What are the types of magnetic fields? Permanent magnets. Magnetic field of permanent magnets

If you insert a hardened steel rod into a current coil, then, unlike an iron rod, it does not demagnetize after switches off the current, and retains magnetization for a long time.

Bodies that retain magnetization for a long time are called permanent magnets or simply magnets.

The French scientist Ampere explained the magnetization of iron and steel by electric currents that circulate inside each molecule of these substances. At the time of Ampere, nothing was known about the structure of the atom, so the nature of molecular currents remained unknown. Now we know that in every atom there are negatively charged electron particles, which, when moving, create magnetic fields, they cause the magnetization of iron and. become.

Magnets can have a wide variety of shapes. Figure 290 shows an arc and strip magnets.

Those places of the magnet where the strongest are found magnetic actions are called magnet poles(Fig. 291). Every magnet, like the magnetic needle we know, necessarily has two poles; northern (N) and southern (S).

By holding a magnet close to objects made from various materials, you can find that very few of them are attracted by the magnet. Fine attracted by magnet cast iron, steel, iron and some alloys that are much weaker - nickel and cobalt.

Natural magnets are found in nature (Fig. 292) - iron ore (the so-called magnetic iron ore). Rich deposits We have magnetic iron ore in the Urals, in Ukraine, in the Karelian Autonomous Soviet Socialist Republic, Kursk region and in many other places.

Iron, steel, nickel, cobalt and some other alloys acquire magnetic properties in the presence of magnetic iron ore. Magnetic iron ore allowed people to become familiar with the magnetic properties of bodies for the first time.

If a magnetic needle is brought closer to another similar needle, they will turn and set opposite poles against each other (Fig. 293). The arrow interacts with any magnet in the same way. By bringing a magnet close to the poles of a magnetic needle, you will notice that the north pole of the needle is repelled by the north pole of the magnet and attracted to the south pole. The south pole of the arrow is repelled by the south pole of the magnet and attracted by the north pole.

Based on the experiments described, it is possible draw the following conclusion; different names Magnetic poles attract, like poles repel.

The interaction of magnets is explained by the fact that there is a magnetic field around every magnet. The magnetic field of one magnet acts on another magnet, and, conversely, the magnetic field of the second magnet acts on the first magnet.

Using iron filings you can get an idea of ​​the magnetic field of permanent magnets. Figure 294 gives an idea of ​​the magnetic field of a bar magnet. Both the magnetic lines of the magnetic field of the current and the magnetic lines of the magnetic field of the magnet are closed lines. Outside the magnet, magnetic lines leave the north pole of the magnet and enter the south pole, closing inside the magnet.

Figure 295a shows magnetic magnetic field lines of two magnets, facing each other with like poles, and in Figure 295, b - two magnets facing each other with opposite poles. Figure 296 shows the magnetic field lines of an arc-shaped magnet.

All these pictures are easy to obtain through experience.

Questions. 1. What is the difference in magnetizing a piece of iron and a piece of steel using current? 2, What bodies are called permanent magnets? 3. How did Ampere explain the magnetization of iron? 4. How can we now explain Ampere’s molecular currents? 5. What are the magnetic poles of a magnet called? 6. Which substances do you know that are attracted by a magnet? 7. How do the poles of magnets interact with each other? 8. How can you use a magnetic needle to determine the poles of a magnetized steel rod? 9. How can you get an idea of ​​the magnetic field of a magnet? 10. What are the magnetic field lines of a magnet?

Earth's magnetic field

A magnetic field is a force field that acts on moving electric charges and on bodies that have a magnetic moment, regardless of their state of motion.

The sources of the macroscopic magnetic field are magnetized bodies, current-carrying conductors, and moving electrically charged bodies. The nature of these sources is the same: the magnetic field arises as a result of the movement of charged microparticles (electrons, protons, ions), as well as due to the presence of the microparticles’ own (spin) magnetic moment.

An alternating magnetic field also occurs when the electric field changes over time. In turn, when the magnetic field changes over time, an electric field appears. A complete description of the electric and magnetic fields in their relationship is given by Maxwell's equations. To characterize the magnetic field, the concept of field lines (magnetic induction lines) is often introduced.

Various types of magnetometers are used to measure the characteristics of the magnetic field and the magnetic properties of substances. The unit of magnetic field induction in the CGS system of units is Gauss (G), in the International System of Units (SI) - Tesla (T), 1 T = 104 G. The intensity is measured, respectively, in oersteds (Oe) and amperes per meter (A/m, 1 A/m = 0.01256 Oe; magnetic field energy - in Erg/cm2 or J/m2, 1 J/m2 = 10 erg/cm2.

