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 is the strength characteristic of a magnetic field. 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
To begin with, we should 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 of the translational movement of the gimlet.
It is the main characteristic of a magnetic field.
Created by a single current, under equal conditions, the field will vary in 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 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 strength of ferromagnets is 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, the magnetic fields of which are close in direction to the direction of the external field. 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 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 to create permanent magnets from substances with a high index of residual magnetism. Cores for electrical machines and devices are created from substances that have the ability to remagnetize.
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 into mechanical energy.
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, the rule of the right hand is used: 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, 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 of an electrical 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. 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 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 region of space in which the configuration of bions, transmitters of all interactions, represents a dynamic, mutually consistent rotation.
The direction of action of magnetic forces coincides with the axis of rotation of bions using the right screw rule. The strength characteristic of the magnetic field is determined by the rotation frequency of the bions. The higher the rotation speed, the stronger the field. It would be more correct to call the magnetic field electrodynamic, since it arises only when charged particles move, and acts only on moving charges.
Let us explain why the magnetic field is dynamic. For a magnetic field to arise, it is necessary for the bions to begin to rotate, and only a moving charge that will attract one of the bion’s poles can make them rotate. If the charge does not move, then the bion will not rotate.
A magnetic field is formed only around electric charges that are in motion. That is why the magnetic and electric fields are integral and together form the electromagnetic field. The components of the magnetic field are interconnected and influence each other, changing their properties.
Properties of magnetic field:
- A magnetic field arises under the influence of driving charges of electric current.
- At any point, a magnetic field is characterized by a vector of a physical quantity called magnetic induction, which is a force characteristic of a magnetic field.
- A magnetic field can only affect magnets, current-carrying conductors and moving charges.
- The magnetic field can be of constant and variable type
- The magnetic field is measured only by special instruments and cannot be perceived by human senses.
- The magnetic field is electrodynamic, since it is generated only by the movement of charged particles and affects only charges that are in motion.
- Charged particles move along a perpendicular trajectory.
The size of the magnetic field depends on the rate of change of the magnetic field. According to this feature, there are two types of magnetic field: dynamic magnetic field and gravitational magnetic field. The gravitational magnetic field arises only near elementary particles and is formed depending on the structural features of these particles.
A magnetic moment occurs when a magnetic field acts on a conductive frame. In other words, the magnetic moment is a vector that is located on the line that runs perpendicular to the frame.
The magnetic field can be represented graphically using magnetic field lines. These lines are drawn in such a direction that the direction of the field forces coincides with the direction of the field line itself. Magnetic lines of force are continuous and closed at the same time. The direction of the magnetic field is determined using a magnetic needle. The lines of force also determine the polarity of the magnet, the end with the output of the force lines is the north pole, and the end with the input of these lines is the south pole.
The magnetic field has long raised many questions in humans, but even now remains a little-known phenomenon. Many scientists tried to study its characteristics and properties, because the benefits and potential of using the field were undeniable facts.
Let's look at everything in order. So, how does any magnetic field operate and form? That's right, from electric current. And current, according to physics textbooks, is a directional flow of charged particles, isn’t it? So, when a current passes through any conductor, a certain type of matter begins to act around it - a magnetic field. A magnetic field can be created by a 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 influence the flow of charged particles, and they change the initial direction of movement perpendicular to the field itself.
A magnetic field can also 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 moving electric charge can make them rotate and move. Bions transmit any possible interactions in this region of space. Therefore, a moving charge attracts one pole of all bions and makes them rotate. Only he can bring them out of their state of rest, nothing else, because other forces will not be able to influence them.
In an electric field there are charged particles that move very quickly and can travel 300,000 km in just a second. Light has the same speed. A magnetic field cannot exist 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 one. This law is also reverse.
We talk a lot about the magnetic field here, but how can we 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 detect it using various devices. But in order to study something, you need to have at least some idea about it. It is also often necessary to depict a magnetic field in diagrams. To make it easier to understand, 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 using small metal filings and an ordinary magnet. Let's pour these sawdust onto a flat surface and expose them to 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 the magnetic field. All forces and, accordingly, lines of force are continuous and closed in this place.
