What is a magnetic field? Magnetic field and its characteristics - lecture.

Magnetic fields occur naturally and can be created artificially. The man noticed them useful features which have learned to apply in Everyday life. What is the source of the magnetic field?

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Earth's magnetic field

How the doctrine of the magnetic field developed

The magnetic properties of some substances were noticed in antiquity, but their study really began in medieval Europe. Using small steel needles, a scientist from France, Peregrine, discovered the intersection of magnetic lines of force at certain points - the poles. Only three centuries later, guided by this discovery, Gilbert continued to study it and subsequently defended his hypothesis that the Earth has its own magnetic field.

The rapid development of the theory of magnetism began at the beginning of the 19th century, when Ampère discovered and described the influence of an electric field on the occurrence of a magnetic field, and Faraday's discovery of electromagnetic induction established an inverse relationship.

What is a magnetic field

The magnetic field manifests itself in the force effect on electric charges that are in motion, or on bodies that have a magnetic moment.

Magnetic field sources:

1. conductors through which electric current passes;
2. permanent magnets;
3. changing electric field.

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Magnetic field sources

The root cause of the magnetic field is identical for all sources: electric microcharges - electrons, ions or protons - have their own magnetic moment or are in directional motion.

Important! Mutually generate each other electric and magnetic fields that change over time. This relationship is determined by Maxwell's equations.

Magnetic field characteristics

The characteristics of the magnetic field are:

1. Magnetic flux, a scalar quantity that determines how many magnetic field lines pass through a given section. Designated with the letter F. Calculated according to the formula:

F = B x S x cos α,

where B is the magnetic induction vector, S is the section, α is the angle of inclination of the vector to the perpendicular drawn to the section plane. Unit of measurement - weber (Wb);

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magnetic flux

1. The magnetic induction vector (B) shows the force acting on the charge carriers. It is directed towards the north pole, where the usual magnetic needle points. Quantitatively, magnetic induction is measured in teslas (Tl);
2. MP tension (N). It is determined by the magnetic permeability of various media. In a vacuum, permeability is taken as unity. The direction of the intensity vector coincides with the direction of the magnetic induction. Unit of measurement - A / m.

How to represent a magnetic field

It is easy to see the manifestations of the magnetic field on the example of a permanent magnet. It has two poles, and depending on the orientation, the two magnets attract or repel. The magnetic field characterizes the processes occurring in this case:

1. MP is mathematically described as a vector field. It can be constructed by means of many vectors of magnetic induction B, each of which is directed towards the north pole of the compass needle and has a length depending on the magnetic force;
2. An alternative way of representing is to use lines of force. These lines never intersect, never start or stop anywhere, forming closed loops. The MF lines combine in more frequent regions where the magnetic field is strongest.

Important! The density of field lines indicates the strength of the magnetic field.

Although the MF cannot be seen in reality, the lines of force can be easily visualized in the real world by placing iron filings in the MF. Each particle behaves like a tiny magnet with north and south pole. The result is a pattern similar to lines of force. A person is not able to feel the impact of MP.

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Magnetic field lines

Magnetic field measurement

Since this is a vector quantity, there are two parameters for measuring MF: force and direction. Direction is easy to measure with a compass connected to the field. An example is a compass placed in the Earth's magnetic field.

Measurement of other characteristics is much more difficult. Practical magnetometers only appeared in the 19th century. Most of them work using the force that the electron feels when moving through the magnetic field.

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Magnetometer

Very accurate measurement of small magnetic fields has become practical since the discovery in 1988 of giant magnetoresistance in layered materials. This discovery in fundamental physics was quickly applied to magnetic hard drive technology for data storage in computers, resulting in a thousandfold increase in storage capacity in just a few years.

In generally accepted measurement systems, MF is measured in tests (T) or in gauss (G). 1 T = 10000 gauss. Gauss is often used because the Tesla is too large a field.

Interesting. A small fridge magnet creates an MF equal to 0.001 T, and the Earth's magnetic field, on average, is 0.00005 T.

The nature of the magnetic field

Magnetism and magnetic fields are manifestations of the electromagnetic force. There are two possible ways how to organize an energy charge in motion and, consequently, a magnetic field.

The first is to connect the wire to a current source, an MF is formed around it.