Compass reacts
to the Earth's magnetic field

Magnetic fields in nature are extremely diverse both in their scale and in the effects they cause. The Earth's magnetic field, which forms the Earth's magnetosphere, extends to a distance of 70-80 thousand km in the direction of the Sun and many millions of km in the opposite direction. At the Earth's surface, the magnetic field is on average 50 μT, at the boundary of the magnetosphere ~ 10 -3 G. The geomagnetic field shields the Earth's surface and biosphere from the flow of charged particles of the solar wind and partially cosmic rays. Magnetobiology studies the influence of the geomagnetic field itself on the life activity of organisms. In near-Earth space, the magnetic field forms a magnetic trap for charged particles of high energy - the Earth's radiation belt. The particles contained in the radiation belt pose a significant danger when flying into space. The origin of the Earth's magnetic field is associated with convective movements of conductive liquid matter in the earth's core.

Direct measurements using spacecraft have shown that the cosmic bodies closest to the Earth - the Moon, the planets Venus and Mars - do not have their own magnetic field similar to the Earth's. Of the other planets in the Solar System, only Jupiter and, apparently, Saturn have their own magnetic fields sufficient to create planetary magnetic traps. Magnetic fields up to 10 G and a number of characteristic phenomena (magnetic storms, synchrotron radio emission, and others) have been discovered on Jupiter, indicating a significant role of the magnetic field in planetary processes.

© Photo: http://www.tesis.lebedev.ru
Sun Photography
in a narrow spectrum

The interplanetary magnetic field is mainly the field of the solar wind (the continuously expanding plasma of the solar corona). Near the Earth's orbit, the interplanetary field is ~ 10 -4 -10 -5 Gs. The regularity of the interplanetary magnetic field can be disrupted due to the development of various types of plasma instability, the passage of shock waves and the propagation of streams of fast particles generated by solar flares.

In all processes on the Sun - flares, the appearance of spots and prominences, the birth of solar cosmic rays, the magnetic field plays a vital role. Measurements based on the Zeeman effect have shown that the magnetic field of sunspots reaches several thousand Gauss, the prominences are held by fields of ~ 10-100 Gauss (with an average value of the total magnetic field of the Sun ~ 1 Gauss).

Magnetic storms

Magnetic storms are strong disturbances in the Earth’s magnetic field, sharply disrupting the smooth daily cycle of the elements of the earth’s magnetism. Magnetic storms last from several hours to several days and are observed simultaneously throughout the entire Earth.

As a rule, magnetic storms consist of preliminary, initial and main phases, as well as a recovery phase. In the preliminary phase, minor changes in the geomagnetic field are observed (mainly at high latitudes), as well as the excitation of characteristic short-period field oscillations. The initial phase is characterized by a sudden change in individual field components throughout the Earth, and the main phase is characterized by large field fluctuations and a strong decrease in the horizontal component. During the recovery phase of the magnetic storm, the field returns to its normal value.

Influence of solar wind
to the Earth's magnetosphere

Magnetic storms are caused by streams of solar plasma from active regions of the Sun superimposed on the calm solar wind. Therefore, magnetic storms are more often observed near the maxima of the 11-year cycle of solar activity. Reaching the Earth, solar plasma streams increase the compression of the magnetosphere, causing the initial phase of a magnetic storm, and partially penetrate into the Earth's magnetosphere. The entry of high-energy particles into the upper atmosphere of the Earth and their impact on the magnetosphere leads to the generation and intensification of electric currents in it, reaching their greatest intensity in the polar regions of the ionosphere, which is associated with the presence of a high-latitude zone of magnetic activity. Changes in magnetospheric-ionospheric current systems manifest themselves on the Earth's surface in the form of irregular magnetic disturbances.

In the phenomena of the microworld, the role of the magnetic field is as significant as on a cosmic scale. This is explained by the existence of a magnetic moment in all particles - structural elements of matter (electrons, protons, neutrons), as well as the effect of a magnetic field on moving electric charges.

Application of magnetic fields in science and technology. Magnetic fields are usually divided into weak (up to 500 Gs), medium (500 Gs - 40 kGs), strong (40 kGs - 1 MGs) and ultra-strong (over 1 MGs). Almost all electrical engineering, radio engineering and electronics are based on the use of weak and medium magnetic fields. Weak and medium magnetic fields are obtained using permanent magnets, electromagnets, uncooled solenoids, and superconducting magnets.

