§16. Magnetic field and its characteristics and properties
Magnetic field and its characteristics. When an electric current passes through a conductor, a a magnetic field. A magnetic field is one of the types of matter. It has energy, which manifests itself in the form of electromagnetic forces acting on individual moving electric charges (electrons and ions) and on their flows, i.e. electric current. Under the influence of electromagnetic forces, moving charged particles deviate from their original path in a direction perpendicular to the field (Fig. 34). The magnetic field is formed only around moving electric charges, and its action also extends only to moving charges. Magnetic and electric fields are inseparable and form together 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. Electromagnetic field propagates at the speed of light, i.e. 300,000 km/s.
Graphical representation of the magnetic field. Graphically, the magnetic field is represented by magnetic lines of force, which are drawn so that the direction of the line of force at each point of the field coincides with the direction of the field forces; magnetic field lines are always continuous and closed. The direction of the magnetic field at each point can be determined using a magnetic needle. The north pole of the arrow is always set in the direction of the field forces. The end of the permanent magnet, from which the lines of force come out (Fig. 35, a), is considered to be the north pole, and the opposite end, which includes the lines of force, is the south pole (the lines of force passing inside the magnet are not shown). The distribution of lines of force between the poles of a flat magnet can be detected using steel filings sprinkled on a sheet of paper placed on the poles (Fig. 35, b). The magnetic field in the air gap between two parallel opposite poles of a permanent magnet is characterized by a uniform distribution of magnetic lines of force (Fig. 36) (field lines passing inside the magnet are not shown).
Rice. 37. Magnetic flux penetrating the coil at perpendicular (a) and inclined (b) its positions with respect to the direction of magnetic lines of force.
For a more visual representation of the magnetic field, the lines of force are located less often or thicker. In those places where the magnetic role is stronger, the lines of force are located closer to each other, in the same place where it is weaker, further apart. The lines of force do not intersect anywhere.
In many cases, it is convenient to consider magnetic lines of force as some elastic stretched threads that tend to contract and also mutually repel each other (have mutual lateral expansion). Such a mechanical representation of the lines of force makes it possible to clearly explain the emergence of electromagnetic forces during the interaction of a magnetic field and a conductor with a current, as well as two magnetic fields.
The main characteristics of a magnetic field are magnetic induction, magnetic flux, magnetic permeability and magnetic field strength.
Magnetic induction and magnetic flux. The intensity of the magnetic field, i.e., its ability to do work, is determined by a quantity called magnetic induction. The stronger the magnetic field created by a permanent magnet or electromagnet, the greater the induction it has. Magnetic induction B can be characterized by the density of magnetic lines of force, i.e., the number of lines of force passing through an area of 1 m 2 or 1 cm 2 located perpendicular to the magnetic field. Distinguish between homogeneous and inhomogeneous magnetic fields. In a uniform magnetic field, the magnetic induction at each point of the field has the same value and direction. The field in the air gap between the opposite poles of a magnet or electromagnet (see Fig. 36) can be considered homogeneous at some distance from its edges. The magnetic flux Ф passing through any surface is determined by the total number of magnetic lines of force penetrating this surface, for example, coil 1 (Fig. 37, a), therefore, in a uniform magnetic field
F = BS (40)
where S is the cross-sectional area of the surface through which the magnetic lines of force pass. It follows that in such a field the magnetic induction is equal to the flux divided by the cross-sectional area S:
B = F/S (41)
If any surface is inclined with respect to the direction of the magnetic field lines (Fig. 37, b), then the flux penetrating it will be less than when it is perpendicular, i.e. Ф 2 will be less than Ф 1.
In the SI system of units, magnetic flux is measured in webers (Wb), this unit has the dimension V * s (volt-second). Magnetic induction in the SI system of units is measured in teslas (T); 1 T \u003d 1 Wb / m 2.
Magnetic permeability. Magnetic induction depends not only on the strength of the current passing through a straight conductor or coil, but also on the properties of the medium in which the magnetic field is created. The quantity characterizing the magnetic properties of the medium is the absolute magnetic permeability? A. Its unit is the henry per meter (1 H/m = 1 Ohm*s/m).