A magnetic needle has similar characteristics and properties to a compass, and is used to determine the direction of lines of force. If it falls into the zone of action of a magnetic field, we can see the direction of action of the forces from its north pole. Then let us highlight several conclusions from here: the top of an ordinary permanent magnet, from which the lines of force emanate, is designated 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 have a fairly wide application, 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 such as magnetic permeability and induction are inextricably linked with it. To explain all the reasons for the appearance of a magnetic field, we must rely on real scientific facts and confirmation. Otherwise, in more complex problems, an incorrect approach may violate the integrity of the theory.
Now let's give examples. We all know our planet. Will you say that it has no magnetic field? You may be right, but scientists say that processes and interactions inside the Earth's core give rise to a huge magnetic field that stretches for thousands of kilometers. But in any magnetic field there must be its poles. And they exist, they are just located a little away from the geographic pole. How do we feel it? For example, birds have developed navigation abilities, and they navigate, in particular, by the magnetic field. So, with his help, the geese arrive safely in Lapland. Special navigation devices also use this phenomenon.
Topic: Magnetic field
Prepared by: Baygarashev D.M.
Checked by: Gabdullina A.T.
A magnetic field
If two parallel conductors are connected to a current source so that an electric current passes through them, then, depending on the direction of the current in them, the conductors either repel or attract.
An explanation of this phenomenon is possible from the position of the emergence of a special type of matter around the conductors - a magnetic field.
The forces with which current-carrying conductors interact are called magnetic.
A magnetic field- this is a special type of matter, the specific feature of which is the effect on a moving electric charge, current-carrying conductors, bodies with a magnetic moment, with a force depending on the charge velocity vector, the direction of the current in the conductor and the direction of the magnetic moment of the body.
The history of magnetism goes back to ancient times, to the ancient civilizations of Asia Minor. It was on the territory of Asia Minor, in Magnesia, that rocks were found, samples of which were attracted to each other. Based on the name of the area, such samples began to be called “magnets”. Any bar or horseshoe-shaped magnet has two ends called poles; It is in this place that its magnetic properties are most pronounced. If you hang a magnet on a string, one pole will always point north. The compass is based on this principle. The north-facing pole of a free-hanging magnet is called the magnet's north pole (N). The opposite pole is called the south pole (S).
Magnetic poles interact with each other: like poles repel, and unlike poles attract. Similar to the concept of an electric field surrounding an electric charge, the concept of a magnetic field around a magnet is introduced.
In 1820, Oersted (1777-1851) discovered that a magnetic needle located next to an electrical conductor is deflected when current flows through the conductor, i.e., a magnetic field is created around the current-carrying conductor. If we take a frame with current, then the external magnetic field interacts with the magnetic field of the frame and has an orienting effect on it, i.e. there is a position of the frame at which the external magnetic field has a maximum rotating effect on it, and there is a position when the torque force is zero.
The magnetic field at any point can be characterized by vector B, which is called vector of magnetic induction or magnetic induction at the point.
Magnetic induction B is a vector physical quantity, which is a force characteristic of the magnetic field at a point. It is equal to the ratio of the maximum mechanical moment of forces acting on a frame with current placed in a uniform field to the product of the current strength in the frame and its area:
The direction of the magnetic induction vector B is taken to be the direction of the positive normal to the frame, which is related to the current in the frame by the rule of the right screw, with a mechanical torque equal to zero.
In the same way as the electric field strength lines were depicted, the magnetic field induction lines are depicted. The magnetic field line is an imaginary line, the tangent to which coincides with the direction B at a point.
The directions of the magnetic field at a given point can also be defined as the direction that indicates
the north pole of the compass needle placed at this point. It is believed that the magnetic field lines are directed from the north pole to the south.
The direction of the magnetic induction lines of the magnetic field created by an electric current that flows through a straight conductor is determined by the gimlet or right-hand screw rule. The direction of the magnetic induction lines is taken to be the direction of rotation of the screw head, which would ensure its translational movement in the direction of the electric current (Fig. 59).
where n01 = 4 Pi 10 -7 V s/(A m). - magnetic constant, R - distance, I - current strength in the conductor.