Magnetic field sources

All sources of magnetic fields can be divided into artificial and natural. The main natural sources of the magnetic field are the planet Earth's own magnetic field and the solar wind. Artificial sources include all the electromagnetic fields that are so abundant in our modern world, and our homes in particular. Read more about and read on ours.

Electrically driven vehicles are a powerful source of magnetic field in the range from 0 to 1000 Hz. Rail transport uses alternating current. City transport is constant. The maximum values ​​of magnetic field induction in suburban electric transport reach 75 μT, the average values ​​are about 20 μT. Average values ​​for DC-driven vehicles are recorded at 29 µT. In trams, where the return wire is the rails, the magnetic fields cancel each other over a much greater distance than in the trolleybus wires, and inside the trolleybus the magnetic field fluctuations are small even during acceleration. But the largest fluctuations in the magnetic field are in the subway. When the train departs, the magnetic field on the platform is 50-100 µT or more, exceeding the geomagnetic field. Even when the train has long disappeared into the tunnel, the magnetic field does not return to its previous value. Only after the train has passed the next connection point to the contact rail will the magnetic field return to its old value. True, sometimes it doesn’t have time: the next train is already approaching the platform and when it slows down, the magnetic field changes again. In the carriage itself, the magnetic field is even stronger - 150-200 µT, that is, ten times more than in a regular train.

The induction values ​​of magnetic fields that we most often encounter in everyday life are shown in the diagram below. Looking at this diagram, it is clear that we are exposed to magnetic fields all the time and everywhere. According to some scientists, magnetic fields with induction above 0.2 µT are considered harmful. It is natural that certain precautions should be taken to protect ourselves from the harmful effects of the fields around us. Simply by following a few simple rules, you can significantly reduce the impact of magnetic fields on your body.

The current SanPiN 2.1.2.2801-10 “Changes and additions No. 1 to SanPiN 2.1.2.2645-10 “Sanitary and epidemiological requirements for living conditions in residential buildings and premises” says the following: “The maximum permissible level of attenuation of the geomagnetic field in the premises of residential buildings is established equal to 1.5". The maximum permissible values ​​of the intensity and strength of a magnetic field with a frequency of 50 Hz have also been established:

• in residential premises - 5 µT or 4 A/m;
• in non-residential premises of residential buildings, in residential areas, including on the territory of garden plots - 10 µT or 8 A/m.

Based on these standards, everyone can calculate how many electrical appliances can be turned on and in a standby state in each specific room, or on the basis of which recommendations will be issued for normalizing the living space.

Related videos

References

1. Great Soviet Encyclopedia.

This article presents the results of studies of vector and scalar magnetic fields of permanent magnets and the determination of their distribution.

permanent magnet

electromagnet

vector magnetic field

scalar magnetic field.

2. Borisenko A.I., Tarapov I.E. Vector analysis and the beginnings of tensor calculus. – M.: Higher School, 1966.

3. Kumpyak D.E. Vector and tensor analysis: tutorial. – Tver: Tver State University, 2007. – 158 p.

4. McConnell A.J. Introduction to tensor analysis with applications to geometry, mechanics and physics. – M.: Fizmatlit, 1963. – 411 p.

5. Borisenko A.I., Tarapov I.E. Vector analysis and the beginnings of tensor calculus. – 3rd ed. – M.: Higher School, 1966.

Permanent magnets. Constant magnetic field.

Magnet- these are bodies that have the ability to attract iron and steel objects and repel some others due to the action of their magnetic field. The magnetic field lines pass from the south pole of the magnet and exit from the north pole (Fig. 1).

Rice. 1. Magnet and magnetic field lines

A permanent magnet is a product made of a hard magnetic material with a high residual magnetic induction that maintains its magnetization state for a long time. Permanent magnets are manufactured in various shapes and are used as autonomous (non-energy consuming) sources of magnetic field (Fig. 2).

An electromagnet is a device that creates a magnetic field when an electric current passes. Typically, an electromagnet consists of a winding of an ferromagnetic core, which acquires the properties of a magnet when an electric current passes through the winding.

Rice. 2. Permanent magnet

Electromagnets, designed primarily to create mechanical force, also contain an armature (a moving part of the magnetic circuit) that transmits force.

Permanent magnets made from magnetite have been used in medicine since ancient times. Queen Cleopatra of Egypt wore a magnetic amulet.

In ancient China, the “Imperial Book on Internal Medicine” addressed the issue of using magnetic stones to correct Qi energy in the body - “living force”.