In a medium with greater magnetic permeability, an electric current of a certain strength creates a magnetic field with greater induction. It has been established that the magnetic permeability of air and all substances, with the exception of ferromagnetic materials (see § 18), has approximately the same value as the magnetic permeability of vacuum. The absolute magnetic permeability of vacuum is called the magnetic constant, ? o \u003d 4? * 10 -7 Gn / m. The magnetic permeability of ferromagnetic materials is thousands and even tens of thousands of times greater than the magnetic permeability of non-ferromagnetic substances. Permeability ratio? and any substance to the magnetic permeability of vacuum? o is called the relative magnetic permeability:
? = ? A /? O (42)
Magnetic field strength. The intensity And does not depend on the magnetic properties of the medium, but takes into account the influence of the current strength and the shape of the conductors on the intensity of the magnetic field at a given point in space. Magnetic induction and intensity are related by the relation
H=B/? a = b/(?? o) (43)
Consequently, in a medium with a constant magnetic permeability, the magnetic field induction is proportional to its strength.
Magnetic field strength is measured in amperes per meter (A/m) or amperes per centimeter (A/cm).
Determination of the magnetic field. His sources
Definition
A magnetic field is one of the forms of an electromagnetic field that acts only on moving bodies that have an electric charge or magnetized bodies, regardless of their movement.
The sources of this field are direct electric currents, moving electric charges (bodies and particles), magnetized bodies, alternating electric fields. Sources of a constant magnetic field are direct currents.
Magnetic field properties
At a time when the study of magnetic phenomena had just begun, researchers paid special attention to the existence of poles in magnetized bars. In them, the magnetic properties were especially pronounced. It was clearly seen that the poles of the magnet are different. Opposite poles attracted, and like poles repelled. Hilbert expressed the idea of the existence of "magnetic charges". These representations were supported and developed by Coulomb. On the basis of Coulomb's experiments, the force characteristic of the magnetic field became the force with which the magnetic field acts on a magnetic charge equal to unity. Coulomb drew attention to the essential differences between the phenomena in electricity and magnetism. The difference is already manifested in the fact that electric charges can be divided and bodies with an excess of positive or negative charge can be obtained, while it is impossible to separate the north and south poles of a magnet and get a body with only one pole. From the impossibility of dividing the magnet into exclusively "northern" or "southern" Coulomb decided that these two types of charges are inseparable in each elementary particle of the magnetizing substance. Thus, it was recognized that each particle of matter - an atom, a molecule, or a group of them - is something like a micro magnet with two poles. The magnetization of the body in this case is the process of orientation of its elementary magnets under the influence of an external magnetic field (analogous to the polarization of dielectrics).
The interaction of currents is realized by means of magnetic fields. Oersted discovered that a magnetic field is excited by a current and has an orienting effect on a magnetic needle. Oersted's conductor with current was located above the magnetic needle, which could rotate. When the current flowed in the conductor, the arrow turned perpendicular to the wire. A change in the direction of the current caused a reorientation of the arrow. It followed from Oersted's experiment that the magnetic field has a direction and must be characterized by a vector quantity. This quantity was called magnetic induction and denoted: $\overrightarrow(B).$ $\overrightarrow(B)$ is similar to the intensity vector for the electric field ($\overrightarrow(E)$). The analogue of the displacement vector $\overrightarrow(D)\$ for the magnetic field is the vector $\overrightarrow(H)$, called the vector of the magnetic field strength.
A magnetic field only affects a moving electric charge. A magnetic field is generated by moving electric charges.
The magnetic field of a moving charge. The magnetic field of a coil with current. Superposition principle
The magnetic field of an electric charge that moves at a constant speed has the form:
\[\overrightarrow(B)=\frac((\mu )_0)(4\pi )\frac(q\left[\overrightarrow(v)\overrightarrow(r)\right])(r^3)\left (1\right),\]
where $(\mu )_0=4\pi \cdot (10)^(-7)\frac(H)(m)(v\SI)$ is the magnetic constant, $\overrightarrow(v)$ is the velocity charge motion, $\overrightarrow(r)$ is the radius vector that determines the location of the charge, q is the charge value, $\left[\overrightarrow(v)\overrightarrow(r)\right]$ is the vector product.
Magnetic induction of an element with current in the SI system:
where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is given by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. The direction of the vector $\overrightarrow(dB)$ is perpendicular to the plane containing $\overrightarrow(dl)$ and $\overrightarrow(r)$. Determined by the right screw rule.
For a magnetic field, the superposition principle holds:
\[\overrightarrow(B)=\sum((\overrightarrow(B))_i\left(3\right),)\]
where $(\overrightarrow(B))_i$ are individual fields generated by moving charges, $\overrightarrow(B)$ is the total induction of the magnetic field.
