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 emanate, is designated by the north pole of the 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.

A MAGNETIC FIELD

The magnetic field is a special kind of matter, invisible and intangible to humans,
existing independently of our consciousness.
Even in ancient times, scientists-thinkers guessed that something exists around the magnet.

Magnetic needle.

A magnetic needle is a device necessary for studying the magnetic action of an electric current.
It is a small magnet mounted on the tip of the needle, has two poles: north and south. The magnetic needle can rotate freely on the tip of the needle.
The north end of the magnetic needle always points north.
The line connecting the poles of the magnetic needle is called the axis of the magnetic needle.
A similar magnetic needle is in any compass - a device for orienteering on the ground.

Where does the magnetic field originate?

Oersted's experiment (1820) - shows how a conductor with current and a magnetic needle interact.

When the electric circuit is closed, the magnetic needle deviates from its original position, when the circuit is opened, the magnetic needle returns to its original position.

In the space around a conductor with current (and in the general case around any moving electric charge) a magnetic field arises.
The magnetic forces of this field act on the needle and turn it.

In general, one can say
that a magnetic field arises around moving electric charges.
Electric current and magnetic field are inseparable from each other.

INTERESTING WHAT...

Many celestial bodies - planets and stars - have their own magnetic fields.
However, our nearest neighbors - the Moon, Venus and Mars - do not have a magnetic field,
similar to earth.
___

Gilbert discovered that when a piece of iron is brought near one pole of a magnet, the other pole begins to attract more strongly. This idea was patented only 250 years after Hilbert's death.

In the first half of the 90s, when new Georgian coins appeared - lari,
local pickpockets got magnets,
because the metal from which these coins were made was well attracted by a magnet!

If you take a dollar bill around the corner and bring it to a powerful magnet
(for example, horseshoe), creating a non-uniform magnetic field, a piece of paper
deviate towards one of the poles. It turns out that the color of the dollar bill contains iron salts,
having magnetic properties, so the dollar is attracted to one of the poles of the magnet.

If you bring a large magnet to the carpenter's bubble level, the bubble will move.
The fact is that the bubble level is filled with a diamagnetic liquid. When such a liquid is placed in a magnetic field, a magnetic field of the opposite direction is created inside it, and it is pushed out of the field. Therefore, the bubble in the liquid approaches the magnet.

YOU SHOULD KNOW ABOUT THEM!

The organizer of the magnetic compass business in the Russian Navy was a well-known deviator scientist,
captain of the 1st rank, author of scientific works on the theory of the compass I.P. Belavan.
Member of a round-the-world trip on the frigate "Pallada" and a participant in the Crimean War of 1853-56. he was the first in the world to demagnetize a ship (1863)
and solved the problem of installing compasses inside an iron submarine.
In 1865 he was appointed head of the country's first Compass Observatory in Kronstadt.

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 rule of the gimlet, 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 graphic 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 electrical 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.

We still remember about the magnetic field from school, that's just what it is, "pops up" in the memories of not everyone. Let's refresh what we've been through, and maybe tell you something new, useful and interesting.

Determination of the magnetic field

A magnetic field is a force field that acts on moving electric charges (particles). Due to this force field, objects are attracted to each other. There are two types of magnetic fields:

1. Gravitational - is formed exclusively near elementary particles and viruetsya in its strength based on the features and structure of these particles.
2. Dynamic, produced in objects with moving electric charges (current transmitters, magnetized substances).

For the first time, the designation of the magnetic field was introduced by M. Faraday in 1845, although its meaning was a little erroneous, since it was believed that both electric and magnetic effects and interactions are based on the same material field. Later in 1873, D. Maxwell "presented" the quantum theory, in which these concepts began to be separated, and the previously derived force field was called the electromagnetic field.

How does a magnetic field appear?

The magnetic fields of various objects are not perceived by the human eye, and only special sensors can fix it. The source of the appearance of a magnetic force field on a microscopic scale is the movement of magnetized (charged) microparticles, which are:

• ions;
• electrons;
• protons.

Their movement occurs due to the spin magnetic moment, which is present in each microparticle.

Magnetic field, where can it be found?

No matter how strange it may sound, but almost all objects around us have their own magnetic field. Although in the concept of many, only a pebble called a magnet has a magnetic field, which attracts iron objects to itself. In fact, the force of attraction is in all objects, it only manifests itself in a lower valency.

It should also be clarified that the force field, called magnetic, appears only under the condition that electric charges or bodies are moving.

Immovable charges have an electric force field (it can also be present in moving charges). It turns out that the sources of the magnetic field are:

• permanent magnets;
• mobile charges.

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.

With

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 follows the rule of the left hand: 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:

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