Important! As the current (the number of charges in motion) increases, the MP increases proportionally. As you move away from the wire, the field decreases with distance. This is described by Ampère's law.

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Ampère's law

Some materials with higher magnetic permeability are capable of concentrating magnetic fields.

Since the magnetic field is a vector, it is necessary to determine its direction. For an ordinary current flowing through a straight wire, the direction can be found by the rule right hand.

To use the rule, one must imagine that the wire is grasped by the right hand, and the thumb indicates the direction of the current. Then the other four fingers will show the direction of the magnetic induction vector around the conductor.

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Right hand rule

The second way to create an MF is to use the fact that electrons appear in some substances that have their own magnetic moment. This is how permanent magnets work:

1. Although atoms often have many electrons, they are mostly connected in such a way that the total magnetic field of the pair cancels out. Two electrons paired in this way are said to have opposite spins. Therefore, in order to magnetize something, you need atoms that have one or more electrons with the same spin. For example, iron has four such electrons and is suitable for making magnets;
2. Billions of electrons in atoms can be randomly oriented, and there will be no common magnetic field, no matter how many unpaired electrons the material has. It must be stable at a low temperature in order to provide an overall preferred electron orientation. The high magnetic permeability causes the magnetization of such substances under certain conditions outside the influence of the magnetic field. These are ferromagnets;
3. Other materials may exhibit magnetic properties in the presence of an external magnetic field. External field serves to equalize all electron spins, which disappears after the removal of the magnetic field. These substances are paramagnetic. Refrigerator door metal is an example of a paramagnet.

Earth's magnetic field

The earth can be represented in the form of capacitor plates, the charge of which has the opposite sign: "minus" - at the earth's surface and "plus" - in the ionosphere. Between them is atmospheric air as an insulating pad. The giant capacitor retains a constant charge due to the influence of the earth's magnetic field. Using this knowledge, it is possible to create a scheme for obtaining electrical energy from the Earth's magnetic field. True, the result will be low voltage values.

Have to take:

• grounding device;
• the wire;
• Tesla transformer, capable of generating high-frequency oscillations and creating a corona discharge, ionizing the air.

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Tesla Coil

The Tesla coil will act as an electron emitter. The whole structure is connected together, and in order to ensure a sufficient potential difference, the transformer must be raised to a considerable height. Thus, an electrical circuit will be created, through which a small current will flow. It is impossible to get a large amount of electricity using this device.

Electricity and magnetism dominate many of the worlds surrounding man: from the most fundamental processes in nature to cutting-edge electronic devices.

Video

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 the state of their motion.

The sources of a 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), and also due to the presence of their own (spin) magnetic moment in the microparticles.

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 arises. Full description electric and magnetic fields in their relationship give the Maxwell equations. To characterize the magnetic field, the concept of field lines of force (lines of magnetic induction) is often introduced.

To measure the characteristics of the magnetic field and the magnetic properties of substances, various types magnetometers. The unit of magnetic field induction in the CGS system of units is Gauss (Gs), in international system units (SI) - Tesla (T), 1 T = 104 Gs. The intensity is measured, respectively, in oersteds (Oe) and amperes per meter (A / m, 1 A / m \u003d 0.01256 Oe; magnetic field energy - in Erg / cm 2 or J / m 2, 1 J / m 2 \u003d 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 up to a distance of 70-80 thousand km in the direction of the Sun and for 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 the biosphere from the flow of charged particles from the solar wind and partly from cosmic rays. The influence of the geomagnetic field itself on the vital activity of organisms is studied by magnetobiology. In near-Earth space, the magnetic field forms a magnetic trap for high-energy charged particles - the Earth's radiation belt. Particles contained in the radiation belt pose a significant danger during space flights. The origin of the Earth's magnetic field is associated with convective movements conductive liquid substance in the earth's core.

Direct measurements with the help of 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. From other planets solar system only Jupiter and, apparently, Saturn have their own magnetic fields, sufficient to create planetary magnetic traps. Magnetic fields up to 10 gauss and a number of characteristic phenomena have been detected on Jupiter ( magnetic storms, synchrotron radio emission, and others), indicating a significant role of the magnetic field in planetary processes.

