Without a doubt, everyone loved playing with a magnet as a child. It was very easy to get a permanent magnet: to do this, you had to find an old speaker, remove the sound-reproducing speaker from it and, after simple “vandal actions,” remove the ring magnet from it. It is not surprising that many experimented with metal filings and a sheet of paper. The sawdust was arranged in stripes along the field strength lines.
In electrical engineering, not permanent magnets, but electromagnets have become much more widespread. It is known from a physics course that when an electric current flows through a conductor, a magnetic field is created around the latter, the magnitude of which is directly related to the effective value of the current.
Doubters can repeat Oersted’s simplest experiment, when a compass is placed next to a straight conductor carrying current. In this case, the arrow will deviate from the geographic north pole of the planet (perpendicular to the wire). The direction of deflection can be determined using the right hand rule: place the right hand parallel to the guide, palm down. 4 fingers should point. Then the thumb bent 90 degrees will indicate the direction of the arrow deviation. Around a straight wire, the magnetic field looks like a cylinder with a wire in the middle. But the tension lines form rings.
In electrical engineering, these are used primarily in coils. You can often hear the expression “magnetic field of the solenoid.” Let's imagine an ordinary nail and a thin wire in insulation. By evenly winding the wire around the nail, we get a solenoid. In this case, the nail affects the magnetic field of the solenoid, but this is a topic for a completely different article. It is important to understand what exactly is meant by the term. If you now connect the coil to a magnetic field will appear around it.
The solenoid field is directly proportional to the inductance value and the square of the current passing through the turns. In turn, inductance depends on the square of the number of turns. In this case, it is necessary to take into account the design of the winding: this can be a simple case with a single layer of turns, as well as a multilayer structure, where the direction of the current in the turns has a corrective effect on the total energy. Solenoids are used in circuits of trams, cutting mechanisms, contactors, etc.
The magnetic field of the solenoid consists of rings extending from one end of the winding and entering the other. Inside the coil, the power lines are not interrupted, but are distributed in a dielectric medium or along a conducting core. Consequence: the solenoid field is polar. The lines leave the magnetic north pole and return to the south. It is not difficult to guess that the magnetic field of the solenoid depends on the polarity of the current source connected to the ends of the wire. The magnetic properties of the solenoid practically coincide with this. This allows the solenoid to be used as an electromagnet. In production you can see cranes that have an electromagnet disk instead of a hook. This is the “big brother” of the solenoid - the winding on the core. The peculiarity of all electromagnets is that magnetic properties exist only when current flows through the turns.
In addition to solenoids, toroids are often used. These are the same turns of wire, but wound on a round magnetic core. Accordingly, the magnetic fields of the solenoid and toroid are different. The main feature is that the power lines propagate along the base-magnetic circuit inside the coil itself, and not outside it, as in the case of a solenoid. All this indicates a higher efficiency of coils based on ring magnetically conductive material. Consequence: they are reliable and have fewer losses than their conventional counterparts.
Devices and accessories: laboratory setup with solenoid, power supply, millivoltmeter, ammeter.
Brief theory
Solenoid called a cylindrical coil containing a large number of turns of wire through which current flows. If the pitch of the helical line of the conductor forming the coil is small, then each turn with current can be considered as a separate circular current, and the solenoid as a system of series-connected circular currents of the same radius, having a common axis.
The magnetic field inside the solenoid can be thought of as the sum of the magnetic fields created by each turn. The magnetic field induction vector inside the solenoid is perpendicular to the plane of the turns, i.e. is directed along the axis of the solenoid and forms a right-handed system with the direction of the ring currents of the turns. An approximate picture of the magnetic field lines of the solenoid is shown in Fig. 1. The magnetic field lines are closed.
Figure 2 shows a cross-section of a solenoid with length L and a number of turns N and a cross-sectional radius R. Circles with dots indicate sections of coil turns through which current I flows, directed from the drawing to us, and circles with crosses indicate sections of turns in which the current is directed behind the drawing. We denote the number of turns per unit length of the solenoid.