Unlike electrostatic field lines, which begin at a positive charge and end at a negative charge, magnetic field lines are always closed. No magnetic charge similar to electric charge was detected.
One tesla (1 T) is taken as a unit of induction - the induction of such a uniform magnetic field in which a maximum mechanical torque of 1 N m acts on a frame with an area of 1 m2, through which a current of 1 A flows.
The magnetic field induction can also be determined by the force acting on a current-carrying conductor in a magnetic field.
A current-carrying conductor placed in a magnetic field is acted upon by an Ampere force, the magnitude of which is determined by the following expression:
where I is the current strength in the conductor, l- the length of the conductor, B is the magnitude of the magnetic induction vector, and is the angle between the vector and the direction of the current.
The direction of the Ampere force can be determined by the rule of the left hand: we place the palm of the left hand so that the magnetic induction lines enter the palm, we place four fingers in the direction of the current in the conductor, then the bent thumb shows the direction of the Ampere force.
Taking into account that I = q 0 nSv, and substituting this expression into (3.21), we obtain F = q 0 nSh/B sin a. The number of particles (N) in a given volume of a conductor is N = nSl, then F = q 0 NvB sin a.
Let us determine the force exerted by the magnetic field on an individual charged particle moving in a magnetic field:
This force is called the Lorentz force (1853-1928). The direction of the Lorentz force can be determined by the rule of the left hand: we place the palm of the left hand so that the lines of magnetic induction enter the palm, four fingers show the direction of movement of the positive charge, the large bent finger shows the direction of the Lorentz force.
The interaction force between two parallel conductors carrying currents I 1 and I 2 is equal to:
Where l- part of a conductor located in a magnetic field. If the currents are in the same direction, then the conductors attract (Fig. 60), if they are in the opposite direction, they repel. The forces acting on each conductor are equal in magnitude and opposite in direction. Formula (3.22) is the basis for determining the unit of current 1 ampere (1 A).
The magnetic properties of a substance are characterized by a scalar physical quantity - magnetic permeability, which shows how many times the induction B of the magnetic field in a substance that completely fills the field differs in magnitude from the induction B 0 of the magnetic field in a vacuum:
According to their magnetic properties, all substances are divided into diamagnetic, paramagnetic And ferromagnetic.
Let us consider the nature of the magnetic properties of substances.
Electrons in the shell of atoms of a substance move in different orbits. To simplify, we consider these orbits to be circular, and each electron orbiting an atomic nucleus can be considered as a circular electric current. Each electron, like a circular current, creates a magnetic field, which we call orbital. In addition, an electron in an atom has its own magnetic field, called a spin field.
If, when introduced into an external magnetic field with induction B 0, induction B is created inside the substance< В 0 , то такие вещества называются диамагнитными (n< 1).
IN diamagnetic In materials in the absence of an external magnetic field, the magnetic fields of electrons are compensated, and when they are introduced into a magnetic field, the induction of the magnetic field of the atom becomes directed against the external field. The diamagnetic material is pushed out of the external magnetic field.
U paramagnetic materials, the magnetic induction of electrons in atoms is not completely compensated, and the atom as a whole turns out to be like a small permanent magnet. Usually in a substance all these small magnets are oriented randomly, and the total magnetic induction of all their fields is zero. If you place a paramagnet in an external magnetic field, then all the small magnets - atoms will turn in the external magnetic field like compass needles and the magnetic field in the substance will increase ( n >= 1).
Ferromagnetic are those materials in which n" 1. In ferromagnetic materials, so-called domains are created, macroscopic regions of spontaneous magnetization.
In different domains, magnetic field inductions have different directions (Fig. 61) and in a large crystal
mutually compensate each other. When a ferromagnetic sample is introduced into an external magnetic field, the boundaries of individual domains shift so that the volume of domains oriented along the external field increases.
With an increase in the induction of the external field B 0, the magnetic induction of the magnetized substance increases. At some values of B 0, the induction stops sharply increasing. This phenomenon is called magnetic saturation.
A characteristic feature of ferromagnetic materials is the phenomenon of hysteresis, which consists in the ambiguous dependence of the induction in the material on the induction of the external magnetic field when it changes.