© Photo: http://www.tesis.lebedev.ru
Photograph of the Sun
in a narrow spectrum

The interplanetary magnetic field is mainly the field of the solar wind (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 disturbed 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 an important role. Measurements based on the Zeeman effect showed that the magnetic field of sunspots reaches several thousand gauss, 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 of the Earth's magnetic field that sharply disrupt the smooth daily course elements of terrestrial magnetism. Magnetic storms last from several hours to several days and are observed simultaneously throughout the Earth.

As a rule, magnetic storms consist of preliminary, initial and main phases, as well as a recovery phase. In the preliminary phase, insignificant 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. In the magnetic storm recovery phase, the field returns to its normal value.

Influence of the solar wind
to the earth's magnetosphere

Magnetic storms are caused by flows of solar plasma from active regions of the Sun, superimposed on a 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 flows 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 Earth's upper atmosphere and their impact on the magnetosphere lead to the generation and amplification of electric currents in it, reaching the highest intensity in the polar regions of the ionosphere, which is the reason for the presence of a high-latitude zone of magnetic activity. Changes in the magnetospheric-ionospheric current systems manifest themselves on the Earth's surface in the form of irregular magnetic disturbances.

In the phenomena of the microcosm, the role of the magnetic field is just as essential as on a cosmic scale. This is due to the existence of all particles - the structural elements of matter (electrons, protons, neutrons), a magnetic moment, as well as the action of a magnetic field on moving electric charges.

Application of magnetic fields in science and technology. Magnetic fields are usually subdivided into weak (up to 500 Gs), medium (500 Gs - 40 kGs), strong (40 kGs - 1 MGs) and superstrong (over 1 MGs). Practically 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, 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 Earth's own magnetic field and the solar wind. Artificial sources include all the electromagnetic fields that so abound in our modern world and our houses in particular. Read more about, and read on ours.

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

The values ​​of the induction of magnetic fields that we most often encounter in everyday life are shown in the diagram below. Looking at this diagram, it becomes clear that we are exposed to magnetic fields all the time and everywhere. According to some scientists, magnetic fields with an induction over 0.2 µT are considered harmful. Naturally, certain precautions should be taken to protect ourselves from the harmful effects of the fields around us. Just 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” states the following: “The maximum permissible level of weakening of the geomagnetic field in the premises of residential buildings is set equal to 1.5". The maximum permissible values ​​of the intensity and strength of the magnetic field with a frequency of 50 Hz are also established:

• in living quarters - 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 on and in the standby state in each particular room, or on the basis of which recommendations will be issued on the normalization of living space.

Related videos

References

1. Great Soviet Encyclopedia.

To understand what is a characteristic of a magnetic field, many phenomena should be defined. At the same time, you need to remember in advance how and why it appears. Find out what is the power characteristic of a magnetic field. It is also important that such a field can occur not only in magnets. In this regard, it does not hurt to mention the characteristics of the earth's magnetic field.

Emergence of the field

To begin with, it is necessary to describe the appearance of the field. After that, you can describe the magnetic field and its characteristics. It appears during the movement of charged particles. Can affect especially conductive conductors. The interaction between a magnetic field and moving charges, or conductors through which current flows, occurs due to forces called electromagnetic.

The intensity or power characteristic of the magnetic field at a certain spatial point is determined using magnetic induction. The latter is denoted by the symbol B.

Graphical representation of the field

The magnetic field and its characteristics can be represented graphically using induction lines. This definition is called lines, the tangents to which at any point will coincide with the direction of the vector y of the magnetic induction.

These lines are included in the characteristics of the magnetic field and are used to determine its direction and intensity. The higher the intensity of the magnetic field, the more data lines will be drawn.

What are magnetic lines

The magnetic lines of straight conductors with current have the shape of a concentric circle, the center of which is located on the axis of this conductor. The direction of the magnetic lines near the conductors with current is determined by the gimlet rule, which sounds like this: if the gimlet is located so that it will be screwed into the conductor in the direction of the current, then the direction of rotation of the handle corresponds to the direction of the magnetic lines.

For a coil with current, the direction of the magnetic field will also be determined by the gimlet rule. It is also required to rotate the handle in the direction of the current in the turns of the solenoid. The direction of the lines of magnetic induction will correspond to the direction of the translational movement of the gimlet.

It is the main characteristic of the magnetic field.

Created by one current, under equal conditions, the field will differ in its intensity in different media due to the different magnetic properties in these substances. The magnetic properties of the medium are characterized by absolute magnetic permeability. It is measured in henries per meter (g/m).

