Inductors and magnetic fields. Magnetic field on the axis of a short coil with current How to find the magnetic field of a coil

To concentrate the magnetic field in a certain part of space, a coil is made from a wire through which a current is passed.

An increase in the magnetic induction of the field is achieved by increasing the number of turns of the coil and placing it on a steel core, the molecular currents of which, creating their own field, increase the resulting field of the coil.

Rice. 3-11. Ring coil.

A ring coil (Figure 3-11) has w turns evenly distributed along a nonmagnetic core. The surface bounded by a circle of radius coinciding with the average magnetic line is penetrated by a full current.

Due to symmetry, the field strength H at all points lying on the average magnetic line is the same, therefore the ppm.

According to the law of total current

whence the magnetic field strength on the average magnetic line coinciding with the center line of the ring coil,

and magnetic induction

When the magnetic induction on the center line can be considered with sufficient accuracy equal to its average value, and, consequently, the magnetic flux through the cross section of the coil

Equation (3-20) can be given the form of Ohm's law for a magnetic circuit

where Ф is magnetic flux; - m.d.s.; - resistance of the magnetic circuit (core).

Equation (3-21) is similar to the equation of Ohm’s law for an electric circuit, i.e., the magnetic flux is equal to the ratio of the ppm. to the magnetic resistance of the circuit.

Rice. 3-12. Cylindrical coil.

The cylindrical coil (Fig. 3-12) can be considered as part of a ring coil with a sufficiently large radius and with the winding located only on a part of the core whose length is equal to the length of the coil. The field strength and magnetic induction on the axial line in the center of the cylindrical coil are determined by formulas (3-18) and (3-19), which in this case are approximate and applicable only for coils with (Fig. 3-12).

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 of maximum magnetic flux density (where there are the most lines of flux 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 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 relationship. We are talking about the one that exists between the magnetic flux and the current in coils with an air core.

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 is an important part of the topic that interests 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 the magnetic flux allows the flux created by an electric current in a magnetic field to be used to produce mechanical motion. 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 a 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. It has been widely used for many years, in particular on 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.

Creates a magnetic field around itself. A person would not be himself if he had not figured out how to use such a wonderful property of current. Based on this phenomenon, man created electromagnets.

Their use is very widespread and ubiquitous in the modern world. Electromagnets are remarkable because, unlike permanent magnets, they can be turned on and off as needed, and the strength of the magnetic field around them can be changed. How are the magnetic properties of current used? How are electromagnets created and used?

Magnetic field of a current coil

As a result of experiments, it was possible to find out that the magnetic field around a current-carrying conductor can be strengthened if the wire is coiled in the shape of a spiral. It turns out to be a kind of coil. The magnetic field of such a coil is much greater than the magnetic field of a single conductor.

Moreover, the magnetic field lines of the current-carrying coil are located in a similar way to the field lines of a conventional rectangular magnet. The coil has two poles and magnetic lines diverging in arcs along the coil. Such a magnet can be turned on and off at any time, respectively, turning on and off the current in the coil wires.

Ways to influence the magnetic forces of a coil

However, it turned out that the current coil has other remarkable properties. The more turns the coil consists of, the stronger the magnetic field becomes. This allows you to collect magnets of different strengths. However, there are simpler ways to influence the magnitude of the magnetic field.

So, when the current in the coil wires increases, the strength of the magnetic field increases, and, conversely, when the current decreases, the magnetic field weakens. That is, with a simple connection of a rheostat, we get an adjustable magnet.

The magnetic field of a current-carrying coil can be significantly enhanced by introducing an iron rod inside the coil. It's called the core. The use of a core allows you to create very powerful magnets. For example, in production they use magnets capable of lifting and holding several tens of tons of weight. This is achieved as follows.

The core is bent in the form of an arc, and two coils are put on its two ends, through which current is passed. The coils are connected with 4e wires so that their poles coincide. The core enhances their magnetic field. From below, a plate with a hook is attached to this structure, on which the load is suspended. Such devices are used in factories and ports to move very heavy loads. These weights are easily connected and disconnected when turning the current in the coils on and off.

Electromagnets and their applications

Electromagnets are used so widely that it is perhaps difficult to name an electromechanical device in which they are not used. The doors in the entrances are held by electromagnets.

Electric motors in a wide variety of devices convert electrical energy into mechanical energy using electromagnets. The sound in the speakers is created using magnets. And this is not a complete list. A huge number of conveniences of modern life owe their existence to the use of electromagnets.

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.