The theory of magnetism was first developed by the French physicist Andre Marie Ampere. According to his theory, the magnetization of iron is explained by the existence of electric currents that circulate within the substance. Ampere made his first reports on the results of his experiments at a meeting of the Paris Academy of Sciences in the fall of 1820. The concept of “magnetic field” was introduced into physics by the English physicist Michael Faraday. Magnets interact through a magnetic field, and he also introduced the concept of magnetic lines of force.

Vector magnetic field

A vector field is a mapping that associates each point in the space under consideration with a vector with a beginning at that point. For example, the wind speed vector at a given time varies from point to point and can be described by a vector field (Fig. 3).

Scalar magnetic field

If each point M of a given region of space (most often of dimension 2 or 3) is associated with a certain (usually real) number u, then they say that a scalar field is specified in this region. In other words, a scalar field is a function that maps Rn to R (scalar function of a point in space).

Gennady Vasilyevich Nikolaev tells in a simple way, shows and uses simple experiments to prove the existence of a second type of magnetic field, which science, for some strange reason, has not found. Since the time of Ampere there has still been an assumption that it exists. He called the field discovered by Nikolaev scalar, but it is still often called by his name. Nikolaev brought electromagnetic waves to a complete analogy with ordinary mechanical waves. Now physics considers electromagnetic waves as exclusively transverse, but Nikolaev is confident and proves that they are also longitudinal or scalar and this is logical, how a wave can propagate forward without direct pressure is simply absurd. According to the scientist, the longitudinal field was hidden by science on purpose, possibly in the process of editing theories and textbooks. This was done with simple intent and was consistent with other cuts.

Rice. 3. Vector magnetic field

The first cut that was made was the lack of airtime. Why?! Because ether is energy, or a medium that is under pressure. And this pressure, if the process is organized correctly, can be used as a free source of energy!!! The second cut is the removal of the longitudinal wave, this is a consequence that if the ether is a source of pressure, that is, energy, then if only transverse waves are added to it, then no free or free energy can be obtained, a longitudinal wave is required.

Then the counter superposition of waves makes it possible to pump out the ether pressure. This technology is often called zero point, which is generally correct. It is at the border of the connection of plus and minus (high and low pressure), with counter-movement of waves, that you can get the so-called Bloch zone or simply a dip in the medium (ether), where additional energy of the medium will be attracted.

The work is an attempt to practically repeat some of the experiments described in the book by G.V. Nikolaev “Modern electrodynamics and the reasons for its paradoxical nature” and to reproduce the generator and motor of Stefan Marinov, as far as possible at home.

Experience G.V. Nikolaev with magnets: Two round magnets from speakers were used

Two flat magnets with opposite poles located on a plane. They attract each other (Fig. 4), whereas when they are perpendicular (regardless of the orientation of the poles), there is no force of attraction (only torque is present) (Fig. 5).

Now let’s cut the magnets in the middle and connect them in pairs with different poles, forming magnets of the original size (Fig. 6).

When these magnets are located in the same plane (Fig. 7), they will again, for example, be attracted to each other, while when positioned perpendicularly they will already repel (Fig. 8). In the latter case, the longitudinal forces acting along the cut line of one magnet are a reaction to the transverse forces acting on the side surfaces of the other magnet, and vice versa. The existence of longitudinal force contradicts the laws of electrodynamics. This force is the result of the scalar magnetic field present at the cut site of the magnets. Such a composite magnet is called siberian colia.

A magnetic well is a phenomenon when a vector magnetic field repels, and a scalar magnetic field attracts, and a distance is created between them.

Bibliographic link

A magnetic field- this is the material medium through which interaction occurs between conductors with current or moving charges.

Properties of magnetic field:

Characteristics of the magnetic field:

To study the magnetic field, a test circuit with current is used. It is small in size, and the current in it is much less than the current in the conductor creating the magnetic field. On opposite sides of the current-carrying circuit, forces from the magnetic field act that are equal in magnitude, but directed in opposite directions, since the direction of the force depends on the direction of the current. The points of application of these forces do not lie on the same straight line. Such forces are called a couple of forces. As a result of the action of a pair of forces, the circuit cannot move translationally; it rotates around its axis. The rotating action is characterized torque.

, Where l–leverage couple of forces(distance between points of application of forces).

As the current in the test circuit or the area of ​​the circuit increases, the torque of the pair of forces will increase proportionally. The ratio of the maximum moment of force acting on the circuit with current to the magnitude of the current in the circuit and the area of ​​the circuit is a constant value for a given point in the field. It's called magnetic induction.