The characteristic of the magnetic field includes the absolute magnetic permeability of the vacuum, called the magnetic constant. The value that determines how many times the absolute magnetic permeability of the medium will differ from the constant is called the relative magnetic permeability.

Magnetic permeability of substances

This is a dimensionless quantity. Substances with a permeability value of less than one are called diamagnetic. In these substances, the field will be weaker than in vacuum. These properties are present in hydrogen, water, quartz, silver, etc.

Media with a magnetic permeability greater than unity are called paramagnetic. In these substances, the field will be stronger than in vacuum. These media and substances include air, aluminum, oxygen, platinum.

In the case of paramagnetic and diamagnetic substances, the value of magnetic permeability will not depend on the voltage of the external, magnetizing field. This means that the value is constant for a particular substance.

Ferromagnets belong to a special group. For these substances, the magnetic permeability will reach several thousand or more. These substances, which have the property of being magnetized and amplifying the magnetic field, are widely used in electrical engineering.

Field strength

To determine the characteristics of the magnetic field, together with the magnetic induction vector, a value called the magnetic field strength can be used. This term defines the intensity of the external magnetic field. The direction of the magnetic field in a medium with the same properties in all directions, the intensity vector will coincide with the magnetic induction vector at the field point.

The strengths of ferromagnets are explained by the presence in them of arbitrarily magnetized small parts, which can be represented as small magnets.

In the absence of a magnetic field, a ferromagnetic substance may not have pronounced magnetic properties, since the domain fields acquire different orientations, and their total magnetic field is zero.

According to the main characteristic of the magnetic field, if a ferromagnet is placed in an external magnetic field, for example, in a coil with current, then under the influence of the external field, the domains will turn in the direction of the external field. Moreover, the magnetic field at the coil will increase, and the magnetic induction will increase. If the external field is sufficiently weak, then only a part of all domains whose magnetic fields approach the direction of the external field will flip over. As the strength of the external field increases, the number of rotated domains will increase, and at a certain value of the external field voltage, almost all parts will be rotated so that the magnetic fields are located in the direction of the external field. This state is called magnetic saturation.

Relationship between magnetic induction and intensity

The relationship between the magnetic induction of a ferromagnetic substance and the strength of an external field can be depicted using a graph called the magnetization curve. At the bend of the curve graph, the rate of increase in magnetic induction decreases. After a bend, where the tension reaches a certain value, saturation occurs, and the curve slightly rises, gradually acquiring the shape of a straight line. In this section, the induction is still growing, but rather slowly and only due to an increase in the strength of the external field.

The graphical dependence of these indicators is not direct, which means that their ratio is not constant, and the magnetic permeability of the material is not a constant indicator, but depends on the external field.

Changes in the magnetic properties of materials

With an increase in the current strength to full saturation in a coil with a ferromagnetic core and its subsequent decrease, the magnetization curve will not coincide with the demagnetization curve. With zero intensity, the magnetic induction will not have the same value, but will acquire some indicator called the residual magnetic induction. The situation with the lagging of magnetic induction from the magnetizing force is called hysteresis.

To completely demagnetize the ferromagnetic core in the coil, it is necessary to give a reverse current, which will create the necessary tension. For different ferromagnetic substances, a segment of different lengths is needed. The larger it is, the more energy is needed for demagnetization. The value at which the material is completely demagnetized is called the coercive force.

With a further increase in the current in the coil, the induction will again increase to the saturation index, but with a different direction of the magnetic lines. When demagnetizing in the opposite direction, residual induction will be obtained. The phenomenon of residual magnetism is used to create permanent magnets from substances with a high residual magnetism. From substances that have the ability to remagnetize, cores are created for electrical machines and devices.

left hand rule

The force acting on a conductor with current has a direction determined by the rule of the left hand: when the palm of the virgin hand is located in such a way that the magnetic lines enter it, and four fingers are extended in the direction of the current in the conductor, the bent thumb will indicate the direction of force. This force is perpendicular to the induction vector and the current.

A current-carrying conductor moving in a magnetic field is considered a prototype of an electric motor, which changes electrical energy into mechanical energy.