Example 1
Task: Find the ratio of the forces of the magnetic and Coulomb interaction of two electrons that move with the same speed $v$ in parallel. The distance between particles is constant.
\[\overrightarrow(F_m)=q\left[\overrightarrow(v)\overrightarrow(B)\right]\left(1.1\right).\]
The field that the second moving electron creates is:
\[\overrightarrow(B)=\frac((\mu )_0)(4\pi )\frac(q\left[\overrightarrow(v)\overrightarrow(r)\right])(r^3)\left (1.2\right).\]
Let the distance between electrons be $a=r\ (constant)$. We use the algebraic property of the vector product (the Lagrange identity ($\left[\overrightarrow(a)\left[\overrightarrow(b)\overrightarrow(c)\right]\right]=\overrightarrow(b)\left(\overrightarrow(a )\overrightarrow(c)\right)-\overrightarrow(c)\left(\overrightarrow(a)\overrightarrow(b)\right)$))
\[(\overrightarrow(F))_m=\frac((\mu )_0)(4\pi )\frac(q^2)(a^3)\left[\overrightarrow(v)\left[\overrightarrow (v)\overrightarrow(a)\right]\right]=\left(\overrightarrow(v)\left(\overrightarrow(v)\overrightarrow(a)\right)-\overrightarrow(a)\left(\overrightarrow (v)\overrightarrow(v)\right)\right)=-\frac((\mu )_0)(4\pi )\frac(q^2\overrightarrow(a)v^2)(a^3) \ ,\]
$\overrightarrow(v)\left(\overrightarrow(v)\overrightarrow(a)\right)=0$ because $\overrightarrow(v\bot )\overrightarrow(a)$.
Force modulus $F_m=\frac((\mu )_0)(4\pi )\frac(q^2v^2)(a^2),\ $q=q_e=1.6\cdot 10^( -19)Cl$.
The modulus of the Coulomb force that acts on an electron in the field is equal to:
Let's find the ratio of forces $\frac(F_m)(F_q)$:
\[\frac(F_m)(F_q)=\frac((\mu )_0)(4\pi )\frac(q^2v^2)(a^2):\frac(q^2)((4 \pi (\varepsilon )_0a)^2)=(\mu )_0((\varepsilon )_0v)^2.\]
Answer: $\frac(F_m)(F_q)=(\mu )_0((\varepsilon )_0v)^2.$
Example 2
Task: A direct current of force I circulates along a coil with current in the form of a circle of radius R. Find the magnetic induction at the center of the circle.
We select an elementary section on a current-carrying conductor (Fig. 1), as a basis for solving the problem, we use the formula for the induction of a coil element with current:
where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is given by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. Based on Fig. 1 $\vartheta=90()^\circ $, therefore (2.1) will be simplified, in addition, the distance from the center of the circle (the point where we are looking for the magnetic field) of the conductor element with current is constant and equal to the radius of the coil (R), therefore we have:
All current elements will generate magnetic fields that are directed along the x axis. This means that the resulting magnetic field induction vector can be found as the sum of the projections of individual vectors $\ \ \overrightarrow(dB).$ Then, according to the superposition principle, the total magnetic field induction can be obtained by going to the integral:
Substituting (2.2) into (2.3), we get:
Answer: $B$=$\frac((\mu )_0)(2)\frac(I)(R).$
On the Internet there are a lot of topics devoted to the study of the magnetic field. It should be noted that many of them differ from the average description that exists in school textbooks. My task is to collect and systematize all the freely available material on the magnetic field in order to focus the New Understanding of the magnetic field. The study of the magnetic field and its properties can be done using a variety of techniques. With the help of iron filings, for example, a competent analysis was carried out by Comrade Fatyanov at http://fatyf.narod.ru/Addition-list.htm
With the help of a kinescope. I do not know the name of this person, but I know his nickname. He calls himself "The Wind". When a magnet is brought to the kinescope, a "honeycomb picture" is formed on the screen. You might think that the "grid" is a continuation of the kinescope grid. This is a method of visualizing the magnetic field.
I began to study the magnetic field with the help of a ferrofluid. It is the magnetic fluid that maximally visualizes all the subtleties of the magnetic field of the magnet.
From the article "what is a magnet" we found out that a magnet is fractalized, i.e. a scaled-down copy of our planet, the magnetic geometry of which is as identical as possible to a simple magnet. The planet earth, in turn, is a copy of what it was formed from - the sun. We found out that a magnet is a kind of inductive lens that focuses on its volume all the properties of the global magnet of the planet earth. There is a need to introduce new terms with which we will describe the properties of the magnetic field.
