The picture shows a uniform magnetic field. Homogeneous means the same at all points in a given volume. A surface with area S is placed in a field. The field lines intersect the surface.
Determination of magnetic flux:
Magnetic flux Ф through the surface S is the number of lines of the magnetic induction vector B passing through the surface S.
Magnetic flux formula:
here α is the angle between the direction of the magnetic induction vector B and the normal to the surface S.
From the magnetic flux formula it is clear that the maximum magnetic flux will be at cos α = 1, and this will happen when vector B is parallel to the normal to surface S. The minimum magnetic flux will be at cos α = 0, this will be when vector B is perpendicular to the normal to surface S, because in this case the lines of vector B will be slide along surface S without crossing it.
And according to the definition of magnetic flux, only those lines of the magnetic induction vector are taken into account that intersect a given surface.
Magnetic flux is measured in webers (volt-seconds): 1 wb = 1 v * s. In addition, Maxwell is used to measure magnetic flux: 1 wb = 10 8 μs. Accordingly, 1 μs = 10 -8 vb.
Magnetic flux is a scalar quantity.
ENERGY OF THE MAGNETIC FIELD OF CURRENT
Around a current-carrying conductor there is a magnetic field that has energy. Where does it come from? The current source included in the electrical circuit has a reserve of energy. At the moment of closing the electrical circuit, the current source spends part of its energy to overcome the effect of the self-inductive emf that arises. This part of the energy, called the current’s own energy, goes to the formation of a magnetic field. The energy of the magnetic field is equal to the intrinsic energy of the current. The current's own energy is numerically equal to the work that the current source must do to overcome Self-induced emf to create current in the circuit.
The energy of the magnetic field created by the current is directly proportional to the square of the current. Where does the magnetic field energy go after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)
4.1. Law of electromagnetic induction. Self-induction. Inductance
Basic formulas
· Law electromagnetic induction(Faraday's law):
,
(39)
where is the induction emf; is the total magnetic flux (flux linkage).
· Magnetic flux created by current in the circuit,
where is the inductance of the circuit; is the current strength.
· Faraday's law as applied to self-induction
· Induction emf, which occurs when the frame rotates with current in a magnetic field,
where is the magnetic field induction; is the area of the frame; is the angular velocity of rotation.
Solenoid inductance
,
(43)
where is the magnetic constant; is the magnetic permeability of the substance; is the number of turns of the solenoid; is the cross-sectional area of the turn; is the length of the solenoid.
Current strength when opening the circuit
where is the current established in the circuit; is the inductance of the circuit; is the resistance of the circuit; is the opening time.
Current strength when closing the circuit
.
(45)
Relaxation time
Examples of problem solving
Example 1.
The magnetic field changes according to the law 
, where = 15 mT,. A circular conducting coil with a radius = 20 cm is placed in a magnetic field at an angle to the direction of the field (at the initial moment of time). Find the induced emf arising in the coil at time = 5 s.
Solution
According to the law of electromagnetic induction, the inductive emf arising in a coil is , where is the magnetic flux coupled in the coil.
where is the area of the turn; is the angle between the direction of the magnetic induction vector and the normal to the contour:.
Let's substitute the numerical values: = 15 mT,, = 20 cm = = 0.2 m,.
Calculations give 
.
|
Example 2 In a uniform magnetic field with induction = 0.2 T, there is a rectangular frame, the moving side of which, length = 0.2 m, moves at a speed = 25 m/s perpendicular to the field induction lines (Fig. 42). Determine the induced emf arising in the circuit. Solution When conductor AB moves in a magnetic field, the area of the frame increases, therefore, the magnetic flux through the frame increases and an induced emf occurs. |
|
According to Faraday's law, where, then, but, therefore.
The “–” sign shows that the induced emf and induced current directed counterclockwise.
SELF-INDUCTION
Each conductor through which electric current flows is in its own magnetic field.
When the current strength changes in the conductor, the m.field changes, i.e. the magnetic flux created by this current changes. A change in magnetic flux leads to the emergence of a vortex electric field and an induced emf appears in the circuit. 