Right hand rule

During the movement of the conductor in a magnetic field, an electromotive force is induced inside it, which has a value proportional to the magnetic induction, the length of the conductor involved and the speed of its movement. This dependence is called electromagnetic induction. When determining the direction of the induced EMF in the conductor, the right hand rule is used: when the right hand is located in the same way as in the example from the left, the magnetic lines enter the palm, and the thumb indicates the direction of movement of the conductor, the outstretched fingers indicate the direction of the induced EMF. A conductor moving in a magnetic flux under the influence of an external mechanical force is the simplest example of an electric generator in which mechanical energy is converted into electrical energy.

It can be formulated differently: in a closed circuit, an EMF is induced, with any change in the magnetic flux covered by this circuit, the EDE in the circuit is numerically equal to the rate of change of the magnetic flux that covers this circuit.

This form provides an average EMF indicator and indicates the dependence of the EMF not on the magnetic flux, but on the rate of its change.

Lenz's Law

You also need to remember Lenz's law: the current induced by a change in the magnetic field passing through the circuit, with its magnetic field, prevents this change. If the turns of the coil are pierced by magnetic fluxes of different magnitudes, then the EMF induced on the whole coil is equal to the sum of the EMF in different turns. The sum of the magnetic fluxes of different turns of the coil is called flux linkage. The unit of measurement of this quantity, as well as the magnetic flux, is weber.

When the electric current in the circuit changes, the magnetic flux created by it also changes. In this case, according to the law of electromagnetic induction, an EMF is induced inside the conductor. It appears in connection with a change in current in the conductor, therefore this phenomenon is called self-induction, and the EMF induced in the conductor is called self-induction EMF.

Flux linkage and magnetic flux depend not only on the strength of the current, but also on the size and shape of a given conductor, and the magnetic permeability of the surrounding substance.

conductor inductance

The coefficient of proportionality is called the inductance of the conductor. It denotes the ability of a conductor to create flux linkage when electricity passes through it. This is one of the main parameters of electrical circuits. For certain circuits, inductance is a constant. It will depend on the size of the contour, its configuration and the magnetic permeability of the medium. In this case, the current strength in the circuit and the magnetic flux will not matter.

The above definitions and phenomena provide an explanation of what a magnetic field is. The main characteristics of the magnetic field are also given, with the help of which it is possible to define this phenomenon.

For a long time, the magnetic field has raised many questions in humans, but even now it remains a little-known phenomenon. Many scientists tried to study its characteristics and properties, because the benefits and potential of using the field were indisputable facts.

Let's take everything in order. So, how does any magnetic field act and form? That's right, electric current. And the current, according to physics textbooks, is a stream of charged particles with a direction, isn't it? So, when a current passes through any conductor, a certain kind of matter begins to act around it - a magnetic field. The magnetic field can be created by the current of charged particles or by the magnetic moments of electrons in atoms. Now this field and matter have energy, we see it in electromagnetic forces that can affect the current and its charges. The magnetic field begins to act on the flow of charged particles, and they change the initial direction of motion perpendicular to the field itself.

Another magnetic field can be called electrodynamic, because it is formed near moving particles and affects only moving particles. Well, it is dynamic due to the fact that it has a special structure in rotating bions in a region of space. An ordinary electric moving charge can make them rotate and move. Bions transmit any possible interactions in this region of space. Therefore, the moving charge attracts one pole of all bions and causes them to rotate. Only he can bring them out of a state of rest, nothing else, because other forces will not be able to influence them.

In an electric field are charged particles that move very fast and can travel 300,000 km in just a second. Light has the same speed. There is no magnetic field without an electric charge. This means that the particles are incredibly closely related to each other and exist in a common electromagnetic field. That is, if there are any changes in the magnetic field, then there will be changes in the electric field. This law is also reversed.

We talk a lot about the magnetic field here, but how can you imagine it? We cannot see it with our human naked eye. Moreover, due to the incredibly fast propagation of the field, we do not have time to fix it with the help of various devices. But in order to study something, one must have at least some idea of ​​it. It is also often necessary to depict the magnetic field in diagrams. In order to make it easier to understand it, conditional field lines are drawn. Where did they get them from? They were invented for a reason.

Let's try to see the magnetic field with the help of small metal filings and an ordinary magnet. We will pour these sawdust on a flat surface and introduce them into the action of a magnetic field. Then we will see that they will move, rotate and line up in a pattern or pattern. The resulting image will show the approximate effect of forces in a magnetic field. All forces and, accordingly, lines of force are continuous and closed in this place.