, Where
-magnetic moment circuit with current.

Unit magnetic induction – Tesla [T].

Magnetic moment of the circuit– vector quantity, the direction of which depends on the direction of the current in the circuit and is determined by right screw rule: clench your right hand into a fist, point four fingers in the direction of the current in the circuit, then the thumb will indicate the direction of the magnetic moment vector. The magnetic moment vector is always perpendicular to the contour plane.

Behind direction of the magnetic induction vector take the direction of the vector of the magnetic moment of the circuit, oriented in the magnetic field.

Magnetic induction line– a line whose tangent at each point coincides with the direction of the magnetic induction vector. Magnetic induction lines are always closed and never intersect. Magnetic induction lines of a straight conductor with current have the form of circles located in a plane perpendicular to the conductor. The direction of the magnetic induction lines is determined by the right-hand screw rule. Magnetic induction lines of circular current(turns with current) also have the form of circles. Each coil element is length
can be imagined as a straight conductor that creates its own magnetic field. For magnetic fields, the principle of superposition (independent addition) applies. The total vector of magnetic induction of the circular current is determined as the result of the addition of these fields in the center of the turn according to the right-hand screw rule.

If the magnitude and direction of the magnetic induction vector are the same at every point in space, then the magnetic field is called homogeneous. If the magnitude and direction of the magnetic induction vector at each point do not change over time, then such a field is called permanent.

Magnitude magnetic induction at any point in the field is directly proportional to the current strength in the conductor creating the field, inversely proportional to the distance from the conductor to a given point in the field, depends on the properties of the medium and the shape of the conductor creating the field.

, Where
ON 2 ; Gn/m – magnetic constant of vacuum,

-relative magnetic permeability of the medium,

-absolute magnetic permeability of the medium.

Depending on the value of magnetic permeability, all substances are divided into three classes:

As the absolute permeability of the medium increases, the magnetic induction at a given point in the field also increases. The ratio of magnetic induction to the absolute magnetic permeability of the medium is a constant value for a given poly point, e is called tension.

.

The vectors of tension and magnetic induction coincide in direction. The magnetic field strength does not depend on the properties of the medium.

Ampere power– the force with which the magnetic field acts on a current-carrying conductor.

Where l– length of the conductor, - the angle between the magnetic induction vector and the direction of the current.

The direction of the Ampere force is determined by left hand rule: the left hand is positioned so that the component of the magnetic induction vector, perpendicular to the conductor, enters the palm, four extended fingers are directed along the current, then the thumb bent by 90 0 will indicate the direction of the Ampere force.

The result of the Ampere force is the movement of the conductor in a given direction.

E if = 90 0 , then F=max, if = 0 0 , then F = 0.

Lorentz force– the force of the magnetic field on a moving charge.

, where q is the charge, v is the speed of its movement, - the angle between the vectors of tension and speed.

The Lorentz force is always perpendicular to the magnetic induction and velocity vectors. The direction is determined by left hand rule(fingers follow the movement of the positive charge). If the direction of the particle's velocity is perpendicular to the magnetic induction lines of a uniform magnetic field, then the particle moves in a circle without changing its kinetic energy.

Since the direction of the Lorentz force depends on the sign of the charge, it is used to separate charges.

Magnetic flux– a value equal to the number of magnetic induction lines that pass through any area located perpendicular to the magnetic induction lines.

, Where - the angle between the magnetic induction and the normal (perpendicular) to the area S.

Unit– Weber [Wb].

Magnetic flux measurement methods:

Changing the orientation of the site in a magnetic field (changing the angle)

Changing the area of ​​a circuit placed in a magnetic field

Changing the strength of the current creating a magnetic field

Changing the distance of the circuit from the magnetic field source

Changes in the magnetic properties of the medium.

F Araday recorded an electric current in a circuit that did not contain a source, but was located next to another circuit containing a source. Moreover, the current in the first circuit arose in the following cases: with any change in the current in circuit A, with relative movement of the circuits, with the introduction of an iron rod into circuit A, with the movement of a permanent magnet relative to circuit B. Directed movement of free charges (current) occurs only in an electric field. This means that a changing magnetic field generates an electric field, which sets in motion the free charges of the conductor. This electric field is called induced or vortex.

Differences between a vortex electric field and an electrostatic one:

The source of the vortex field is a changing magnetic field.

The vortex field intensity lines are closed.