This phenomenon is called self-induction. Self-induction is the phenomenon of the occurrence of induced emf in an electrical circuit as a result of a change in current strength. The resulting emf is called self-induced emf
Manifestation of the phenomenon of self-induction
Circuit closure 
When there is a short circuit in the electrical circuit, the current increases, which causes an increase in the magnetic flux in the coil, and a vortex electric field appears, directed against the current, i.e. A self-induction emf arises in the coil, preventing the increase in current in the circuit (the vortex field inhibits the electrons). As a result L1 lights up later, than L2.
Open circuit 
When the electrical circuit is opened, the current decreases, a decrease in the flux in the coil occurs, and a vortex electrical field appears, directed like a current (trying to maintain the same current strength), i.e. A self-induced emf arises in the coil, maintaining the current in the circuit. As a result, L when turned off flashes brightly. Conclusion in electrical engineering, the phenomenon of self-induction manifests itself when the circuit is closed (the electric current increases gradually) and when the circuit is opened (the electric current does not disappear immediately).
INDUCTANCE
What does self-induced emf depend on? Electric current creates its own magnetic field. The magnetic flux through the circuit is proportional to the magnetic field induction (Ф ~ B), the induction is proportional to the current strength in the conductor (B ~ I), therefore the magnetic flux is proportional to the current strength (Ф ~ I). The self-induction emf depends on the rate of change of current in the electrical circuit, on the properties of the conductor (size and shape) and on the relative magnetic permeability of the medium in which the conductor is located. A physical quantity showing the dependence of the self-induction emf on the size and shape of the conductor and on the environment in which the conductor is located is called the self-induction coefficient or inductance. 
Inductance - physical. a value numerically equal to the self-inductive emf that occurs in the circuit when the current changes by 1 Ampere in 1 second. Inductance can also be calculated using the formula:
where Ф is the magnetic flux through the circuit, I is the current strength in the circuit.
SI units of inductance:
The inductance of the coil depends on: the number of turns, the size and shape of the coil and the relative magnetic permeability of the medium (possibly a core).
SELF-INDUCTION EMF
The self-inductive emf prevents the current from increasing when the circuit is turned on and the current from decreasing when the circuit is opened.
To characterize the magnetization of a substance in a magnetic field, it is used magnetic moment (P m ). It is numerically equal to the mechanical torque experienced by a substance in a magnetic field with an induction of 1 Tesla.
The magnetic moment of a unit volume of a substance characterizes it magnetization - I , is determined by the formula:
I=R m /V , (2.4)
Where V - volume of the substance.
Magnetization in the SI system is measured, like intensity, in Vehicle, a vector quantity.
The magnetic properties of substances are characterized volumetric magnetic susceptibility - c O , dimensionless quantity.
If any body is placed in a magnetic field with induction IN 0 , then its magnetization occurs. As a result, the body creates its own magnetic field with induction IN " , which interacts with the magnetizing field.
In this case, the induction vector in the medium (IN) will be composed of vectors:
B = B 0 + B " (vector sign omitted), (2.5)
Where IN " - induction of the own magnetic field of a magnetized substance.
The induction of its own field is determined by the magnetic properties of the substance, which are characterized by volumetric magnetic susceptibility - c O , the following expression is true: IN " = c O IN 0 (2.6)
Divide by m 0 expression (2.6):
IN " /m O = c O IN 0 /m 0
We get: N " = c O N 0 , (2.7)
But N " determines the magnetization of a substance I , i.e. N " = I , then from (2.7):
I = c O N 0 . (2.8)
Thus, if a substance is in an external magnetic field with a strength N 0 , then the induction inside it is determined by the expression:
B=B 0 + B " = m 0 N 0 +m 0 N " = m 0 (N 0 +I)(2.9)
The last expression is strictly true when the core (substance) is completely in an external uniform magnetic field (closed torus, infinitely long solenoid, etc.).
It would be logical to talk about another representative of passive radio elements - inductors. But the story about them will have to start from afar, remembering the existence of a magnetic field, because it is the magnetic field that surrounds and penetrates the coils, and it is in the magnetic field, most often alternating, that the coils work. In short, this is their habitat.
Magnetism as a property of matter
Magnetism is one of the the most important properties substances, as well as, for example, mass or electric field. The phenomena of magnetism, like electricity, have been known for a long time, but the science of that time could not explain the essence of these phenomena. An incomprehensible phenomenon was called “magnetism” after the city of Magnesia, which was once in Asia Minor. It was from ore mined nearby that permanent magnets were obtained.
