When does magnetic occur? Magnetic field and its properties

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

Emergence of the field

First we need to describe the emergence of the field. Then you can describe the magnetic field and its characteristics. It appears during the movement of charged particles. May affect in particular live 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 strength characteristic of a magnetic field at a certain spatial point is determined using magnetic induction. The latter is designated by the symbol B.

Graphical representation of the field

The magnetic field and its characteristics can be represented in graphical form using induction lines. This definition refers to lines whose tangents at any point will coincide with the direction of the magnetic induction vector.

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 of these lines will be drawn.

What are magnetic lines

Magnetic lines in straight current-carrying conductors have the shape of a concentric circle, the center of which is located on the axis of the given conductor. The direction of magnetic lines near current-carrying conductors is determined by the gimlet rule, which sounds like this: if the gimlet is positioned so that it is 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.

In 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 solenoid turns. The direction of the magnetic induction lines will correspond to the direction forward motion gimlet.

It is the main characteristic of a magnetic field.

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

The characteristics of the magnetic field include 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 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 a vacuum. These properties are present in hydrogen, water, quartz, silver, etc.

Media with a magnetic permeability exceeding unity are called paramagnetic. In these substances the field will be stronger than in a vacuum. These environments and substances include air, aluminum, oxygen, and 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 quantity is constant for a certain substance.

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

Field strength

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

The strong magnetic properties of ferromagnets are explained by the presence in them of arbitrarily magnetized small parts, which can be represented in the form of small magnets.

With no magnetic field, a ferromagnetic substance may not have pronounced magnetic properties, since the fields of the domains 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 weak enough, then only a part of all domains will turn over, magnetic fields whose direction is close to the direction of the external field. As the external field strength increases, the number of rotated domains will increase, and with a certain value voltage of the external field, almost all parts will be rotated so that the magnetic fields will be located in the direction of the external field. This state is called magnetic saturation.

Relationship between magnetic induction and tension

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

The graphical dependence of the indicator data 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

When the current strength is increased to complete saturation in a coil with a ferromagnetic core and then decreased, 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 a certain indicator called residual magnetic induction. The situation where magnetic induction lags behind 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 voltage. Different ferromagnetic substances require a piece of different lengths. The larger it is, the greater the amount of energy required for demagnetization. The value at which complete demagnetization of the material occurs is called coercive force.

With a further increase in the current in the coil, the induction will again increase to saturation, 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 when creating permanent magnets from substances with a high index of residual magnetism. Cores are created from substances that have the ability to remagnetize electric machines and instruments.

Left hand rule

The force affecting a current-carrying conductor has a direction determined by the left-hand rule: when the palm of the virgin hand is positioned 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 the force. This force is perpendicular to the induction vector and current.

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

Right hand rule

When a conductor moves in a magnetic field, an electromotive force is induced within 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 a conductor, use the rule right hand: when the right hand is positioned in the same way as in the example with the left, the magnetic lines enter the palm, and the thumb indicates the direction of movement of the conductor, the extended fingers will 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 electric generator, in which mechanical energy is converted into electrical energy.

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

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 when the magnetic field passing through the circuit changes, its magnetic field prevents this change. If the turns of a coil are penetrated by magnetic fluxes of different magnitudes, then the EMF induced throughout the whole coil is equal to the sum of the EDE in different turns. The sum of the magnetic fluxes of different turns of the coil is called flux linkage. The unit of measurement for this quantity, as well as for magnetic flux, is Weber.

When the electric current in the circuit changes, the magnetic flux it creates also changes. At the same time, according to the law 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 current strength, but also on the size and shape of a given conductor, and the magnetic permeability of the surrounding substance.

Conductor inductance

The proportionality factor is called the inductance of the conductor. It refers to 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 value. It will depend on the size of the circuit, 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 this phenomenon can be defined.

A magnetic field is a special form of matter that is created by magnets, conductors with current (moving charged particles) and which can be detected by the interaction of magnets, conductors with current (moving charged particles).

Oersted's experience

The first experiments (conducted in 1820) showed that between electrical and magnetic phenomena There is a deep connection; there were experiments by the Danish physicist H. Oersted.

A magnetic needle located near a conductor rotates through a certain angle when the current in the conductor is turned on. When the circuit is opened, the arrow returns to its original position.

From the experience of G. Oersted it follows that there is a magnetic field around this conductor.

Ampere's experience
Two parallel conductors carrying electricity, interact with each other: they attract if the currents are in the same direction, and repel if the currents are in the opposite direction. This occurs due to the interaction of magnetic fields arising around the conductors.

Properties of magnetic field

1. Materially, i.e. exists independently of us and our knowledge about it.

2. Created by magnets, conductors with current (moving charged particles)

3. Detected by the interaction of magnets, conductors with current (moving charged particles)

4. Acts on magnets, current-carrying conductors (moving charged particles) with some force

5. There are no magnetic charges in nature. It is impossible to separate the northern and south poles and get a body with one pole.