The induction flow is the flow that originates at the poles of the planet and passes through us in a funnel geometry. The planet's north pole is the entrance to the funnel, the planet's south pole is the exit of the funnel. Some scientists call this stream the ethereal wind, saying that it is "of galactic origin." But this is not an "ethereal wind" and no matter what the ether is, it is an "induction river" that flows from pole to pole. The electricity in lightning is of the same nature as the electricity produced by the interaction of a coil and a magnet.
The best way to understand what a magnetic field is - to see him. It is possible to think and make countless theories, but from the standpoint of understanding the physical essence of the phenomenon, it is useless. I think that everyone will agree with me, if I repeat the words, I don’t remember who, but the essence is that the best criterion is experience. Experience and more experience.
At home, I did simple experiments, but they allowed me to understand a lot. A simple cylindrical magnet ... And he twisted it this way and that. Poured magnetic fluid on it. It costs an infection, does not move. Then I remembered that on some forum I read that two magnets squeezed by the same poles in a sealed area increase the temperature of the area, and vice versa lower it with opposite poles. If temperature is a consequence of the interaction of fields, then why shouldn't it be the cause? I heated the magnet using a "short circuit" of 12 volts and a resistor by simply leaning the heated resistor against the magnet. The magnet heated up and the magnetic fluid began to twitch at first, and then completely became mobile. The magnetic field is excited by temperature. But how is it, I asked myself, because in the primers they write that temperature weakens the magnetic properties of a magnet. And this is true, but this "weakening" of the kagba is compensated by the excitation of the magnetic field of this magnet. In other words, the magnetic force does not disappear, but is transformed into the force of excitation of this field. Excellent Everything rotates and everything spins. But why does a rotating magnetic field have just such a geometry of rotation, and not some other one? At first glance, the movement is chaotic, but if you look through a microscope, you can see that in this movement system is present. The system does not belong to the magnet in any way, but only localizes it. In other words, a magnet can be considered as an energy lens that focuses perturbations in its volume.
The magnetic field is excited not only by an increase in temperature, but also by its decrease. I think that it would be more correct to say that the magnetic field is excited by a temperature gradient than by one of its specific signs. The fact of the matter is that there is no visible "restructuring" of the structure of the magnetic field. There is a visualization of the disturbance that passes through the region of this magnetic field. Imagine a perturbation that moves in a spiral from the north pole to the south through the entire volume of the planet. So the magnetic field of the magnet = the local part of this global flow. Do you understand? However, I'm not sure which particular thread...But the fact is that the thread. And there are not one stream, but two. The first is external, and the second is inside it and together with the first moves, but rotates in the opposite direction. The magnetic field is excited due to the temperature gradient. But we again distort the essence when we say "the magnetic field is excited." The fact is that it is already in an excited state. When we apply a temperature gradient, we distort this excitation into a state of unbalance. Those. we understand that the process of excitation is a constant process in which the magnetic field of the magnet is located. The gradient distorts the parameters of this process in such a way that we optically notice the difference between its normal excitation and the excitation caused by the gradient.
But why is the magnetic field of a magnet stationary in a stationary state? NO, it is also mobile, but relative to moving frames of reference, for example us, it is motionless. We move in space with this perturbation of Ra and it seems to us to be moving. The temperature we apply to the magnet creates some kind of local imbalance in this focusable system. A certain instability appears in the spatial lattice, which is the honeycomb structure. After all, bees do not build their houses from scratch, but they stick around the structure of space with their building material. Thus, based on purely experimental observations, I conclude that the magnetic field of a simple magnet is a potential system of local imbalance of the lattice of space, in which, as you may have guessed, there is no place for atoms and molecules that no one has ever seen. Temperature is like an "ignition key" in this local system, includes an imbalance. At the moment, I am carefully studying the methods and means of managing this imbalance.
What is a magnetic field and how is it different from an electromagnetic field?
What is a torsion or energy-informational field?
It's all one and the same, but localized by different methods.
Current strength - there is a plus and a repulsive force,
tension is a minus and a force of attraction,
a short circuit, or let's say a local imbalance of the lattice - there is a resistance to this interpenetration. Or the interpenetration of father, son and holy spirit. Let's remember that the metaphor "Adam and Eve" is an old understanding of X and YG chromosomes. For the understanding of the new is a new understanding of the old. "Strength" - a whirlwind emanating from the constantly rotating Ra, leaving behind an informational weave of itself. Tension is another vortex, but inside the main vortex of Ra and moving along with it. Visually, this can be represented as a shell, the growth of which occurs in the direction of two spirals. The first is external, the second is internal. Or one inside itself and clockwise, and the second out of itself and counterclockwise. When two vortices interpenetrate each other, they form a structure, like the layers of Jupiter, which move in different directions. It remains to understand the mechanism of this interpenetration and the system that is formed.