But permanent magnets are not particularly interesting within the scope of this article. Since it was promised to talk about inductors, then we'll talk, most likely, about electromagnetism, because it is far from a secret that even around a wire with current there is a magnetic field.
IN modern conditions It is quite easy to study the phenomenon of magnetism at least at an initial level. To do this, you need to assemble a simple electrical circuit from a battery and a light bulb for a flashlight. You can use a regular compass as an indicator of the magnetic field, its direction and strength.
DC magnetic field
As you know, a compass shows the direction to the North. If the wires mentioned above are located nearby the simplest scheme, and turn on the light bulb, the compass needle will deviate slightly from its normal position.
By connecting another light bulb in parallel, you can double the current in the circuit, causing the angle of rotation of the arrow to increase slightly. This indicates that the magnetic field of the current-carrying wire has become larger. It is on this principle that pointer measuring instruments work.
If the polarity of the battery is reversed, then the compass needle will turn the other end - the direction of the magnetic field in the wires has also changed in direction. When the circuit is turned off, the compass needle will return to its rightful position. There is no current in the coil, and there is no magnetic field.
In all these experiments, the compass plays the role of a test magnetic needle, just as the study of a constant electric field is carried out by a test electric charge.
Based on such simple experiments, we can conclude that magnetism is born due to electric current: the stronger this current, the stronger the magnetic properties of the conductor. Where then does the magnetic field of permanent magnets come from, since no one connected a battery with wires to them?
Fundamental scientific research It has been proven that permanent magnetism is based on electrical phenomena: each electron is in its own electric field and has elementary magnetic properties. Only in most substances these properties mutually neutralize, and in some for some reason they combine into one large magnet.
Of course, in reality everything is not so primitive and simple, but, in general, even permanent magnets have their wonderful properties due to movement electric charges.
What are they like? magnetic lines?
Magnetic lines can be seen visually. IN school experience In physics lessons, for this purpose, metal filings are poured onto a sheet of cardboard, and a permanent magnet is placed below. By lightly tapping on a sheet of cardboard you can achieve the picture shown in Figure 1.
Picture 1.
It is easy to see that magnetic power lines leave the North Pole and enter the South Pole without breaking apart. Of course, we can say that it’s just the opposite, from the south to the north, but that’s the way it is, so from the north to the south. In the same way as they once accepted the direction of current from plus to minus.
If instead permanent magnet Pass a wire with current through the cardboard, then metal filings will show it, the conductor, the magnetic field. This magnetic field looks like concentric circular lines.
To study the magnetic field, you can do without sawdust. It is enough to move a test magnetic needle around a current-carrying conductor to see that the magnetic lines of force are indeed closed concentric circles. If you move the test arrow in the direction where the magnetic field deflects it, you will certainly return to the same point from where you started moving. Just like walking around the Earth: if you go without turning anywhere, then sooner or later you will come to the same place.
Figure 2.
The direction of the magnetic field of a current-carrying conductor is determined by the rule of a gimlet, a tool for drilling holes in wood. Everything is very simple here: the gimlet must be rotated so that its forward movement coincides with the direction of the current in the wire, then the direction of rotation of the handle will show where the magnetic field is directed.
Figure 3.
“The current is coming from us” - the cross in the middle of the circle is the feather of an arrow flying beyond the plane of the drawing, and where “The current is coming to us” shows the tip of an arrow flying from behind the plane of the sheet. At least, this is the explanation of these notations given in physics lessons at school.
Figure 4.
If we apply the gimlet rule to each conductor, then having determined the direction of the magnetic field in each conductor, we can confidently say that conductors with the same direction of current attract, and their magnetic fields add up. Conductors with currents of different directions repel each other, their magnetic field is compensated.
Inductor
If a current-carrying conductor is made in the form of a ring (turn), then it has its own magnetic poles, north and south. But the magnetic field of one turn is usually small. Much best results can be achieved by winding the wire in the form of a coil. This part is called an inductor or simply an inductor. In this case magnetic fields individual turns add up, mutually reinforcing each other.
Figure 5.
Figure 5 shows how the sum of the magnetic fields of the coil can be obtained. It seems that each turn can be powered from its own source, as shown in Fig. 5.2, but it’s easier to connect the turns in series (just wind them with one wire).