The magnetic hysteresis loop is a closed curve (cdc`d`c), expressing the dependence of the induction in the material on the amplitude of the induction of the external field with a periodic rather slow change in the latter (Fig. 62).
The hysteresis loop is characterized by the following values: B s, Br, B c. B s - maximum value of material induction at B 0s; In r is the residual induction, equal to the induction value in the material when the induction of the external magnetic field decreases from B 0s to zero; -B c and B c - coercive force - a value equal to the induction of the external magnetic field necessary to change the induction in the material from residual to zero.
For each ferromagnet there is a temperature (Curie point (J. Curie, 1859-1906), above which the ferromagnet loses its ferromagnetic properties.
There are two ways to bring a magnetized ferromagnet into a demagnetized state: a) heat above the Curie point and cool; b) magnetize the material with an alternating magnetic field with a slowly decreasing amplitude.
Ferromagnets with low residual induction and coercive force are called soft magnetic. They find application in devices where ferromagnets often have to be remagnetized (cores of transformers, generators, etc.).
Magnetically hard ferromagnets, which have a high coercive force, are used to make permanent magnets.
A magnetic field- this is the material medium through which interaction occurs between conductors with current or moving charges.
Properties of magnetic field:
Characteristics of the magnetic field:
To study the magnetic field, a test circuit with current is used. It is small in size, and the current in it is much less than the current in the conductor creating the magnetic field. On opposite sides of the current-carrying circuit, forces from the magnetic field act that are equal in magnitude, but directed in opposite directions, since the direction of the force depends on the direction of the current. The points of application of these forces do not lie on the same straight line. Such forces are called a couple of forces. As a result of the action of a pair of forces, the circuit cannot move translationally; it rotates around its axis. The rotating action is characterized torque.
, Where l–leverage couple of forces(distance between points of application of forces).
As the current in the test circuit or the area of the circuit increases, the torque of the pair of forces will increase proportionally. The ratio of the maximum moment of force acting on the circuit with current to the magnitude of the current in the circuit and the area of the circuit is a constant value for a given point in the field. It's called magnetic induction.
, Where 
-magnetic moment circuit with current.
Unit magnetic induction – Tesla [T].
Magnetic moment of the circuit– vector quantity, the direction of which depends on the direction of the current in the circuit and is determined by right screw rule: clench your right hand into a fist, point four fingers in the direction of the current in the circuit, then the thumb will indicate the direction of the magnetic moment vector. The magnetic moment vector is always perpendicular to the contour plane.
Behind direction of the magnetic induction vector take the direction of the vector of the magnetic moment of the circuit, oriented in the magnetic field.
Magnetic induction line– a line whose tangent at each point coincides with the direction of the magnetic induction vector. Magnetic induction lines are always closed and never intersect. Magnetic induction lines of a straight conductor with current have the form of circles located in a plane perpendicular to the conductor. The direction of the magnetic induction lines is determined by the right-hand screw rule. Magnetic induction lines of circular current(turns with current) also have the form of circles. Each coil element is length 
can be imagined as a straight conductor that creates its own magnetic field. For magnetic fields, the principle of superposition (independent addition) applies. The total vector of magnetic induction of the circular current is determined as the result of the addition of these fields in the center of the turn according to the right-hand screw rule.
If the magnitude and direction of the magnetic induction vector are the same at every point in space, then the magnetic field is called homogeneous. If the magnitude and direction of the magnetic induction vector at each point do not change over time, then such a field is called permanent.
Magnitude magnetic induction at any point in the field is directly proportional to the current strength in the conductor creating the field, inversely proportional to the distance from the conductor to a given point in the field, depends on the properties of the medium and the shape of the conductor creating the field.
, Where 
ON 2 ; Gn/m – magnetic constant of vacuum,
-relative magnetic permeability of the medium,
-absolute magnetic permeability of the medium.
Depending on the value of magnetic permeability, all substances are divided into three classes:
As the absolute permeability of the medium increases, the magnetic induction at a given point in the field also increases. The ratio of magnetic induction to the absolute magnetic permeability of the medium is a constant value for a given poly point, e is called tension.