The magnetic needle has similar characteristics and properties to a compass and is used to determine the direction of the lines of force. If it falls into the zone of action of a magnetic field, we can see the direction of action of forces by its north pole. Then we will single out several conclusions from here: the top of an ordinary permanent magnet, from which the lines of force come, denote north pole magnet. Whereas the south pole denotes the point where the forces are closed. Well, the lines of force inside the magnet are not highlighted in the diagram.

The magnetic field, its properties and characteristics are quite widely used, because in many problems it has to be taken into account and studied. This is the most important phenomenon in the science of physics. More complex things are inextricably linked with it, such as magnetic permeability and induction. To explain all the reasons for the appearance of a magnetic field, one must rely on real scientific facts and confirmations. Otherwise, in more complex problems, the wrong approach can violate the integrity of the theory.

Now let's give examples. We all know our planet. You say that it has no magnetic field? You may be right, but scientists say that the processes and interactions inside the Earth's core create a huge magnetic field that stretches for thousands of kilometers. But any magnetic field must have its poles. And they exist, just located a little away from the geographic pole. How do we feel it? For example, birds have developed navigation abilities, and they orient themselves, in particular, by the magnetic field. So, with his help, the geese arrive safely in Lapland. Special navigation devices also use this phenomenon.

Magnetic field and its characteristics

Lecture plan:

Magnetic field, its properties and characteristics.

A magnetic field- the form of existence of matter surrounding moving electric charges (conductors with current, permanent magnets).

This name is due to the fact that, as the Danish physicist Hans Oersted discovered in 1820, it has an orienting effect on the magnetic needle. Oersted's experiment: a magnetic needle was placed under a wire with current, rotating on a needle. When the current was turned on, it was installed perpendicular to the wire; when changing the direction of the current, it turned in the opposite direction.

The main properties of the magnetic field:

generated by moving electric charges, conductors with current, permanent magnets and an alternating electric field;

acts with force on moving electric charges, conductors with current, magnetized bodies;

an alternating magnetic field generates an alternating electric field.

It follows from Oersted's experience that the magnetic field is directional and must have a vector force characteristic. It is designated and called magnetic induction.

The magnetic field is depicted graphically using magnetic lines of force or lines of magnetic induction. magnetic force lines are called lines along which iron filings or axes of small magnetic arrows are located in a magnetic field. At each point of such a line, the vector is directed tangentially.

The lines of magnetic induction are always closed, which indicates the absence of magnetic charges in nature and the vortex nature of the magnetic field.

Conventionally, they leave the north pole of the magnet and enter the south. The density of the lines is chosen so that the number of lines per unit area perpendicular to the magnetic field is proportional to the magnitude of the magnetic induction.

H

Magnetic solenoid with current

The direction of the lines is determined by the rule of the right screw. Solenoid - a coil with current, the turns of which are located close to each other, and the diameter of the turn is much less than the length of the coil.

The magnetic field inside the solenoid is uniform. A magnetic field is called homogeneous if the vector is constant at any point.

The magnetic field of a solenoid is similar to the magnetic field of a bar magnet.

FROM

The olenoid with current is an electromagnet.

Experience shows that for a magnetic field, as well as for an electric field, superposition principle: the induction of the magnetic field created by several currents or moving charges is equal to the vector sum of the inductions of the magnetic fields created by each current or charge:

The vector is entered in one of 3 ways:

a) from Ampère's law;

b) by the action of a magnetic field on a loop with current;

c) from the expression for the Lorentz force.

BUT mper experimentally established that the force with which the magnetic field acts on the element of the conductor with current I, located in a magnetic field, is directly proportional to the force

current I and the vector product of the length element and the magnetic induction:

- Ampère's law

H
The direction of the vector can be found according to the general rules of the vector product, from which the rule of the left hand follows: if the palm of the left hand is positioned so that the magnetic lines of force enter it, and 4 outstretched fingers are directed along the current, then the bent thumb will show the direction of the force.

The force acting on a wire of finite length can be found by integrating over the entire length.

For I = const, B=const, F = BIlsin

If  =90 0 , F = BIl

Magnetic field induction- a vector physical quantity numerically equal to the force acting in a uniform magnetic field on a conductor of unit length with unit current, located perpendicular to the magnetic field lines.

