Vortex electric field - Knowledge Hypermarket. Vortex electric field. Self-induction. Self-induced emf. Inductance. Magnetic field energy How a vortex electric field is created

The following can occur through a circuit: 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 (2.1), 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 intensity 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 the calede plate.

In § 7 it was noted that there are magnetic insulators - ferrites. 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 magnetic induction flux remains virtually unchanged 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.

1. What is the nature of external forces that cause the appearance of induced current in a stationary conductor!
2. What is the difference between a vortex electric field and an electrostatic or stationary one!
3. What are Foucault currents!
4. What are the advantages of ferrites compared to conventional ferromagnets!

Myakishev G. Ya., Physics. 11th grade: educational. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; edited by V. I. Nikolaeva, N. A. Parfentieva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

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Let us consider the case of electromagnetic induction, when the wire circuit in which the current is induced is stationary, and changes in the magnetic flux are caused by changes in the magnetic field. The appearance of an induced current indicates that changes in the magnetic field cause the appearance of external forces in the circuit acting on current carriers. These external forces are not associated with either chemical or thermal processes in the wire; they also cannot be magnetic forces, because such forces do not do work on charges. It remains to conclude that the induced current is caused by the electric field arising in the wire. Let us denote the strength of this field (this designation, as well as the designation used below, is auxiliary; subsequently we will omit the indices). The electromotive force is equal to the circulation of the vector along a given contour:

Substituting expression (69.1) for and expression for Ф into the formula leads to the relation

(the integral on the right side of the equality is taken over an arbitrary surface supported by the contour). Since the contour and surface are stationary, the operations of differentiation with respect to time and integration with respect to the surface can be swapped:

In connection with that. that vector B depends, generally speaking, on both time and coordinates, we wrote under the integral sign the symbol of the partial derivative with respect to time (the integral is a function only of time).

Let us transform the left side of equality (69.2) using Stokes' theorem. As a result we get

Due to the arbitrariness of the choice of the integration surface, the equality must be satisfied

The field rotor at each point in space is equal to the time derivative of vector B taken with the opposite sign.

Maxwell suggested that a magnetic field changing over time causes a field to appear in space, regardless of the presence of a wire circuit in this space. The presence of a circuit only makes it possible to detect, by the appearance of an induction current in it, the existence of an electric field at the corresponding points in space.

So, according to Maxwell's idea, a magnetic field changing over time generates an electric field. This field is significantly different from the electrostatic field generated by stationary charges. The electrostatic field is potential, its intensity lines begin and end at the charges. The rotor of the vector at any point is zero:

(see formula (12.3)). According to (69.3), the curl of the vector is different from zero. Consequently, the field E, like the magnetic field, is a vortex. The field strength lines are closed.

Thus; the electric field can be either potential or vortex. In the general case, the electric field can be composed of the field created by charges and the field caused by the magnetic field changing over time. Adding together relations (69.4) and (69.3), we obtain the following equation for the rotor of the total field strength:

This equation is one of the main ones in Maxwell's electromagnetic theory.

The existence of a relationship between the electric and magnetic fields (expressed, in particular, by equation (69.5)) is the reason that separate consideration of the electric and magnetic fields has only a relative meaning.

Indeed, the electric field is created by a system of stationary charges. However, if the charges are stationary relative to some inertial frame of reference, then relative to other inertial frames these charges move and, therefore, generate not only an electric, but also a magnetic field. A stationary wire carrying a constant current creates a constant magnetic field at every point in space. However, relative to other inertial systems, this wire is in motion. Therefore, the magnetic field it creates at any point with given coordinates x, y, z will change and, therefore, generate a vortex electric field. Thus, a field that turns out to be “purely” electric or “purely” magnetic relative to some reference system, relative to other reference systems, will be a combination of electric and magnetic fields forming a single electromagnetic field.

If a closed conductor located in a magnetic field is stationary, then the occurrence of induced emf cannot be explained by the action of the Lorentz force, since it acts only on moving charges.

It is known that the movement of charges can also occur under the influence of an electric 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 an alternating magnetic field. This conclusion was first reached by J. Maxwell.

The electric field created by an alternating magnetic field is called induced electric field. It is created at any point in space where there is an alternating magnetic field, regardless of whether there is a conducting circuit there or not. The circuit only allows one to detect the emerging electric field. Thus, J. Maxwell generalized M. Faraday’s ideas about the phenomenon of electromagnetic induction, showing that it is in the occurrence of an induced electric field caused by a change in the magnetic field that the physical meaning of the phenomenon of electromagnetic induction lies.

The induced electric field differs from the known electrostatic and stationary electric fields.

1. It is caused not by some distribution of charges, but by an alternating magnetic field.

2. Unlike electrostatic and stationary electric field lines, which begin on positive charges and end on negative charges, induced field strength lines - closed lines. Therefore this field is vortex field.

Research has shown that the magnetic field induction lines and the vortex electric field intensity lines are located in mutually perpendicular planes. The vortex electric field is related to the alternating magnetic field inducing it by the rule left screw:

if the tip of the left screw moves progressively in the direction ΔΒ , then turning the screw head will indicate the direction of the induced electric field strength lines (Fig. 1).

3. Induced electric field not potential. The potential difference between any two points of a conductor through which an induced current passes is equal to 0. The work done by this field when moving a charge along a closed path is not zero. The induced emf is the work of the induced electric field to move a unit charge along the closed circuit under consideration, i.e. not the potential, but the induced emf is the energy characteristic of the induced field.