.
The vectors of tension and magnetic induction coincide in direction. The magnetic field strength does not depend on the properties of the medium.
Ampere power– the force with which the magnetic field acts on a current-carrying conductor.
Where l– length of the conductor, 
- the angle between the magnetic induction vector and the direction of the current.
The direction of the Ampere force is determined by left hand rule: the left hand is positioned so that the component of the magnetic induction vector, perpendicular to the conductor, enters the palm, four extended fingers are directed along the current, then the thumb bent by 90 0 will indicate the direction of the Ampere force.
The result of the Ampere force is the movement of the conductor in a given direction.
E 
if 
= 90 0 , then F=max, if 
= 0 0 , then F = 0.
Lorentz force– the force of the magnetic field on a moving charge.
, where q is the charge, v is the speed of its movement, 
- the angle between the vectors of tension and speed.
The Lorentz force is always perpendicular to the magnetic induction and velocity vectors. The direction is determined by left hand rule(fingers follow the movement of the positive charge). If the direction of the particle's velocity is perpendicular to the magnetic induction lines of a uniform magnetic field, then the particle moves in a circle without changing its kinetic energy.
Since the direction of the Lorentz force depends on the sign of the charge, it is used to separate charges.
Magnetic flux– a value equal to the number of magnetic induction lines that pass through any area located perpendicular to the magnetic induction lines.
, Where 
- the angle between the magnetic induction and the normal (perpendicular) to the area S.
Unit– Weber [Wb].
Magnetic flux measurement methods:
Changing the orientation of the site in a magnetic field (changing the angle)
Changing the area of a circuit placed in a magnetic field
Changing the strength of the current creating a magnetic field
Changing the distance of the circuit from the magnetic field source
Changes in the magnetic properties of the medium.
F 
Araday recorded an electric current in a circuit that did not contain a source, but was located next to another circuit containing a source. Moreover, the current in the first circuit arose in the following cases: with any change in the current in circuit A, with relative movement of the circuits, with the introduction of an iron rod into circuit A, with the movement of a permanent magnet relative to circuit B. Directed movement of free charges (current) occurs only in an electric field. This means that a changing magnetic field generates an electric field, which sets in motion the free charges of the conductor. This electric field is called induced or vortex.
Differences between a vortex electric field and an electrostatic one:
The source of the vortex field is a changing magnetic field.
The vortex field intensity lines are closed.
The work done by this field to move a charge along a closed circuit is not zero.
The energy characteristic of a vortex field is not the potential, but induced emf– a value equal to the work of external forces (forces of non-electrostatic origin) to move a unit of charge along a closed circuit.
.Measured in Volts[IN].
A vortex electric field occurs with any change in the magnetic field, regardless of whether there is a conducting closed circuit or not. The circuit only allows one to detect the vortex electric field.
Electromagnetic induction- this is the occurrence of induced emf in a closed circuit with any change in the magnetic flux through its surface.
The induced emf in a closed circuit generates an induced current.
.
Direction of induction current determined by Lenz's rule: the induced current is in such a direction that the magnetic field created by it counteracts any change in the magnetic flux that generated this current.
Faraday's law for electromagnetic induction: The induced emf in a closed loop is directly proportional to the rate of change of magnetic flux through the surface bounded by the loop.
T 
oki fuko– eddy induction currents that arise in large conductors placed in a changing magnetic field. The resistance of such a conductor is low, since it has a large cross-section S, so the Foucault currents can be large in value, as a result of which the conductor heats up.
Self-induction- this is the occurrence of induced emf in a conductor when the current strength in it changes.
A conductor carrying current creates a magnetic field. Magnetic induction depends on the current strength, therefore the intrinsic magnetic flux also depends on the current strength.
, where L is the proportionality coefficient, inductance.
Unit inductance – Henry [H].
Inductance conductor depends on its size, shape and magnetic permeability of the medium.
Inductance increases with increasing length of the conductor, the inductance of a turn is greater than the inductance of a straight conductor of the same length, the inductance of a coil (a conductor with a large number of turns) is greater than the inductance of one turn, the inductance of a coil increases if an iron rod is inserted into it.
