Determination of the magnetic field of the coil. Magnetic field of a current-carrying coil. Designation on diagrams

We continue to study the issues electromagnetic phenomena. And in today's lesson we will consider the magnetic field of a coil with current and an electromagnet.

Of greatest practical interest is the magnetic field of a current-carrying coil. To get a coil, you need to take an insulated conductor and wind it around a frame. Such a coil contains a large number of turns of wire. Please note: these wires are wound around a plastic frame and this wire has two terminals (Fig. 1).

Rice. 1. Reel

Research magnetic field The coils were studied by two famous scientists: Andre-Marie Ampère and François Arago. They found that the magnetic field of the coil completely corresponds to the magnetic field of a permanent magnet (Fig. 2).

Rice. 2. Magnetic field of the coil and permanent magnet

Why do the magnetic lines of the coil look like this?

If there is flow through a straight conductor D.C., a magnetic field appears around it. The direction of the magnetic field can be determined by the “gimlet rule” (Fig. 3).

Rice. 3. Magnetic field of a conductor

We bend this conductor in a spiral. The direction of the current remains the same, the magnetic field of the conductor also exists around the conductor, the field of different sections of the conductor adds up. The magnetic field will be concentrated inside the coil. As a result, we obtain the following picture of the magnetic field of the coil (Fig. 4).

Rice. 4. Magnetic field of the coil

There is a magnetic field around the current-carrying coil. It's like the field straight conductor, can be detected using sawdust (Fig. 5). The magnetic field lines of the current-carrying coil are also closed.

Rice. 5. Location of metal filings near the current coil

If a coil with current is suspended on thin and flexible conductors, then it will be installed in the same way as the magnetic needle of a compass. One end of the coil will face north, the other will face south. This means that a coil with current, like a magnetic needle, has two poles - north and south (Fig. 6).

Rice. 6. Coil poles

On electrical diagrams, the coil is designated as follows:

Rice. 7. Coil designation on diagrams

Current-carrying coils are widely used in technology as magnets. They are convenient because their magnetic effect can be varied within wide limits.

The magnetic field of the coil is large compared to the magnetic field of the conductor (at the same current).

When current is passed through a coil, a magnetic field is created around it. The more current flows through the coil, the stronger the magnetic field will be.

It can be fixed using a magnetic needle or metal shavings.
Also, the magnetic field of the coil depends on the number of turns. The magnetic field of a current-carrying coil is stronger than larger number turns in it. That is, we can regulate the field of the coil by changing the number of its turns or electricity flowing through the coil.

But the most interesting discovery was the discovery of the English engineer Sturgeon. He demonstrated the following: the scientist took and put a coil on an iron core. The point is that by passing electric current through the turns of these coils, the magnetic field increased many times over - and all the iron objects that were around began to be attracted to this device (Fig. 8). This device is called an “electromagnet”.

Rice. 8. Electromagnet

When they figured out to make an iron hook and attach it to this device, they were able to drag various loads. So what is an electromagnet?

Definition

Electromagnet is a coil with a large number of winding turns, placed on an iron core, which acquires the properties of a magnet when an electric current passes through the winding.

The electromagnet in the diagram is designated as a coil, and there is a horizontal line on top (Fig. 9). This line represents the iron core.

Rice. 9. Electromagnet designation

When we studied electrical phenomena, we said that electric current has different properties, including magnetic ones. And one of the experiments that we discussed was related to the fact that we take a wire connected to a current source, wind it around an iron nail and observe how various iron objects begin to be attracted to this nail (Fig. 10). This is the simplest electromagnet. And now we understand that the simplest electromagnet is provided by the flow of current in a coil, a large number of turns and, of course, a metal core.

Rice. 10. The simplest electromagnet

Today, electromagnets are very widespread. Electromagnets work almost anywhere and everywhere. For example, if we need to drag quite large loads, we use electromagnets. And by adjusting the current strength, we will, accordingly, either increase or decrease the strength. Another example of the use of electromagnets is the electric bell.

Opening and closing doors and some brakes Vehicle(for example, trams) are also provided with electromagnets.

Bibliography

1. Gendenshtein L.E., Kaidalov A.B., Kozhevnikov V.B. Physics 8 / Ed. Orlova V.A., Roizena I.I. - M.: Mnemosyne.
2. Peryshkin A.V. Physics 8. - M.: Bustard, 2010.
3. Fadeeva A.A., Zasov A.V., Kiselev D.F. Physics 8. - M.: Enlightenment.

1. Internet portal “site” ()
2. Internet portal “site” ()
3. Internet portal “class-fizika.narod.ru” ()

Homework

1. What is a reel?
2. Does any coil have a magnetic field?
3. Describe the simplest electromagnet.

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 most important properties of matter, just like, 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 will most likely talk 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 collect the simplest electrical circuit from a battery and a light bulb 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 produced 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 kind of magnetic lines are they?