The magnetic field induction at point A, located on the axis of the solenoid, is determined by integrating the magnetic fields created by each turn, and is equal to
, (1)
where and are the angles formed with the axis of the solenoid by the radius vectors and drawn from point A to the outer turns of the solenoid, is the magnetic permeability of the medium, 
magnetic constant.
Thus, magnetic induction B is directly proportional to the current strength, the magnetic permeability of the medium filling the solenoid, and the number of turns per unit length. Magnetic induction also depends on the position of point A relative to the ends of the solenoid. Let's consider several special cases:
1. Let point A be at the center of the solenoid, then , 
And 
. If the solenoid is long enough, then 
and 2)
2. Let point A be in the center of the outermost turn, then , And . If the solenoid is long enough, then , and (3)
From formulas (2) and (3) it is clear that the magnetic induction of the solenoid at its edge is half as much as its value at the center.
3. If the length of the solenoid is many times greater than the radius of its turns
(an “infinitely” long solenoid), then for all points lying inside
solenoid on its axis, you can put . Then
the field can be considered uniform in the central part of the solenoid and calculated using the formula
The uniformity of the magnetic field is disrupted near the edges of the solenoid. In this case, the induction can be determined by the formula
where k is a coefficient taking into account the inhomogeneity of the field.
The experimental study of the magnetic field of the solenoid in this work is carried out using a special probe - a small coil mounted inside a rod with a scale ruler. The axis of the coil coincides with the axis of the solenoid; the coil is connected to an alternating current millivoltmeter, the input resistance of which is much greater than the resistance of the probe coil. If there is alternating current flowing through the solenoid 
standard frequency ( = 50 Hz), then inside the solenoid and at its edges the induction of the alternating magnetic field changes according to the law (see (5)):
The amplitude of the magnetic induction in this formula depends on the position of the point inside the solenoid. If you place a probe coil in the solenoid, then in accordance with the law of electromagnetic induction, an induced emf appears in it:
, (6)
where N 1 is the number of turns in the coil, S is the cross-sectional area of the coil, F is the magnetic flux (since the axis of the coil coincides with the axis of the solenoid and, therefore, the magnetic induction vector is perpendicular to the cross-sectional plane of the coil.).
Since the magnitude of induction B changes according to the law 
, , then from (6) we obtain the formula for calculating the EMF:
From expression (7) it is clear that the amplitude of the EMF depends on . Thus, by measuring the amplitude of the EMF, we can determine:
The coefficient k, which takes into account the inhomogeneity of the magnetic field of the solenoid at the edges, can be determined using the formula. (5), knowing and:
(9)
where is the amplitude of the alternating current passing through the solenoid.
From formulas (7) and (9) it follows that the amplitude of the induced emf is directly proportional to the amplitude of the alternating current:
An ammeter and a millivoltmeter connected to an alternating current circuit measure effective values of current and emf, which are associated with amplitudes and ratios:
For effective values of current and EMF, formula (10) has the form
(11)
From formula (11) it follows that the ratio is proportional to the coefficient K of the inhomogeneity of the magnetic field induction at the point of the solenoid where the measurements are taken
(12)
where A is the proportionality coefficient.
In this work, two tasks are required: 1) determine the distribution of induction along the axis of the solenoid at a certain constant current value; 2) determine the value of the coefficient k.
Safety precautions:
1. Do not independently connect the power source and millivoltmeter to the 220 V network.
2. Do not switch live circuits.
Do not touch uninsulated parts of circuits.
3. Do not leave the switched on circuit unattended.
Work order
Task No. 1. Study of the distribution of magnetic field induction along the axis of the solenoid.
1. Assemble the measuring circuit according to the diagram shown in Fig. 3. To do this, connect a power source and an ammeter to the solenoid circuit, and a millivoltmeter to the terminals of the probe coil (for measuring). In this installation, the probe coil has the following parameters: = 200 turns, S = 2 * 10 -4 m 2, frequency AC = 50 Hz, Number of turns per unit length of solenoid n = 2400 1/m
1- laboratory stand Z - rod "
2- probe coil
3- solenoid
5 ammeter
6 - power supply with output voltage (current) regulator, 7 - millivoltmeter.