6. The reason why bodies have magnetic properties was found by the French scientist Ampere. Ampere put forward the conclusion that the magnetic properties of any body are determined by closed electric currents inside it.

These currents represent the movement of electrons around orbits in an atom.

If the planes in which these currents circulate are located randomly in relation to each other due to thermal movement molecules that make up the body, then their interactions are mutually compensated and the body does not exhibit any magnetic properties.

And vice versa: if the planes in which the electrons rotate are parallel to each other and the directions of the normals to these planes coincide, then such substances enhance the external magnetic field.

7. Magnetic forces act in a magnetic field in certain directions, which are called magnetic lines of force. With their help, you can conveniently and clearly show the magnetic field in a particular case.

In order to more accurately depict the magnetic field, we agreed to show in those places where the field is stronger power lines located more densely, i.e. closer to each other. And vice versa, in places where the field is weaker, fewer field lines are shown, i.e. less frequently located.

8. The magnetic field is characterized by the magnetic induction vector.

The magnetic induction vector is a vector quantity characterizing the magnetic field.

The direction of the magnetic induction vector coincides with the direction of the north pole of the free magnetic needle at a given point.

The direction of the field induction vector and current strength I are related by the “right screw (gimlet) rule”:

if you screw in a gimlet in the direction of the current in the conductor, then the direction of the speed of movement of the end of its handle at a given point will coincide with the direction of the magnetic induction vector at that point.

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

Change in current strength 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 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 closed loop.

.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 free vibrations in the circuit:

Energy electric field 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 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, the tension lines of which 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 point 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 connected 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 (macroemitters), as well as excited atoms and molecules (microemitters). The higher the oscillation frequency, the better they radiate in space electromagnetic waves.

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 The electromagnetic field consists of the volumetric energy densities of the 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 carrying rapidly alternating currents.

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.

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:

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

, Where
-magnetic moment circuit with current.

Unit magnetic induction – Tesla [T].

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.

, 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:

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 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.

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

Change in current strength 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].

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.

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.

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.

Faraday's law for self-induction:
.

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

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 electrical resistance of the circuit should be low.

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

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:

Total energy of the oscillatory system:
.

IN ideal contour the total energy does not change.

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):

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

For circuit with capacitor and resistor:
.

Maxwell's theory of the electromagnetic field:

1 position:

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

Electromagnetic wave– this is the propagation in space of vortex electric and magnetic fields connected 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.

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 The electromagnetic field consists of the volumetric energy densities of the 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 carrying rapidly alternating currents.

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.

Magnetic field is called a special, different from substance, type of matter through which the action of a magnet is transmitted to other bodies.

A magnetic field occurs in the space surrounding moving electric charges and permanent magnets. It only affects moving charges. Under the influence of electromagnetic forces, moving charged particles are deflected

From its original path in a direction perpendicular to the field.

Magnetic and electric fields are inseparable and together form a single electromagnetic field. Any change electric field leads to the appearance of a magnetic field, and, conversely, any change in the magnetic field is accompanied by the appearance of an electric field. The electromagnetic field propagates at the speed of light, i.e. 300,000 km/s.

The effect of permanent magnets and electromagnets on ferromagnetic bodies, the existence and inextricable unity of the poles of magnets and their interaction (opposite poles attract, like poles repel) are well known. Similarly

with the magnetic poles of the Earth, the poles of magnets are called northern and southern.

The magnetic field is clearly depicted by magnetic lines of force, which determine the direction of the magnetic field in space (Fig..1). These lines have neither beginning nor end, i.e. are closed.

The magnetic field lines of a straight conductor are concentric circles surrounding the wire. The stronger the current, the stronger the magnetic field around the wire. As you move away from the current-carrying wire, the magnetic field weakens.

In the space surrounding a magnet or electromagnet, the direction from North Pole to South Pole. The more intense the magnetic field, the higher the density of field lines.

The direction of the magnetic field lines is determined gimlet rule:.

Rice. 1. Magnetic field of magnets:

a - direct; b - horseshoe-shaped

Rice. 2. Magnetic field:

a - straight wire; b - inductive coil

If you screw in the screw in the direction of the current, then the magnetic field lines will be directed along the direction of the screw (Fig. 2 a)

To obtain a stronger magnetic field, inductive coils with wire windings are used. In this case, the magnetic fields of the individual turns of the inductive coil add up and their lines of force merge into a common magnetic flux.

Magnetic lines of force come out of the inductive coil

at the end where the current is directed counterclockwise, i.e. this end is the north magnetic pole (Fig. 2, b).

When the direction of the current in the inductive coil changes, the direction of the magnetic field will also change.