Faraday's law for self-induction:
.
Self-induced emf is directly proportional to the rate of change of current.
Self-induced emf generates a self-induction current, which always prevents any change in the current in the circuit, that is, if the current increases, the self-induction current is directed in the opposite direction; when the current in the circuit decreases, the self-induction current is directed in the same direction. The greater the inductance of the coil, the greater the self-inductive emf that occurs in it.
Magnetic field energy is equal to the work that the current does to overcome the self-induced emf during the time while the current increases from zero to the maximum value.
.
Electromagnetic vibrations– these are periodic changes in charge, current strength and all characteristics of electric and magnetic fields.
Electrical oscillatory system(oscillating circuit) consists of a capacitor and an inductor.
Conditions for the occurrence of oscillations:
The system must be brought out of equilibrium; to do this, charge the capacitor. Electric field energy of a charged capacitor:
.
The system must return to a state of equilibrium. Under the influence of an electric field, charge transfers from one plate of the capacitor to another, that is, an electric current appears in the circuit, which flows through the coil. As the current increases in the inductor, a self-induction emf arises; the self-induction current is directed in the opposite direction. When the current in the coil decreases, the self-induction current is directed in the same direction. Thus, the self-induction current tends to return the system to a state of equilibrium.
The electrical resistance of the circuit should be low.
Ideal oscillatory circuit has no resistance. The vibrations in it are called free.
For any electrical circuit, Ohm's law is satisfied, according to which the emf acting in the circuit is equal to the sum of the voltages in all sections of the circuit. There is no current source in the oscillatory circuit, but a self-inductive emf appears in the inductor, which is equal to the voltage across the capacitor.
Conclusion: the charge of the capacitor changes according to a harmonic law.
Capacitor voltage:
.
Current strength in the circuit:
.
Magnitude 
- current amplitude.
The difference from the charge on 
.
Period of free oscillations in the circuit:
Electric field energy of a capacitor:
Coil magnetic field energy:
The energies of the electric and magnetic fields vary according to a harmonic law, but the phases of their oscillations are different: when the energy of the electric field is maximum, the energy of the magnetic field is zero.
Total energy of the oscillatory system:
.
IN ideal contour the total energy does not change.
During the oscillation process, the energy of the electric field is completely converted into the energy of the magnetic field and vice versa. This means that the energy at any moment in time is equal to either the maximum energy of the electric field or the maximum energy of the magnetic field.
Real oscillatory circuit contains resistance. The vibrations in it are called fading.
Ohm's law will take the form:
Provided that the damping is small (the square of the natural frequency of oscillations is much greater than the square of the damping coefficient), the logarithmic damping decrement is:
With strong damping (the square of the natural frequency of oscillation is less than the square of the oscillation coefficient):
This equation describes the process of discharging a capacitor into a resistor. In the absence of inductance, oscillations will not occur. According to this law, the voltage on the capacitor plates also changes.
Total Energy in a real circuit 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 (macro-emitters), as well as excited atoms and molecules (micro-emitters). The higher the oscillation frequency, the better electromagnetic waves are emitted in space.
Properties of electromagnetic waves:
All electromagnetic waves are transverse
In a homogeneous medium, electromagnetic waves propagate at a constant speed, which depends on the properties of the environment:
- relative dielectric constant of the medium
- dielectric constant of vacuum, 
F/m, Cl 2 /nm 2
- relative magnetic permeability of the medium
- magnetic constant of vacuum, 
ON 2 ; Gn/m
Electromagnetic waves reflected from obstacles, absorbed, scattered, refracted, polarized, diffracted, interfered.
Volumetric energy density electromagnetic field consists of volumetric energy densities of electric and magnetic fields:
Wave energy flux density - wave intensity:
-Umov-Poynting vector.
All electromagnetic waves are arranged in a series of frequencies or wavelengths ( 
). This row is electromagnetic wave scale.
Low frequency vibrations. 0 – 10 4 Hz. Obtained from generators. They radiate poorly
Radio waves. 10 4 – 10 13 Hz. They are emitted by solid conductors 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.