It is quite obvious that the more turns a coil has, the stronger its magnetic field. The magnetic field also depends on the current through the coil. Therefore, it is quite legitimate to estimate the ability of a coil to create a magnetic field by simply multiplying the current through the coil (A) by the number of turns (W). This value is called ampere - turns.
Core coil
The magnetic field created by the coil can be significantly increased if a core of ferromagnetic material is inserted inside the coil. Figure 6 shows a table with the relative magnetic permeability of various substances.
For example, transformer steel will make the magnetic field approximately 7..7.5 thousand times stronger than in the absence of a core. In other words, inside the core the magnetic field will rotate the magnetic needle 7000 times stronger (this can only be imagined mentally).
Figure 6.
At the top of the table are paramagnetic and diamagnetic substances. Relative magnetic permeability µ is given relative to vacuum. Consequently, paramagnetic substances slightly strengthen the magnetic field, and diamagnetic substances slightly weaken it. In general, these substances do not have much effect on the magnetic field. Although, at high frequencies, brass or aluminum cores are sometimes used to tune circuits.
At the bottom of the table are ferromagnetic substances that significantly enhance the magnetic field of a current-carrying coil. For example, a transformer steel core will make the magnetic field exactly 7500 times stronger.
How and how to measure the magnetic field
When you needed units for measurement electrical quantities, then we took the electron charge as a standard. From the charge of an electron, a very real and even tangible unit was formed - the coulomb, and on its basis everything turned out to be simple: ampere, volt, ohm, joule, watt, farad.
What can be taken as a starting point for measuring magnetic fields? It is very problematic to somehow bind an electron to a magnetic field. Therefore, the unit of measurement in magnetism is the conductor through which flows. D.C. at 1 A.
The main such characteristic is tension (H). It shows the force with which the magnetic field acts on the test conductor mentioned above if this happens in a vacuum. Vacuum is intended to exclude the influence of the environment, therefore this characteristic - tension is considered absolutely pure. The unit of tension is ampere per meter (a/m). This tension appears at a distance of 16cm from the conductor carrying a current of 1A.
The field strength only indicates theoretical ability magnetic field. The real ability to act is reflected by another value, magnetic induction (B). She is the one who shows real strength, with which the magnetic field acts on a conductor with a current of 1A.
Figure 7.
If a current of 1A flows in a conductor 1 m long, and it is pushed (attracted) with a force of 1 N (102 G), then they say that the value of magnetic induction at a given point is exactly 1 tesla.
Magnetic induction is a vector quantity, except numerical value it also has a direction that always coincides with the direction of the test magnetic needle in the magnetic field under study.
Figure 8.
The unit of magnetic induction is the tesla (TL), although in practice more is often used. small unit Gauss: 1TL = 10,000Gs. Is it a lot or a little? The magnetic field near a powerful magnet can reach several Tesla, near the magnetic compass needle no more than 100 Gauss, the Earth's magnetic field near the surface is approximately 0.01 Gauss and even lower.
The magnetic induction vector B characterizes the magnetic field at only one point in space. To evaluate the effect of a magnetic field in a certain space, another concept is introduced: magnetic flux (Φ).
Essentially, it represents the number of lines of magnetic induction passing through given space, through some area: Φ=B*S*cosα. This picture can be represented in the form of raindrops: one line is one drop (B), and all together is the magnetic flux Φ. This is how the magnetic power lines of the individual turns of the coil are connected into a common flux.
Figure 9.
In the SI system, the unit of magnetic flux is Weber (Wb), such a flux occurs when an induction of 1 Tesla acts on an area of 1 sq.m.
Magnetic flux in various devices (motors, transformers, etc.), as a rule, passes through a certain path, called a magnetic circuit or simply a magnetic circuit. If the magnetic circuit is closed (the core of a ring transformer), then its resistance is low, the magnetic flux passes unhindered and is concentrated inside the core. The figure below shows examples of coils with closed and open magnetic circuits.
Figure 10.
But the core can be sawed and a piece pulled out of it to create a magnetic gap. This will increase the overall magnetic resistance of the circuit, therefore reducing the magnetic flux, and overall the induction in the entire core will decrease. It's like soldering a large resistance in series into an electrical circuit.
Figure 11.