The work done by this field to move a charge along a closed circuit is not zero.

The energy characteristic of a vortex field is not the potential, but induced emf– a value equal to the work of external forces (forces of non-electrostatic origin) to move a unit of charge along a closed circuit.

.Measured in Volts[IN].

A vortex electric field occurs with any change in the magnetic field, regardless of whether there is a conducting closed circuit or not. The circuit only allows one to detect the vortex electric field.

Electromagnetic induction- this is the occurrence of induced emf in a closed circuit with any change in the magnetic flux through its surface.

The induced emf in a closed circuit generates an induced current.

.

Direction of induction current determined by Lenz's rule: the induced current is in such a direction that the magnetic field created by it counteracts any change in the magnetic flux that generated this current.

Faraday's law for electromagnetic induction: The induced emf in a closed loop is directly proportional to the rate of change of magnetic flux through the surface bounded by the loop.

T oki fuko– eddy induction currents that arise in large conductors placed in a changing magnetic field. The resistance of such a conductor is low, since it has a large cross-section S, so the Foucault currents can be large in value, as a result of which the conductor heats up.

Self-induction- this is the occurrence of induced emf in a conductor when the current strength in it changes.

A conductor carrying current creates a magnetic field. Magnetic induction depends on the current strength, therefore the intrinsic magnetic flux also depends on the current strength.

, where L is the proportionality coefficient, inductance.

Unit inductance – Henry [H].

Inductance conductor depends on its size, shape and magnetic permeability of the medium.

Inductance increases with increasing length of the conductor, the inductance of a turn is greater than the inductance of a straight conductor of the same length, the inductance of a coil (a conductor with a large number of turns) is greater than the inductance of one turn, the inductance of a coil increases if an iron rod is inserted into it.

Faraday's law for self-induction:
.

Self-induced emf is directly proportional to the rate of change of current.

Self-induced emf generates a self-induction current, which always prevents any change in the current in the circuit, that is, if the current increases, the self-induction current is directed in the opposite direction; when the current in the circuit decreases, the self-induction current is directed in the same direction. The greater the inductance of the coil, the greater the self-inductive emf that occurs in it.

Magnetic field energy is equal to the work that the current does to overcome the self-induced emf during the time while the current increases from zero to the maximum value.

.

Electromagnetic vibrations– these are periodic changes in charge, current strength and all characteristics of electric and magnetic fields.

Electrical oscillatory system(oscillating circuit) consists of a capacitor and an inductor.

Conditions for the occurrence of oscillations:

The system must be brought out of equilibrium; to do this, charge the capacitor. Electric field energy of a charged capacitor:

.

The system must return to a state of equilibrium. Under the influence of an electric field, charge transfers from one plate of the capacitor to another, that is, an electric current appears in the circuit, which flows through the coil. As the current increases in the inductor, a self-induction emf arises; the self-induction current is directed in the opposite direction. When the current in the coil decreases, the self-induction current is directed in the same direction. Thus, the self-induction current tends to return the system to a state of equilibrium.

The electrical resistance of the circuit should be low.

Ideal oscillatory circuit has no resistance. The vibrations in it are called free.

For any electrical circuit, Ohm's law is satisfied, according to which the emf acting in the circuit is equal to the sum of the voltages in all sections of the circuit. There is no current source in the oscillatory circuit, but a self-inductive emf appears in the inductor, which is equal to the voltage across the capacitor.

Conclusion: the charge of the capacitor changes according to a harmonic law.

Capacitor voltage:
.

Current strength in the circuit:
.

Magnitude
- current amplitude.

The difference from the charge on
.

Period of free oscillations in the circuit:

Electric field energy of a capacitor:

Coil magnetic field energy:

The energies of the electric and magnetic fields vary according to a harmonic law, but the phases of their oscillations are different: when the energy of the electric field is maximum, the energy of the magnetic field is zero.

Total energy of the oscillatory system:
.

IN ideal contour the total energy does not change.

During the oscillation process, the energy of the electric field is completely converted into the energy of the magnetic field and vice versa. This means that the energy at any moment in time is equal to either the maximum energy of the electric field or the maximum energy of the magnetic field.

Real oscillatory circuit contains resistance. The vibrations in it are called fading.

Ohm's law will take the form:

Provided that the damping is small (the square of the natural frequency of oscillations is much greater than the square of the damping coefficient), the logarithmic damping decrement is:

With strong damping (the square of the natural frequency of oscillation is less than the square of the oscillation coefficient):

This equation describes the process of discharging a capacitor into a resistor. In the absence of inductance, oscillations will not occur. According to this law, the voltage on the capacitor plates also changes.