Approximate tasks for 2015
1. Find methods and means of unbalancing control.
2. Identify the materials that most affect the imbalance of the system. Find the dependence on the state of the material according to table 11 of the child.
3. If every living being, in its essence, is the same localized imbalance, then it must be "seen". In other words, it is necessary to find a method for fixing a person in other frequency spectra.
4. The main task is to visualize non-biological frequency spectra in which the continuous process of human creation takes place. For example, with the help of the progress tool, we analyze the frequency spectra that are not included in the biological spectrum of human feelings. But we only register them, but we cannot "realize" them. Therefore, we do not see further than our senses can comprehend. Here is my main goal for 2015. Find a technique for technical awareness of a non-biological frequency spectrum in order to see the information basis of a person. Those. in fact, his soul.
A special kind of study is the magnetic field in motion. If we pour ferrofluid on a magnet, it will occupy the volume of the magnetic field and will be stationary. However, you need to check the experience of "Veterok" where he brought the magnet to the monitor screen. There is an assumption that the magnetic field is already in an excited state, but the volume of liquid kagba restrains it in a stationary state. But I haven't checked yet.
The magnetic field can be generated by applying temperature to the magnet, or by placing the magnet in an induction coil. It should be noted that the liquid is excited only at a certain spatial position of the magnet inside the coil, making up a certain angle to the coil axis, which can be found empirically.
I have done dozens of experiments with moving ferrofluid and set myself goals:
1. Reveal the geometry of fluid motion.
2. Identify the parameters that affect the geometry of this movement.
3. What is the place of fluid movement in the global movement of the planet Earth.
4. Whether the spatial position of the magnet and the geometry of movement acquired by it depend.
5. Why "ribbons"?
6. Why Ribbons Curl
7. What determines the vector of twisting of the tapes
8. Why the cones are displaced only by means of nodes, which are the vertices of the honeycomb, and only three adjacent ribbons are always twisted.
9. Why does the displacement of the cones occur abruptly, upon reaching a certain "twist" in the nodes?
10. Why the size of the cones is proportional to the volume and mass of the liquid poured onto the magnet
11. Why the cone is divided into two distinct sectors.
12. What is the place of this "separation" in terms of interaction between the poles of the planet.
13. How the fluid motion geometry depends on the time of day, season, solar activity, experimenter's intention, pressure and additional gradients. For example, a sharp change "cold hot"
14. Why the geometry of cones identical with Varji geometry- the special weapons of the returning gods?
15. Are there any data in the archives of special services of 5 automatic weapons about the purpose, availability or storage of samples of this type of weapon.
16. What do the gutted pantries of knowledge of various secret organizations say about these cones and whether the geometry of the cones is connected with the Star of David, the essence of which is the identity of the geometry of the cones. (Masons, Jews, Vaticans, and other inconsistent formations).
17. Why there is always a leader among the cones. Those. a cone with a "crown" on top, which "organizes" the movements of 5,6,7 cones around itself.
cone at the moment of displacement. Jerk. "... only by moving the letter "G" I will reach him "...
A magnet is a body that forms a magnetic field around itself.
The force created by the magnet will act on certain metals: iron, nickel and cobalt. Objects made of these metals are attracted by a magnet.
(the match and the cork are not attracted, the nail is only to the right half of the magnet, the paper clip is to any place)
There are two areas where the force of attraction is maximum. They are called poles. If a magnet is suspended on a thin thread, it will unfold in a certain way. One end will always point north and the other end south. Therefore, one pole is called north, and the other is called south. 
You can visually consider the effect of the magnetic field formed around the magnet. Let's place the magnet on the surface, on which the metal filings were previously poured. Under the action of a magnetic field, the sawdust will be arranged in the form of elliptical curves. By the form of these curves, one can imagine how the lines of the magnetic field are located in space. Their direction is usually designated from north to south. 
If we take two identical magnets and try to bring them closer by poles, we will find out that different poles attract, and the same ones repel. 
Our Earth also has a magnetic field called the Earth's magnetic field. The north arrow always points north. Therefore, the geographic north pole of the Earth is the south magnetic pole, since opposite magnetic poles attract. Likewise, the south geographic pole is the north magnetic pole. 