If the resulting gap is blocked with a piece of steel, it turns out that an additional section with lower magnetic resistance has been connected parallel to the gap, which will restore the disturbed magnetic flux. This is very similar to a shunt in electrical circuits. By the way, there is also a law for a magnetic circuit, which is called Ohm’s law for a magnetic circuit.
Figure 12.
The main part of the magnetic flux will go through the magnetic shunt. It is this phenomenon that is used in magnetic recording of audio or video signals: the ferromagnetic layer of the tape covers the gap in the core of the magnetic heads, and the entire magnetic flux is closed through the tape.
The direction of the magnetic flux created by the coil can be determined using the rule right hand: If four extended fingers indicate the direction of current in the coil, then thumb will show the direction of the magnetic lines as shown in Figure 13.
Figure 13.
It is generally accepted that magnetic lines leave the north pole and enter the south. Therefore the thumb is in in this case indicates the location of the south pole. You can check whether this is true again using the compass needle.
How does an electric motor work?
It is known that electricity can create light and heat, participate in electrochemical processes. After introducing the basics of magnetism, you can talk about how electric motors work.
Electric motors can be the most different designs, power and operating principle: for example constant and alternating current, stepper or collector. But with all the variety of designs, the principle of operation is based on the interaction of the magnetic fields of the rotor and stator.
To produce these magnetic fields, current is passed through the windings. The greater the current and the higher the magnetic induction of the external magnetic field, the more powerful the motor. Magnetic cores are used to enhance this field, which is why electric motors have so many steel parts. Some DC motor models use permanent magnets.
Figure 14.
Here, one might say, everything is clear and simple: we passed a current through a wire and got a magnetic field. Interaction with another magnetic field causes this conductor to move and also perform mechanical work.
The direction of rotation can be determined by the left-hand rule. If four extended fingers indicate the direction of the current in the conductor, and the magnetic lines enter the palm, then the bent thumb will indicate the direction of the conductor being pushed out in the magnetic field.
If there is an electrostatic field in the space around stationary electric charges, then in the space around moving charges (as well as around time-varying electric fields, as Maxwell originally assumed) there exists. This is easy to observe experimentally.
It is thanks to the magnetic field that electric currents interact with each other, as well as permanent magnets and currents with magnets. Compared with electrical interaction, magnetic interaction is significantly more powerful. This interaction was once studied by André-Marie Ampère.
In physics, the characteristic of a magnetic field is B, and the larger it is, the stronger the magnetic field. Magnetic induction B is a vector quantity, its direction coincides with the direction of the force acting on the north pole of a conventional magnetic needle placed at some point in the magnetic field - the magnetic field will orient the magnetic needle in the direction of vector B, that is, in the direction of the magnetic field.
Vector B at each point of the magnetic induction line is directed tangentially to it. That is, induction B characterizes the force effect of the magnetic field on the current. A similar role is played by the intensity E for the electric field, which characterizes the force effect of the electric field on the charge.
The simplest experiment with iron filings makes it possible to clearly demonstrate the phenomenon of the action of a magnetic field on a magnetized object, since in a constant magnetic field small pieces of a ferromagnet (such pieces are iron filings) become, magnetized along the field, magnetic needles, like small compass needles.
If you take a vertical copper conductor, and pass it through a hole in a horizontal sheet of paper (or plexiglass, or plywood), and then pour metal filings onto the sheet, and shake it a little, and then pass direct current through the conductor, it is easy to see how the sawdust will line up in the form of a vortex in circles around the conductor, in a plane perpendicular to the current in it.
These circles made of sawdust will be a symbolic image of the lines of magnetic induction B of the magnetic field of a current-carrying conductor. The center of the circles, in this experiment, will be located exactly in the center, along the axis of the conductor with current.
The direction of the magnetic induction vectors B of a current-carrying conductor is easy to determine or by the rule of the right screw: when the screw axis moves forward in the direction of the current in the conductor, the direction of rotation of the screw or the handle of the gimlet (we screw in or out the screw) will indicate the direction of the magnetic field around the current.
Why does the gimlet rule apply? Since the rotor operation (denoted in field theory by rot) used in Maxwell's two equations can be written formally as vector product(with the radar operator), and most importantly because the rotor vector field can be likened (represents an analogy) angular velocity rotation ideal liquid(as Maxwell himself imagined), the flow velocity field of which represents a given vector field, one can use for the rotor the same formulations of the rule that are described for angular velocity.