1Tl is the induction of a uniform magnetic field, in which a 1m-long conductor with a current of 1A, located perpendicular to the magnetic field lines, is acted upon by a force of 1N.

So far, we have considered macrocurrents flowing in conductors. However, according to Ampere's assumption, in any body there are microscopic currents due to the movement of electrons in atoms. These microscopic molecular currents create their own magnetic field and can turn in the fields of macrocurrents, creating an additional magnetic field in the body. The vector characterizes the resulting magnetic field created by all macro- and microcurrents, i.e. for the same macrocurrent, the vector in different media has different values.

The magnetic field of macrocurrents is described by the magnetic intensity vector .

For a homogeneous isotropic medium

,

 0 \u003d 410 -7 H / m - magnetic constant,  0 \u003d 410 -7 N / A 2,

 - magnetic permeability of the medium, showing how many times the magnetic field of macrocurrents changes due to the field of microcurrents of the medium.

magnetic flux. Gauss' theorem for magnetic flux.

vector flow(magnetic flux) through the pad dS is called a scalar value equal to

where is the projection onto the direction of the normal to the site;

 - angle between vectors and .

directional surface element,

The vector flux is an algebraic quantity,

if - when leaving the surface;

if - at the entrance to the surface.

The flux of the magnetic induction vector through an arbitrary surface S is equal to

For a uniform magnetic field =const,

1 Wb - magnetic flux passing through a flat surface of 1 m 2 located perpendicular to a uniform magnetic field, the induction of which is equal to 1 T.

The magnetic flux through the surface S is numerically equal to the number of magnetic lines of force crossing the given surface.

Since the lines of magnetic induction are always closed, for a closed surface the number of lines entering the surface (Ф 0), therefore, the total flux of magnetic induction through a closed surface is zero.

- Gauss theorem: the flux of the magnetic induction vector through any closed surface is zero.

This theorem is a mathematical expression of the fact that in nature there are no magnetic charges on which the lines of magnetic induction would begin or end.

Biot-Savart-Laplace law and its application to the calculation of magnetic fields.

The magnetic field of direct currents of various shapes was studied in detail by fr. scientists Biot and Savart. They found that in all cases the magnetic induction at an arbitrary point is proportional to the strength of the current, depends on the shape, dimensions of the conductor, the location of this point in relation to the conductor and on the medium.

The results of these experiments were summarized by fr. mathematician Laplace, who took into account the vector nature of magnetic induction and hypothesized that the induction at each point is, according to the principle of superposition, the vector sum of the inductions of the elementary magnetic fields created by each section of this conductor.

Laplace in 1820 formulated a law, which was called the Biot-Savart-Laplace law: each element of a conductor with current creates a magnetic field, the induction vector of which at some arbitrary point K is determined by the formula:

- Biot-Savart-Laplace law.

It follows from the Biot-Sovar-Laplace law that the direction of the vector coincides with the direction of the cross product. The same direction is given by the rule of the right screw (gimlet).

Given that ,

Conductor element co-directional with current;

Radius vector connecting with point K;

The Biot-Savart-Laplace law is of practical importance, because allows you to find at a given point in space the induction of the magnetic field of the current flowing through the conductor of finite size and arbitrary shape.

For an arbitrary current, such a calculation is a complex mathematical problem. However, if the current distribution has a certain symmetry, then the application of the superposition principle together with the Biot-Savart-Laplace law makes it possible to calculate specific magnetic fields relatively simply.

Let's look at some examples.

A. Magnetic field of a rectilinear conductor with current.

for a conductor of finite length:

for a conductor of infinite length:  1 = 0,  2 = 

B. Magnetic field at the center of the circular current:

=90 0 , sin=1,

Oersted in 1820 experimentally found that the circulation in a closed circuit surrounding a system of macrocurrents is proportional to the algebraic sum of these currents. The coefficient of proportionality depends on the choice of the system of units and in SI is equal to 1.

C
the circulation of a vector is called a closed-loop integral.

This formula is called circulation theorem or total current law:

the circulation of the magnetic field strength vector along an arbitrary closed circuit is equal to the algebraic sum of the macrocurrents (or total current) covered by this circuit. his characteristics In the space surrounding currents and permanent magnets, there is a force field called magnetic. Availability magnetic fields shows up...