The north end of the compass needle always points north, as it is attracted by the south magnetic pole of the Earth.
If we place a compass under a wire that is stretched in a north-south direction and through which current flows, we will see that the magnetic needle deviates. This proves that electric current creates a magnetic field around itself. 
If we place several compasses under a wire through which an electric current flows, we will see that all the arrows deviate by the same angle. This means that the magnetic field created by the wire is the same in different areas. Therefore, we can conclude that the magnetic field lines for each conductor have the form of concentric circles. 
The direction of the magnetic field lines can be determined using the right hand rule. To do this, mentally wrap your right hand around a conductor with an electric current so that the outstretched thumb of your right hand shows the direction of the electric current, then the bent fingers show the direction of the magnetic field lines. 
If we twist a metal wire into a spiral and run an electric current through it, then the magnetic fields of each individual turn are summed up in the total field of the spiral. 
The action of the magnetic field of the spiral is similar to the action of the magnetic field of a permanent magnet. This principle formed the basis for the creation of an electromagnet. It, like a permanent magnet, has a south and a north pole. The North Pole is where the magnetic field lines come out. 
The strength of a permanent magnet does not change over time. An electromagnet is different. There are three ways to change the strength of an electromagnet.
First way. Place a metal core inside the spiral. In this case, the actions of the magnetic field of the core and the magnetic field of the spiral are summed up.
The second way. Increase the number of turns of the spiral. The more turns the spiral has, the greater the effect of the force of the magnetic field.
The third way. Let's increase the strength of the electric current that flows in the spiral. The magnetic fields of individual coils will increase, therefore, the total magnetic field of the spiral will also increase. 
Speaker
The loudspeaker device includes an electromagnet and a permanent magnet. The electromagnet, which is connected to the loudspeaker membrane, is put on a rigidly fixed permanent magnet. In this case, the membrane remains mobile. Let us pass an alternating electric current through the electromagnet, the form of which depends on sound vibrations. As the electric current changes, the effect of the magnetic field in the electromagnet changes.
As a result, the electromagnet will be attracted or repelled by a permanent magnet with different strengths. Moreover, the loudspeaker membrane will perform exactly the same oscillations as an electromagnet. Thus, what was said into the microphone, we will hear through the loudspeaker. 
call
An electric doorbell can be classified as an electrical relay. The cause of the intermittent sound signal is the periodic short circuits and openings of the electrical circuit.
When the bell button is pressed, the electrical circuit is closed. The bell tongue is attracted by an electromagnet and hits the bell. In this case, the tongue opens the electrical circuit. The current stops flowing, the electromagnet does not work and the tongue returns to its original position. The electric circuit closes again, the tongue is again attracted by the electromagnet and hits the bell. This process will continue as long as we press the call button. 
electric motor
Install a freely rotating magnetic needle in front of the electromagnet and spin it. We can maintain this movement if we turn on the electromagnet at the moment when the magnetic needle turns with the same pole towards the electromagnet.
The force of attraction of the electromagnet is sufficient to keep the rotational motion of the arrow constant. 
(in the picture, the magnet receives a pulse whenever the red arrow is near and the button is pressed. If the button is pressed when the green arrow is near, the electromagnet stops)
This principle is the basis of the electric motor. Only it is not a magnetic needle that rotates in it, but an electromagnet, called an armature, in a statically fixed horseshoe-shaped magnet, which is called a stator. Due to repeated short circuits and openings of the circuit, the electromagnet, i.e. anchor, will continuously rotate. 
Electric current enters the armature through two contacts, which are two isolated half rings. This causes the electromagnet to constantly change polarity. When finding opposite poles one against the other, the motor starts to slow down the rotation. But at this moment, the electromagnet changes polarity, and now one against the other are the same poles. They repel each other and the motor keeps spinning. 
Generator
We connect a voltmeter to the ends of the spiral and begin to swing a permanent magnet in front of its turns. In this case, the voltmeter will show the presence of voltage. From this we can conclude that the electrical conductor is affected by a changing magnetic field.
From this follows the law of electric induction: voltage will exist at the ends of an induction coil as long as the coil is in a changing magnetic field.
The more turns an induction coil has, the more voltage is generated at its ends. The voltage can be increased by making the magnetic field stronger or by making it change faster. The metal core inserted inside the induction coil increases the inductive voltage as the magnetic field increases due to the magnetization of the core. 