Thus, if you twist the gimlet in the direction of the vortex of the vector field, it will screw in the direction of the rotor vector of this field.
As you can see, unlike tension lines electrostatic field, which are open in space, the lines of magnetic induction surrounding the electric current are closed. If the lines electrical tension E start with positive charges and end on negative lines, then the lines of magnetic induction B are simply closed around the current generating them.
Now let's complicate the experiment. Instead of a straight conductor with current, consider a coil with current. Suppose it is convenient for us to position such a contour perpendicular to the plane of the drawing, with the current directed towards us on the left, and away from us on the right. If you now place a compass with a magnetic needle inside the coil with current, then the magnetic needle will indicate the direction of the magnetic induction lines - they will be directed along the axis of the coil.
Why? Because opposite sides from the plane of the coil will be similar to the poles of the magnetic needle. Where do the B lines come from - this is the northern one magnetic pole, which includes - South Pole. This is easy to understand if you first consider a conductor with current and its magnetic field, and then simply roll the conductor into a ring.
To determine the direction of the magnetic induction of a coil with current, they also use the gimlet rule or the right-hand screw rule. Place the tip of the gimlet in the center of the coil and begin to rotate it clockwise. Forward movement the gimlet will coincide in direction with the magnetic induction vector B at the center of the coil.
Obviously, the direction of the magnetic field of the current is related to the direction of the current in the conductor, whether it is a straight conductor or a coil.
It is generally accepted that the side of the coil or turn with current from which the lines of magnetic induction B come out (the direction of vector B is outward) is the north magnetic pole, and where the lines enter (vector B is directed inward) is the south magnetic pole.
If many turns with current form a long coil - a solenoid (the length of the coil is many times greater than its diameter), then the magnetic field inside it is uniform, that is, the magnetic induction lines B are parallel to each other and have the same density along the entire length of the coil. By the way, the magnetic field of a permanent magnet is similar from the outside to the magnetic field of a coil with current.
For a coil with current I, length l, with number of turns N, magnetic induction in vacuum will be numerically equal to:
So, the magnetic field inside the coil with current is uniform, and is directed from south to north pole(inside the coil!) Magnetic induction inside the coil is proportional in magnitude to the number of ampere-turns per unit length of the coil with current.
Electromagnetism is a set of phenomena caused by the connection of electric currents and magnetic fields. Sometimes this connection leads to undesirable effects. For example, current flowing through electrical cables on a ship causes unnecessary deflection of the ship's compass. However, electricity is often deliberately used to create high-intensity magnetic fields. An example is electromagnets. We'll talk about them today.
and magnetic flux
The intensity of the magnetic field can be determined by the number of magnetic flux lines per unit area. occurs wherever electric current flows, and the magnetic flux in the air is proportional to the latter. A straight wire carrying current can be bent into a coil. With a sufficiently small radius of the coil, this leads to an increase in the magnetic flux. In this case, the current strength does not increase.
The effect of magnetic flux concentration can be further enhanced by increasing the number of turns, that is, twisting the wire into a coil. The opposite is also true. The magnetic field of a current-carrying coil can be weakened by reducing the number of turns.
Let us derive an important relation. At the point maximum density magnetic flux (it contains the most flux lines per unit area), the relationship between the electric current I, the number of turns of wire n and the magnetic flux B is expressed as follows: In is proportional to B. A current of 12 A flowing through a coil of 3 turns creates exactly this the same magnetic field as a current of 3 A flowing through a coil of 12 turns. This is important to know when solving practical problems.
Solenoid
A coil of wound wire that creates a magnetic field is called a solenoid. Wires can be wound around iron (iron core). A non-magnetic base (for example, an air core) is also suitable. As you can see, you can use more than just iron to create the magnetic field of a current-carrying coil. In terms of flux magnitude, any non-magnetic core is equivalent to air. That is, the above relationship connecting current, number of turns and flux is satisfied quite accurately in this case. Thus, the magnetic field of a current-carrying coil can be weakened if this principle is applied.
Use of iron in solenoid
What is iron used for in a solenoid? Its presence affects the magnetic field of the current-carrying coil in two ways. It increases the current, often thousands of times or more. However, this may violate one important proportional dependence. It's about about that which exists between the magnetic flux and the current in air-core coils.