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 lines of force leave the north pole and enter the south pole without breaking. 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 of a permanent magnet, you pass a wire with current through the cardboard, then the metal filings will show it, the conductor, a 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 will have its own magnetic poles, north and south. But the magnetic field of one turn is usually small. Much better 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, the magnetic fields of the 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 it is possible to power each turn 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 a conductor through which a direct current of 1 A flows.

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 voltage appears at a distance of 16cm from the conductor carrying a current of 1A.

The field strength only indicates the theoretical ability of the magnetic field. The real ability to act is reflected by another value, magnetic induction (B). It is this that shows the real force 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; in addition to its numerical value, it also has a direction, which 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 the smaller Gauss unit is often used: 1TL = 10,000G. 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).

In fact, it represents the number of lines of magnetic induction passing through a 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 produced by the coil can be determined by using the right hand rule: if four extended fingers indicate the direction of the current in the coil, then the thumb will indicate 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 and participate in electrochemical processes. After introducing the basics of magnetism, you can talk about how electric motors work.

Electric motors can be of very different designs, power and principles of operation: for example, direct and alternating current, stepper or commutator. 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.

Of greatest practical interest is the magnetic field of a current-carrying coil. Figure 97 shows a coil consisting of large number turns of wire wound on a wooden frame. When there is current in the coil, iron filings are attracted to its ends; when the current is turned off, they fall away.

Rice. 97. Attraction of iron filings by a current coil

If a coil with current is suspended on thin and flexible conductors, then it will be installed in the same way as the magnetic needle of a compass. One end of the coil will face north, the other will face south. This means that a coil with current, like a magnetic needle, has two poles - north and south (Fig. 98).

Rice. 98. Current coil poles

There is a magnetic field around the current-carrying coil. It, like the direct current field, can be detected using sawdust (Fig. 99). The magnetic lines of the magnetic field of a current-carrying coil are also closed curves. It is generally accepted that outside the coil they are directed from the north pole of the coil to the south (see Fig. 99).

Rice. 99. Magnetic lines of a current coil

Current-carrying coils are widely used in technology as magnets. They are convenient because their magnetic effect can be changed (strengthened or weakened) over a wide range. Let's look at the ways in which you can do this.

Figure 97 shows an experiment in which the action of the magnetic field of a coil with current is observed. If you replace the coil with another one, with a larger number of turns of wire, then with the same current strength it will attract more iron objects. Means, The magnetic effect of a current-carrying coil is stronger, the greater the number of turns in it.

Let's connect a rheostat to the circuit containing the coil (Fig. 100) and use it to change the current strength in the coil. As the current increases, the effect of the magnetic field of the current coil increases, and as the current decreases, it weakens..

Rice. 100. Effect of the magnetic field of a coil

It also turns out that the magnetic effect of a current-carrying coil can be significantly enhanced without changing the number of its turns and the strength of the current in it. To do this, you need to insert an iron rod (core) inside the coil. Iron introduced inside the coil enhances the magnetic effect of the coil(Fig. 101).

Rice. 101. Effect of the magnetic field of a coil with an iron core

A coil with an iron core inside is called an electromagnet.

An electromagnet is one of the main parts of many technical devices. Figure 102 shows an arc-shaped electromagnet holding an armature (iron plate) with a suspended load.

Rice. 102. Arc-shaped electromagnet

Electromagnets are widely used in technology due to their remarkable properties. They quickly demagnetize when the current is turned off; depending on their purpose, they can be made in a variety of sizes; while the electromagnet is operating, its magnetic action can be adjusted by changing the current strength in the coil.

Electromagnets with a large lifting force are used in factories to carry products made of steel or cast iron, as well as steel and cast iron shavings and ingots (Fig. 103).

Rice. 103. Application of electromagnets

Figure 104 shows a cross-section of a magnetic grain separator. Very fine iron filings are mixed into the grain. These sawdust do not stick to the smooth grains of healthy grains, but they do stick to the grains of weeds. Grains 1 are poured out of the hopper onto a rotating drum 2. Inside the drum there is a strong electromagnet 5. By attracting iron particles 4, it removes weed grains from the grain flow 3 and in this way cleans the grain from weeds and accidentally caught iron objects.

Rice. 104. Magnetic separator

Electromagnets are used in telegraph, telephone and many other devices.

Questions

1. In what direction is a current-carrying coil suspended on long thin conductors installed? What similarities does it have with a magnetic needle?
2. In what ways can the magnetic effect of a current-carrying coil be enhanced?
3. What is an electromagnet called?
4. For what purposes are electromagnets used in factories?
5. How does a magnetic grain separator work?

Exercise 41

1. It is necessary to build an electromagnet, the lifting force of which can be adjusted without changing the design. How to do it?
2. What needs to be done to change the magnetic poles of the current-carrying coil to the opposite?
3. How to build a strong electromagnet if the designer is given the condition that the current in the electromagnet be relatively small?
4. The electromagnets used in the crane have enormous power. The electromagnets used to remove stray iron filings from the eyes are very weak. In what ways is this difference achieved?