(the magnet begins to wave more strongly in front of the coil, as a result of which the voltmeter needle deviates much more)
A generator is the opposite of an electric motor. Anchor, i.e. electromagnet rotates in the magnetic field of a permanent magnet. Due to the rotation of the armature, the magnetic field acting on it is constantly changing. As a result, the resulting inductive voltage changes. During a full rotation of the armature, the voltage will be positive half the time and negative half the time. An example of this is a wind generator that produces alternating voltage. 
Transformer
According to the law of induction, voltage arises if the magnetic field in the induction coil changes. But the magnetic field of the coil will change only if an alternating voltage appears in it.
The magnetic field changes from zero to a finite value. If you connect the coil to a voltage source, then the resulting alternating magnetic field will create a short-term inductive voltage that will counteract the main voltage. It is not necessary to use two coils to observe the occurrence of an inductive voltage. This can be done with one coil, but then such a process is called self-induction. The voltage in the coil reaches its maximum after some time, when the magnetic field stops changing and becomes constant. 
In the same way, the magnetic field changes if we disconnect the coil from the voltage source. In this case, the phenomenon of self-induction also occurs, which counteracts the falling voltage. Therefore, the voltage drops to zero not instantly, but with a certain delay. 
If we constantly connect and disconnect a voltage source to the coil, then the magnetic field around it will constantly change. At the same time, an alternating induction voltage also occurs. Now, instead, connect the coil to an AC voltage source. After some time, an alternating inductive voltage appears. 
Connect the first coil to an AC voltage source. Thanks to the metal core, the resulting alternating magnetic field will also act on the second coil. This means that alternating voltage can be transferred from one electrical circuit to another, even if these circuits are not connected to one another. 
If we take two identical coils, then in the second we can get the same voltage that acts on the first coil. This phenomenon is used in transformers. Only the purpose of the transformer is to create in the second coil a different voltage than the first. To do this, the second coil must have more or less turns. 
If the first coil had 1000 turns and the second coil had 10, then the voltage in the second circuit would be only a hundredth of the voltage in the first. But the current strength increases almost a hundred times. Therefore, high voltage transformers are needed to create a large current. 
Magnetic field and its characteristics
Lecture plan:
Magnetic field, its properties and characteristics.
A magnetic field- the form of existence of matter surrounding moving electric charges (conductors with current, permanent magnets).
This name is due to the fact that, as the Danish physicist Hans Oersted discovered in 1820, it has an orienting effect on the magnetic needle. Oersted's experiment: a magnetic needle was placed under a wire with current, rotating on a needle. When the current was turned on, it was installed perpendicular to the wire; when changing the direction of the current, it turned in the opposite direction.
The main properties of the magnetic field:
generated by moving electric charges, conductors with current, permanent magnets and an alternating electric field;
acts with force on moving electric charges, conductors with current, magnetized bodies;
an alternating magnetic field generates an alternating electric field.
It follows from Oersted's experience that the magnetic field is directional and must have a vector force characteristic. It is designated and called magnetic induction.
The magnetic field is depicted graphically using magnetic lines of force or lines of magnetic induction. magnetic force lines are called lines along which iron filings or axes of small magnetic arrows are located in a magnetic field. At each point of such a line, the vector is directed tangentially.
The lines of magnetic induction are always closed, which indicates the absence of magnetic charges in nature and the vortex nature of the magnetic field.
Conventionally, they leave the north pole of the magnet and enter the south. The density of the lines is chosen so that the number of lines per unit area perpendicular to the magnetic field is proportional to the magnitude of the magnetic induction.
H 
Magnetic solenoid with current
The direction of the lines is determined by the rule of the right screw. Solenoid - a coil with current, the turns of which are located close to each other, and the diameter of the turn is much less than the length of the coil.
The magnetic field inside the solenoid is uniform. A magnetic field is called homogeneous if the vector is constant at any point.
The magnetic field of a solenoid is similar to the magnetic field of a bar magnet.
WITH 
The olenoid with current is an electromagnet.
Experience shows that for a magnetic field, as well as for an electric field, superposition principle: the induction of the magnetic field created by several currents or moving charges is equal to the vector sum of the inductions of the magnetic fields created by each current or charge:
The vector is entered in one of 3 ways:
a) from Ampère's law;
b) by the action of a magnetic field on a loop with current;
c) from the expression for the Lorentz force.
A 
mper experimentally established that the force with which the magnetic field acts on the element of the conductor with current I, located in a magnetic field, is directly proportional to the force
current I and the vector product of the length element and the magnetic induction:
- Ampère's law
H 
The direction of the vector can be found according to the general rules of the vector product, from which the rule of the left hand follows: if the palm of the left hand is positioned so that the magnetic lines of force enter it, and 4 outstretched fingers are directed along the current, then the bent thumb will show the direction of the force.