Microscopic regions in iron, domains (more precisely, they are built in one direction under the action of a magnetic field that is created by a current. As a result, in the presence of an iron core, this current creates a greater magnetic flux per unit cross-section of the wire. Thus, the flux density increases significantly. When all domains line up in the same direction, a further increase in current (or the number of turns in the coil) only slightly increases the magnetic flux density.
Let's now talk a little about induction. This an important part topic of interest to us.
Magnetic field induction of a current coil
Although the magnetic field of an iron-core solenoid is much stronger than the magnetic field of an air-core solenoid, its magnitude is limited by the properties of the iron. There is theoretically no limit to the size that is created by the air core coil. However, it is generally very difficult and expensive to obtain the enormous currents required to produce a field comparable in magnitude to that of an iron core solenoid. You don't always have to go this route.
What happens if you change the magnetic field of a coil carrying current? This action can create an electric current in the same way that a current creates a magnetic field. When a magnet approaches a conductor, the magnetic lines of force crossing the conductor induce a voltage in it. The polarity of the induced voltage depends on the polarity and direction of change of the magnetic flux. This effect is much stronger in a coil than in an individual turn: it is proportional to the number of turns in the winding. In the presence of an iron core, the induced voltage in the solenoid increases. With this method, it is necessary for the conductor to move relative to the magnetic flux. If the conductor does not cross the magnetic flux lines, no voltage will occur.
How do we get energy?
Electric generators produce current based on the same principles. Typically the magnet rotates between the coils. The magnitude of the induced voltage depends on the magnitude of the magnet's field and the speed of its rotation (they determine the rate of change of the magnetic flux). The voltage in a conductor is directly proportional to the speed of the magnetic flux in it.
In many generators, the magnet is replaced by a solenoid. In order to create a magnetic field in a current-carrying coil, the solenoid is connected to What will be the electrical power generated by the generator in this case? It is equal to the product of voltage and current. On the other hand, the relationship between the current in a conductor and magnetic flux makes it possible to use the flux created by an electric current in a magnetic field to obtain mechanical movement. Electric motors and some electrical measuring instruments operate on this principle. However, to create movement in them it is necessary to expend additional electrical power.
Strong magnetic fields
Currently, using it is possible to obtain an unprecedented intensity of the magnetic field of a coil with current. Electromagnets can be very powerful. In this case, the current flows without loss, i.e., does not cause heating of the material. This allows high voltages to be applied to air core solenoids and avoids saturation limitations. Such a powerful magnetic field of a current-carrying coil opens up very great prospects. Electromagnets and their applications are of interest to many scientists for good reason. After all strong fields can be used to move on magnetic levitation and create new types of electric motors and generators. They are capable of high power at low cost.
The energy of the magnetic field of a current coil is actively used by humanity. She is already long years widely used, in particular in railways. We will now talk about how the magnetic field lines of a current-carrying coil are used to regulate the movement of trains.
Magnets on railways
Railways typically use systems in which electromagnets and permanent magnets complement each other for greater safety. How do these systems work? The strong one is attached close to the rail at a certain distance from the traffic lights. As the train passes over the magnet, the axis of the permanent flat magnet in the driver's cabin rotates through a small angle, after which the magnet remains in the new position.
Regulation of traffic on the railway
The movement of a flat magnet triggers an alarm bell or siren. Then the following happens. After a couple of seconds, the driver’s cabin passes over the electromagnet, which is connected to the traffic light. If he gives the train the green light, then the electromagnet becomes energized and the axis of the permanent magnet in the car rotates to its original position, turning off the signal in the cabin. When the traffic light is red or yellow, the electromagnet is turned off, and then after a certain delay the brake is automatically applied, unless, of course, the driver forgot to do this. The brake circuit (as well as the sound signal) is connected to the network from the moment the magnet axis is turned. If the magnet returns to its original position during the delay, the brake does not engage.
Magnetic field and inductance
A magnetic field arises around any conductor through which current flows. This effect is called electromagnetism. Magnetic fields influence leveling electrons in atoms,
and can cause physical strength, capable of developing in space. Like electric fields
, magnetic fields can occupy completely empty space, And influence matter on distance .