Total Energy in a real circuit it decreases, since heat is released into the resistance R during the passage of current.

Transition process– a process that occurs in electrical circuits during the transition from one operating mode to another. Estimated by time ( ), during which the parameter characterizing the transition process will change by e times.

For circuit with capacitor and resistor:
.

Maxwell's theory of the electromagnetic field:

1 position:

Any alternating electric field generates a vortex magnetic field. An alternating electric field was called a displacement current by Maxwell, since it, like an ordinary current, causes a magnetic field.

To detect the displacement current, consider the passage of current through a system in which a capacitor with a dielectric is connected.

Bias current density:
. The current density is directed in the direction of the voltage change.

Maxwell's first equation:
- the vortex magnetic field is generated by both conduction currents (moving electric charges) and displacement currents (alternating electric field E).

2 position:

Any alternating magnetic field generates a vortex electric field - the basic law of electromagnetic induction.

Maxwell's second equation:
- connects the rate of change of magnetic flux through any surface and the circulation of the electric field strength vector that arises at the same time.

Any conductor carrying current creates a magnetic field in space. If the current is constant (does not change over time), then the magnetic field associated with it is also constant. A changing current creates a changing magnetic field. There is an electric field inside a conductor carrying current. Therefore, a changing electric field creates a changing magnetic field.

The magnetic field is vortex, since the lines of magnetic induction are always closed. The magnitude of the magnetic field strength H is proportional to the rate of change of the electric field strength . Direction of the magnetic field strength vector associated with changes in electric field strength right screw rule: clench your right hand into a fist, point your thumb in the direction of the change in electric field strength, then the bent 4 fingers will indicate the direction of the magnetic field strength lines.

Any changing magnetic field creates a vortex electric field, whose tension lines are closed and located in a plane perpendicular to the magnetic field strength.

The magnitude of the intensity E of the vortex electric field depends on the rate of change of the magnetic field . The direction of vector E is related to the direction of change in the magnetic field H by the left screw rule: clench your left hand into a fist, point your thumb in the direction of the change in the magnetic field, bent four fingers will indicate the direction of the lines of intensity of the vortex electric field.

The set of interconnected vortex electric and magnetic fields represents electromagnetic field. The electromagnetic field does not remain at the place of origin, but propagates in space in the form of a transverse electromagnetic wave.

Electromagnetic wave– this is the propagation in space of vortex electric and magnetic fields associated with each other.

Condition for the occurrence of an electromagnetic wave– movement of the charge with acceleration.

Electromagnetic Wave Equation:

- cyclic frequency of electromagnetic oscillations

t – time from the beginning of oscillations

l – distance from the wave source to a given point in space

- wave propagation speed

The time it takes a wave to travel from its source to a given point.

Vectors E and H in an electromagnetic wave are perpendicular to each other and to the speed of propagation of the wave.

Source of electromagnetic waves– conductors through which rapidly alternating currents flow (macro-emitters), as well as excited atoms and molecules (micro-emitters). The higher the oscillation frequency, the better electromagnetic waves are emitted in space.

Properties of electromagnetic waves:

All electromagnetic waves are transverse

In a homogeneous medium, electromagnetic waves propagate at a constant speed, which depends on the properties of the environment:

- relative dielectric constant of the medium

- dielectric constant of vacuum,
F/m, Cl 2 /nm 2

- relative magnetic permeability of the medium

- magnetic constant of vacuum,
ON 2 ; Gn/m

Electromagnetic waves reflected from obstacles, absorbed, scattered, refracted, polarized, diffracted, interfered.

Volumetric energy density electromagnetic field consists of volumetric energy densities of electric and magnetic fields:

Wave energy flux density - wave intensity:

-Umov-Poynting vector.

All electromagnetic waves are arranged in a series of frequencies or wavelengths (
). This row is electromagnetic wave scale.

Low frequency vibrations. 0 – 10 4 Hz. Obtained from generators. They radiate poorly

Radio waves. 10 4 – 10 13 Hz.

They are emitted by solid conductors through which rapidly alternating currents pass. Infrared radiation

– waves emitted by all bodies at temperatures above 0 K, due to intra-atomic and intra-molecular processes. Visible light

– waves that act on the eye, causing visual sensation. 380-760 nm Ultraviolet radiation

. 10 – 380 nm. Visible light and UV arise when the movement of electrons in the outer shells of an atom changes. X-ray radiation

. 80 – 10 -5 nm. Occurs when the movement of electrons in the inner shells of an atom changes. Gamma radiation

. Occurs during the decay of atomic nuclei.