The force acting on a wire of finite length can be found by integrating over the entire length.
For I = const, B=const, F = BIlsin
If =90 0 , F = BIl
Magnetic field induction- a vector physical quantity numerically equal to the force acting in a uniform magnetic field on a conductor of unit length with unit current, located perpendicular to the magnetic field lines.
1Tl - induction of a uniform magnetic field, in which a 1m long conductor with a current of 1A, located perpendicular to the magnetic field lines, is acted upon by a force of 1N.
So far, we have considered macrocurrents flowing in conductors. However, according to Ampere's assumption, in any body there are microscopic currents due to the movement of electrons in atoms. These microscopic molecular currents create their own magnetic field and can turn in the fields of macrocurrents, creating an additional magnetic field in the body. The vector characterizes the resulting magnetic field created by all macro- and microcurrents, i.e. for the same macrocurrent, the vector in different media has different values.
The magnetic field of macrocurrents is described by the magnetic intensity vector .
For a homogeneous isotropic medium
0 \u003d 410 -7 H / m - magnetic constant, 0 \u003d 410 -7 N / A 2,
- magnetic permeability of the medium, showing how many times the magnetic field of macrocurrents changes due to the field of microcurrents of the medium.
magnetic flux. Gauss' theorem for magnetic flux.
vector flow(magnetic flux) through the pad dS is called a scalar value equal to
where is the projection onto the direction of the normal to the site;
- angle between vectors and .
directional surface element,
The vector flux is an algebraic quantity,
If 
- when leaving the surface;
If 
- at the entrance to the surface.
The flux of the magnetic induction vector through an arbitrary surface S is equal to
For a uniform magnetic field =const,
1 Wb - magnetic flux passing through a flat surface of 1 m 2 located perpendicular to a uniform magnetic field, the induction of which is equal to 1 T.
The magnetic flux through the surface S is numerically equal to the number of magnetic lines of force crossing the given surface.
Since the lines of magnetic induction are always closed, for a closed surface the number of lines entering the surface (Ф 0), therefore, the total flux of magnetic induction through a closed surface is zero.
- Gauss theorem: the flux of the magnetic induction vector through any closed surface is zero.
This theorem is a mathematical expression of the fact that in nature there are no magnetic charges on which the lines of magnetic induction would begin or end.
Biot-Savart-Laplace law and its application to the calculation of magnetic fields.
The magnetic field of direct currents of various shapes was studied in detail by fr. scientists Biot and Savart. They found that in all cases the magnetic induction at an arbitrary point is proportional to the strength of the current, depends on the shape, dimensions of the conductor, the location of this point in relation to the conductor and on the medium.
The results of these experiments were summarized by fr. mathematician Laplace, who took into account the vector nature of magnetic induction and hypothesized that the induction at each point is, according to the principle of superposition, the vector sum of the inductions of the elementary magnetic fields created by each section of this conductor.
Laplace in 1820 formulated a law, which was called the Biot-Savart-Laplace law: each element of a conductor with current creates a magnetic field, the induction vector of which at some arbitrary point K is determined by the formula:
- Biot-Savart-Laplace law.
It follows from the Biot-Sovar-Laplace law that the direction of the vector coincides with the direction of the cross product. The same direction is given by the rule of the right screw (gimlet).
Given that ,
Conductor element co-directional with current;
Radius vector connecting with point K;
The Biot-Savart-Laplace law is of practical importance, because allows you to find at a given point in space the induction of the magnetic field of the current flowing through the conductor of finite size and arbitrary shape.
For an arbitrary current, such a calculation is a complex mathematical problem. However, if the current distribution has a certain symmetry, then the application of the superposition principle together with the Biot-Savart-Laplace law makes it possible to calculate specific magnetic fields relatively simply.
Let's look at some examples.
A. Magnetic field of a rectilinear conductor with current.
for a conductor of finite length:
for a conductor of infinite length: 1 = 0, 2 =
B. Magnetic field at the center of the circular current:
=90 0 , sin=1,
Oersted in 1820 experimentally found that the circulation in a closed circuit surrounding a system of macrocurrents is proportional to the algebraic sum of these currents. The coefficient of proportionality depends on the choice of the system of units and in SI is equal to 1.
C 
the circulation of a vector is called a closed-loop integral.
This formula is called circulation theorem or total current law:
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