A magnetic field has two main characteristics: magnetomotive force and magnetic flux. The total amount of field or its effect is called magnetic flux, and the force that creates this magnetic flux in space is called magnetomotive force. These two characteristics are roughly analogous to electric voltage (magnetomotive force) and electric current (magnetic flux) in a conductor. Magnetic flux, unlike electric current(which exists only where there are free electrons) can propagate in completely empty space. Space resists magnetic flow in the same way that a conductor resists electric current. The magnitude of the magnetic flux is equal to the magnetomotive force divided by the resistance of the medium.
The magnetic field is different from the electric field. If the electric field depends on the available number of unlike charges (the more electric charges of one type on one conductor, and the opposite on the other, the greater the electric field between these conductors), then the magnetic field is created by the flow of electrons (the more intense the movement of electrons, the more magnetic field around them).
A device capable of storing magnetic field energy is called an inductor. The shape of the coil creates a much stronger magnetic field than a normal one straight conductor. The structural basis of the inductor is a dielectric frame on which a wire is wound in the form of a spiral (frameless coils also exist). The winding can be either single-layer or multi-layer. Magnetic cores are used to increase inductance. A core placed inside the coil concentrates the magnetic field and thereby increases its inductance.
Symbols for inductors on electrical diagrams look like this:
Since electric current creates a concentrated magnetic field around the coil, the magnetic flux of this field equals energy storage (the conservation of which occurs due to kinetic movement electrons through the coil). The greater the current in the coil, the stronger the magnetic field, and the more energy will store the inductor.
Because inductors save kinetic energy moving electrons in the form of a magnetic field, in electrical circuit they behave completely different than resistors (which are simply dissipate energy in the form of heat). The ability to store energy based on current allows the inductor to maintain that current at a constant level. In other words, it resists changes in current. When the current through the coil increases or decreases, she produces voltage whose polarity is opposite to these changes.
To save more energy, the current through the inductor must be increased. In this case, the magnetic field strength will increase, which will lead to the generation of voltage according to the principle of electromagnetic self-induction. Conversely, to release energy from the coil, the current passing through it must be reduced. In this case, the magnetic field strength will decrease, which will lead to the appearance of a voltage of opposite polarity.
Remember Newton's First Law, which states that every body continues to be kept in a state of rest or uniform and rectilinear movement, until and as long as it is not forced by applied forces to change this state. With inductor coils the situation is approximately similar: “electrons moving through the coil tend to remain in motion, and resting electrons tends to remain quiet." Hypothetically, short-circuited inductor bwill be able to be maintained for as long as desired constant speed
electron flow without external help:
In practice, the inductor is capable of maintaining a constant current only when superconductors are used. The resistance of ordinary wires will inevitably attenuate the flow of electrons (without external source energy).
When the current through the coil increases, it creates a voltage whose polarity is opposite to the flow of electrons. In this case, the inductor acts as a load. It becomes, as they say, "charged" as more and more energy is stored in its magnetic field. In the following picture about pay attention to voltage polarity
Conversely, when the current through the coil decreases, a voltage appears at its terminals, the polarity of which corresponds to the flow of electrons. In this case, the inductor acts as a power source. It releases magnetic field energy into the rest of the circuit. pay attention to voltage polarity relative to the direction of the current:
If a non-magnetized inductor is connected to a power source, then at the initial moment of time it will resist the flow of electrons, passing the entire voltage of the source. As the current begins to increase, the strength of the magnetic field created around the coil will increase, absorbing energy from the power source. Eventually the current will reach maximum value and stop growing. At this moment the coil stops absorb energy from power supply And the voltage at its terminals drops to minimum level
(while the current remains at maximum level). Thus, as more energy is stored, the current through the inductor increases and the voltage across its terminals drops. Note that this behavior is completely opposite to the behavior of a capacitor,in which an increase in the numberstored energy leads to an increase in voltage at its terminals. If capacitors use stored energy to maintain constant value voltage, then the inductors this energy is used for maintaining constant current value.
The type of material from which the coil wire is made has a significant impact on the magnetic flux (and therefore the amount of stored energy) created given value current The material from which the inductor core is made also affects the magnetic flux: a ferromagnetic material (such as iron) will create a stronger flux than a non-magnetic material (such as aluminum or air).
The ability of an inductor to extract energy from an electric current source and store it in the form of a magnetic field is called inductance. Inductance is also a measure of resistance to changes in current. To denote inductance it is used character "L", and it is measured in Henry, abbreviated as "Hn"