Let's understand together what a magnetic field is. After all, many people live in this field all their lives and don’t even think about it. It's time to fix it!

A magnetic field A magnetic field

- a special type of matter. It manifests itself in the action on moving electric charges and bodies that have their own magnetic moment (permanent magnets). Important: the magnetic field does not affect stationary charges!

A magnetic field is also created by moving electric charges, or by a time-varying electric field, or by the magnetic moments of electrons in atoms. That is, any wire through which current flows also becomes a magnet!

A body that has its own magnetic field.

A magnet has poles called north and south. The designations "north" and "south" are given for convenience only (like "plus" and "minus" in electricity). The magnetic field is represented by magnetic power lines

. The lines of force are continuous and closed, and their direction always coincides with the direction of action of the field forces. If metal shavings are scattered around a permanent magnet, the metal particles will show a clear picture of the magnetic field lines coming out of the north pole and entering the south pole. Graphic characteristic of a magnetic field - lines of force.

The main characteristics of the magnetic field are magnetic induction, magnetic flux And magnetic permeability. But let's talk about everything in order.

Let us immediately note that all units of measurement are given in the system SI.

Magnetic induction B – vector physical quantity, which is the main force characteristic of the magnetic field. Denoted by the letter B . Unit of measurement of magnetic induction – Tesla (T).

Magnetic induction shows how strong the field is by determining the force it exerts on a charge. This force is called Lorentz force.

Here q - charge, v - its speed in a magnetic field, B - induction, F - Lorentz force with which the field acts on the charge.

F– a physical quantity equal to the product of magnetic induction by the area of ​​the circuit and the cosine between the induction vector and the normal to the plane of the circuit through which the flux passes. Magnetic flux is a scalar characteristic of a magnetic field.

We can say that magnetic flux characterizes the number of magnetic induction lines penetrating a unit area. Magnetic flux is measured in Weberach (Wb).

Magnetic permeability– coefficient that determines the magnetic properties of the medium. One of the parameters on which the magnetic induction of a field depends is magnetic permeability.

Our planet has been a huge magnet for several billion years. The induction of the Earth's magnetic field varies depending on the coordinates. At the equator it is approximately 3.1 times 10 to the minus fifth power of Tesla. In addition, there are magnetic anomalies where the value and direction of the field differ significantly from neighboring areas. Some of the largest magnetic anomalies on the planet - Kursk And Brazilian magnetic anomalies.

The origin of the Earth's magnetic field still remains a mystery to scientists. It is assumed that the source of the field is the liquid metal core of the Earth. The core is moving, which means the molten iron-nickel alloy is moving, and the movement of charged particles is the electric current that generates the magnetic field. The problem is that this theory ( geodynamo) does not explain how the field is kept stable.

The Earth is a huge magnetic dipole. The magnetic poles do not coincide with the geographic ones, although they are in close proximity. Moreover, the Earth's magnetic poles move. Their displacement has been recorded since 1885. For example, over the past hundred years, the magnetic pole in the Southern Hemisphere has shifted almost 900 kilometers and is now located in the Southern Ocean. The pole of the Arctic hemisphere is moving through the Arctic Ocean to the East Siberian magnetic anomaly; its movement speed (according to 2004 data) was about 60 kilometers per year. Now there is an acceleration of the movement of the poles - on average, the speed is growing by 3 kilometers per year.

What is the significance of the Earth's magnetic field for us? First of all, the Earth's magnetic field protects the planet from cosmic rays and solar wind. Charged particles from deep space do not fall directly to the ground, but are deflected by a giant magnet and move along its lines of force. Thus, all living things are protected from harmful radiation.

Several events have occurred over the course of Earth's history. inversions(changes) of magnetic poles. Pole inversion- this is when they change places. The last time this phenomenon occurred was about 800 thousand years ago, and in total there were more than 400 geomagnetic inversions in the history of the Earth. Some scientists believe that, given the observed acceleration of the movement of the magnetic poles, the next pole inversion should be expected in the next couple of thousand years.

Fortunately, a pole change is not yet expected in our century. This means that you can think about pleasant things and enjoy life in the good old constant field of the Earth, having considered the basic properties and characteristics of the magnetic field. And so that you can do this, there are our authors, to whom you can confidently entrust some of the educational troubles with confidence! and other types of work you can order using the link.