conductor is an electric field.
Any change in the magnetic field generates an induction electric field, regardless of the presence or absence of a closed loop, while if the conductor is open, then a potential difference arises at its ends; if the conductor is closed, then an induction current is observed in it.
The induction electric field is vortex.
The direction of the lines of force of the vortex electric field coincides with the direction of the induction current
An induction electric field has completely different properties than an electrostatic field.
Electrostatic field- created by stationary electric charges, the field lines of the field are open - - potential field, the sources of the field are electric charges, the work of the field forces to move the test charge along a closed path is 0
Induction electric field (vortex electric field)- It is caused by changes in the magnetic field, the lines of force are closed (vortex field), the sources of the field cannot be specified, the work of the field forces to move the test charge along a closed path is equal to the EMF of induction.
Eddy currents
Induction currents in massive conductors are called Foucault currents. Foucault currents can reach very large values since the resistance of massive conductors is low. Therefore, the cores of the transformers are made of insulated plates.
In ferrites - magnetic insulators, eddy currents practically do not occur.
Using eddy currents
Heating and melting of metals in 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 a large amount of heat.
Electromagnetic Field - Cool Physics
Curious
Somersault-mortale click beetle
If you tickle a clicking beetle lying on its back, it jumps up 25 centimeters, and a loud click is heard. Nonsense, you might say.
But, in fact, 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 feet. 400 g - amazing!
Even more surprising is the fact that the power developed during the push is one hundred times more than the power that any of the muscles of the bug can provide. How does a bug manage to develop such enormous power?
How often is he able to make his amazing jumps? What limits 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 a while, he accumulates muscle tension, then, bending sharply, throws himself up.
Before the bug can jump again, it must slowly "tighten" its muscles again.
If the occurrence of an induction current or a potential difference in a conductor moving in a magnetic field can be explained by the action of the Lorentz force, which leads to the movement of charges. How to explain the occurrence of an electric current in a stationary conductor in a changing magnetic field? The presence of an electric field !!! And what is this field?
Any change in the magnetic field generates an inductive electric field in the surrounding space (regardless of the presence or absence of a closed loop, and if the conductor is open, then a potential difference arises at its ends; if the conductor is closed, then an induction current is observed in it).
Electric field electrostatic field 1.created by stationary electric charges 2.the field lines of the field are open - - potential field 3.the sources of the field are electric charges 4.the work of the field forces to move the test charge along a closed path is 0.induction electric field (vortex electric field) 1.Is caused by changes in the magnetic field 2.the lines of force are closed - - vortex field 3.field sources cannot be specified 4.the work of the field forces to move the test charge along a closed path is equal to the EMF of induction
Inductance (or self-induction coefficient) is the coefficient of proportionality between electric shock, flowing in any closed loop, and the magnetic flux created by this current through the surface: Ф = LI, Ф magnetic flux, I current in the circuit, L inductance. Through inductance, the EMF of self-induction in the circuit is expressed, which occurs when the current changes in it: ξ si = -L ΔI / Δt. It follows from this formula that the inductance is numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 A per 1 s. Inductance
Lenz's rule (1883)the induction current excited in a closed loop when the magnetic flux changes is always directed so that the magnetic field generated by it prevents the change in the magnetic flux causing the induction current.
Lenz's experience
Experience description:the closed ring pushes away from the magnet if it is pushed into the ring and attracts if the magnet is pushed out.
The movement of the ring is due to magnetic field of induction current.
Application of Lenz's rule
Example Magnet moves to the right (slides into the contour)
1. Determine the direction of the lines of force of the external fieldB.
2. Determine whether the magnetic flux increases or decreases through
circuit.
3. Determine the direction of the induction magnetic fieldB i
If the magnetic flux increases,B i directed againstBcompensating for this increase. If the magnetic flux decreases,B i directed the same withBcompensating for this decrease.
Determine the direction of the induction current according to the gimbal's rule.
Vortex electric field
The reason for the appearance of the EMF induction in a closed loop when the magnetic flux changes is emergencevortex electric field in any area of space where an alternating magnetic field exists... - Maxwell's hypothesis. Vortex field lines closed.
Let us list the properties of the fields known to us
1. Electrostatic, occurs wherever there is email. charges. Leylines start and end on charges. Potential, i.e. closed loop work is zero. tension, potential.
2. Current field - magnetic, vortex, closed loop work is not zero. The current flows in the direction of decreasing potential. The field acts only on moving charges.
3. Vortex electric field. Works on any charges. Closed loop work is equal to the EMF of induction. EMF of induction is determined by Faraday's law.
Self-induction. Inductance
Self-induction is an important special case
electromagnetic induction when changing
magnetic flux causing induction EMF,
is created current in the circuit itself.
In any circuit through which current flows,
arises a magnetic field. The lines of force of this field
permeate all surrounding space, including, intersect the area of the contour itself.
The magnetic flux, which is caused by the current in this very circuit, is called own magnetic flux.
Since the magnetic flux is proportional magnetic field induction, the intrinsic magnetic flux is proportional to the current in the circuit
Therefore, the proportionality factor can be introduced
Aspect ratioLbetween its own magnetic flux in the circuit and the current in it is called the inductance of the circuit.
The inductance of the conductor depends on dimensions, shape of the conductor, magnetic properties of the medium.
The unit of measurement for inductance is called Henry