Literature

Aksenovich L. A. Physics in secondary school: Theory. Assignments. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P. 350-351.

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.

In contrast to 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 (vortex 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

1. Interaction forces between molecules and atoms in bodies

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Between molecules there are simultaneous forces of attraction and repulsion, called molecular forces. These are forces of electromagnetic nature. The forces acting between two molecules depend on the distance between them. If the distance between molecules is increased, then the forces of intermolecular attraction prevail. At short distances, repulsive forces predominate.

2. What does the rate of diffusion, evaporation, and Brownian motion depend on?

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The rate of diffusion depends on the type of substance, on temperature, and on the state of aggregation of the substance.

The speed of Brownian motion depends on temperature and mass of the Brownian particle.

The rate of evaporation depends on the type of substance, temperature, surface area, and the presence of air movement above the surface (wind)

3. Instruments for measuring temperature, pressure, humidity

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A thermometer is used to measure temperature.

A pressure gauge is used to measure pressure.

To measure humidity, a condensation hygrometer, a hair hygrometer, and a psychrometer are used.

4. Phase transitions (vaporization, melting, sublimation, condensation, crystallization)

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Melting is the process of transition of a substance from a solid to a liquid state.

Crystallization is the process of transition of a substance from a liquid to a solid state.

Sublimation is the process of transition of a substance from a solid to a gaseous state.

Vaporization is the process of transition of a substance from a liquid to a gaseous state.

Condensation is the process of transition of a substance from a gaseous state to a liquid state.

5. Saturated, unsaturated steam, dynamic equilibrium

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Saturated steam is steam that is in dynamic equilibrium with its liquid.

Unsaturated vapor is vapor that has not reached dynamic equilibrium with its liquid.

Dynamic equilibrium is a state between a liquid and its vapor in which the number of molecules leaving the liquid is equal to the number of molecules returning to it.

6. Gas pressure formulas, Clayperon equation, Mendeleev-Cliperon equation, relationship between kinetic energy and temperature

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Gas pressure formula - combined gas law - p = nkT

Clayperon equation

Mendeleev-Clayperon equation

Relationship between kinetic energy and temperature E = (3/2)kT

7. Converting temperature from Celsius to Kelvin, from Kelvin to Celsius

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Relationship between absolute temperature and scale temperature Celsius expressed by the formula T = 273.16 +t, where t is the temperature in degrees Celsius.

An approximate formula is often used:

1) to convert from temperature in Celsius to temperature in Kelvin T = 273 + t

2) to convert from temperature in Kelvin to temperature in Celsius t = T – 273

8. Kelvin scale, Celsius scale

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0 0 on the Celsius scale is the melting temperature of ice.

100 0 on the Kelvin scale is the boiling point of water.

0 0 on the Kelvini scale is absolute zero - the temperature at which the translational motion of molecules should stop.

Celsius scale Kelvin scale

9. Relationship between temperature and gas pressure, between temperature and kinetic energy of gas molecules

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The relationship between temperature and gas pressure p=nkT. There is a directly proportional relationship between p and T(no matter how many times the temperature increases, the gas pressure increases by the same amount).

The relationship between temperature and kinetic energy of gas molecules E = (3/2)kT. There is a directly proportional relationship between p and E(no matter how many times the temperature increases, the kinetic energy of gas molecules increases by the same amount)

10. Basic provisions of the ICT and their experimental justification

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MCT is based on three important principles, confirmed experimentally and theoretically.

1. All bodies consist of tiny particles - atoms, molecules, which include even smaller elementary particles (electrons, protons, neutrons). The structure of any substance is discrete (discontinuous).
2. Atoms and molecules of matter are always in continuous chaotic motion.
3. Between particles of any substance there are forces of interaction - attraction and repulsion. The nature of these forces is electromagnetic.

These provisions are confirmed experimentally.

11. Mass and size of molecules

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Moleculeis the smallest stable particle of a given substance that has its basic chemical properties.

A molecule consists of even smaller particles - atoms, which in turn consist of electrons and nuclei.

Atomis the smallest particle of a given chemical element.

The molecular sizes are very small.

The order of magnitude of the diameter of a molecule is 1·10 -8 cm = 1*10-10 m

Order of magnitude of the volume of a molecule 1·10 -20 m3

Order of magnitude of molecular mass 1·10 - 23 g = 1·10 -26 kg

12. Properties of solids, liquids, gases

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Solids retain volume and retain shape.

Liquids retain volume but do not retain shape.

Gases do not retain volume or shape.

13. Phase transitions occur with the absorption or release of heat.

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Melting occurs with the absorption of heat

Crystallization occurs with the release of heat.

Vaporization occurs with the absorption of heat.

Condensation occurs with the release of heat.

Sublimation occurs with heat absorption

14. Humidity and dew point

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Absolute humidity– a value showing how much water vapor is present in 1 m³ of air.

Relative air humidity –this is a value that shows how far the steam is from saturation. This is the partial pressure ratiop of water vapor contained in the air at a given temperature, to saturated steam pressure p 0 at the same temperature, expressed as a percentage:

If the air does not contain water vapor, then its absolute and relative humidity are 0.

If moist air is cooled, the steam in it can be brought to saturation, and then it will condense.

Dew point –This is the temperature at which water vapor contained in the air becomes saturated.

15. Melting and boiling graph