Exercise

If a straight conductor is rolled into a circle, then the magnetic field of a circular current can be studied.
Let's carry out experiment (1). We will pass the wire in the form of a circle through the cardboard. Let's place several free magnetic arrows on the surface of the cardboard at various points. Let's turn on the current and see that the magnetic arrows in the center of the coil show the same direction, and outside the coil on both sides in the other direction.
Now let's repeat experiment (2), changing the poles, and therefore the direction of the current. We see that the magnetic arrows have changed direction over the entire surface of the cardboard by 180 degrees.
Let us conclude: the magnetic lines of circular current also depend on the direction of the current in the conductor.
Let's carry out experiment 3. Remove the magnetic arrows, turn on the electric current and carefully pour small iron filings over the entire surface of the cardboard. We get a picture of magnetic lines of force, which is called the “spectrum of the magnetic field of a circular current”. How, in this case, can we determine the direction of the magnetic field lines? We apply the gimlet rule again, but applied to a circular current. If the direction of rotation of the handle of the gimlet is combined with the direction of the current in the circular conductor, then the direction of the translational movement of the gimlet will coincide with the direction of the magnetic lines of force.
Let's consider several cases.
1. The plane of the coil lies in the plane of the sheet, the current along the coil flows clockwise. By rotating the coil clockwise, we determine that the magnetic lines of force in the center of the coil are directed inside the coil “away from us.” This is conventionally indicated by a “+” (plus) sign. Those. in the center of the coil we put “+”
2. The plane of the coil lies in the plane of the sheet, the current along the coil flows counterclockwise. By rotating the coil counterclockwise, we determine that the magnetic lines of force come out from the center of the coil “toward us.” This is conventionally indicated by “∙” (dot). Those. in the center of the turn we must put a dot (“∙”).
If a straight conductor is wound around a cylinder, you get a coil with current, or a solenoid.
Let's carry out the experiment (4.) We use the same circuit for the experiment, only the wire is now passed through the cardboard in the form of a coil. Let's place several free magnetic needles on the plane of the cardboard at different points: at both ends of the coil, inside the coil and on both sides outside. Let the coil be positioned horizontally (in the left-to-right direction). Let's turn on the circuit and find that the magnetic arrows located along the axis of the coil show one direction. We note that at the right end of the coil the arrow shows that the lines of force enter the coil, which means this is the “south pole” (S), and at the left the magnetic arrow shows that they come out, this is the “north pole” (N). On the outside of the coil, the magnetic needles have the opposite direction compared to the direction inside the coil.
Let's carry out experiment (5). In the same circuit, let's change the direction of the current. We will find that the direction of all the magnetic needles has changed, they have turned 180 degrees. We conclude: the direction of the magnetic field lines depends on the direction of the current along the turns of the coil.
Let's carry out experiment (6). Let's remove the magnetic arrows and turn on the circuit. Carefully salt the cardboard with iron filings inside and outside the reel. We get a picture of magnetic field lines, which is called the “spectrum of the magnetic field of a coil with current”
How can we determine the direction of magnetic field lines? The direction of the magnetic field lines is determined by the gimlet rule in the same way as for a coil with current: If the direction of rotation of the gimlet handle is combined with the direction of the current in the coils, then the direction of translational movement will coincide with the direction of the magnetic field lines inside the solenoid. The magnetic field of a solenoid is similar to the magnetic field of a permanent bar magnet. The end of the coil from which the field lines exit will be the “north pole” (N), and the end into which the field lines enter will be the “south pole” (S).
After the discovery of Hans Oersted, many scientists began to repeat his experiments, inventing new ones in order to discover evidence of the connection between electricity and magnetism. French scientist Dominique Arago placed an iron rod in a glass tube and wound a copper wire on top of it, through which an electric current was passed. As soon as Arago closed the electrical circuit, the iron rod became so strongly magnetized that it attracted the iron keys to itself. It took a lot of effort to get the keys off. When Arago turned off the power source, the keys fell off on their own! So Arago invented the first electromagnet. Modern electromagnets consist of three parts: winding, core and armature. The wires are placed in a special sheath, which acts as an insulator. A multilayer coil is wound with wire - the winding of an electromagnet. A steel rod is used as the core. The plate that is attracted to the core is called an armature. Electromagnets are widely used in industry due to their properties: they quickly demagnetize when the current is turned off; they can be made in a variety of sizes depending on the purpose; By changing the current strength, you can regulate the magnetic action of the electromagnet. Electromagnets are used in factories to carry steel and cast iron products. These magnets have great lifting force. Electromagnets are also used in electric bells, electromagnetic separators, microphones, and telephones. Today we looked at the magnetic field of a circular current, coils with current. We got acquainted with electromagnets, their use in industry and the national economy.

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 to the electrical interaction, the magnetic interaction is much stronger. 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 of an ideal fluid (as Maxwell himself imagined), the field of flow velocities of which is represented by 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, where they enter - the 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. The forward movement of 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.