2. Install the rod with the scale ruler so that the probe coil is approximately in the middle of the solenoid.
3. Turn on the solenoid power supply and set the solenoid current (according to the ammeter) equal to = 25 mA. Turn on the millivoltmeter and after warming up (5 minutes) take readings.
4. Moving the rod with a linear scale, measure using
millivoltmeter effective value of induced emf through each
centimeter of ruler position. Using formula (8) calculate .
Enter the results of measurements and calculations in Table 1 (note that ).
Let us calculate, using the circulation theorem, the magnetic field induction inside solenoid. Consider a solenoid with length l having N turns through which current flows (Fig. 175). We consider the length of the solenoid to be many times greater than the diameter of its turns, i.e. the solenoid in question is infinitely long. Experimental study of the magnetic field of the solenoid (see Fig. 162, b) shows that inside the solenoid the field is uniform, outside the solenoid it is inhomogeneous and very weak.
In Fig. 175 shows the magnetic induction lines inside and outside the solenoid. The longer the solenoid, the less magnetic induction outside it. Therefore, we can approximately assume that the field of an infinitely long solenoid is concentrated entirely inside it, and the field outside the solenoid can be neglected.
To find magnetic induction IN select a closed rectangular contour ABCDA as shown in fig. 175. Vector circulation IN in a closed loop ABCDA covering everything N turns, according to (118.1), is equal to
Integral over ABCDA can be represented in the form of four integrals: according AB, BC, CD And D.A. At the sites AB And CD the circuit is perpendicular to the lines of magnetic induction and B l = 0. In the area outside the solenoid B=0. Location on D.A. vector circulation IN equal to Bl(the circuit coincides with the magnetic induction line); hence,
(119.1)
From (119.1) we arrive at the expression for the magnetic induction of the field inside the solenoid (in vacuum):
We found that the field inside the solenoid homogeneously(edge effects in areas adjacent to the ends of the solenoid are neglected in calculations). However, we note that the derivation of this formula is not entirely correct (the magnetic induction lines are closed, and the integral over the external portion of the magnetic field is not strictly equal to zero). The field inside the solenoid can be correctly calculated by applying the Biot-Savart-Laplace law; the result is the same formula (119.2).
The magnetic field is also important for practice. toroid- a ring coil, the turns of which are wound on a torus-shaped core (Fig. 176). The magnetic field, as experience shows, is concentrated inside the toroid; there is no field outside it.
The lines of magnetic induction in this case, as follows from symmetry considerations, are circles whose centers are located along the axis of the toroid. As a contour, we choose one such circle of radius r. Then, according to the circulation theorem (118.1), B× 2p r =m 0 NI whence it follows that magnetic induction inside the toroid (in vacuum)
Where N- number of toroid turns.
If the circuit passes outside the toroid, then it does not cover currents and B× 2p r = 0. This means that there is no field outside the toroid (as experience also shows).
Magnetic field of electric current
A magnetic field is created not only by natural or artificial ones, but also by a conductor if an electric current passes through it. Therefore, there is a connection between magnetic and electrical phenomena.
It is not difficult to verify that a magnetic field is formed around a conductor through which current flows. Place a straight conductor above the moving magnetic needle, parallel to it, and pass an electric current through it. The arrow will take a position perpendicular to the conductor.
What forces could make the magnetic needle turn? Obviously, the strength of the magnetic field that arises around the conductor. Turn off the current and the magnetic needle will return to its normal position. This suggests that when the current was turned off, the magnetic field of the conductor also disappeared.
Thus, an electric current passing through a conductor creates a magnetic field. To find out in which direction the magnetic needle will deviate, use the right-hand rule. If you place your right hand over the conductor, palm down, so that the direction of the current coincides with the direction of the fingers, then the bent thumb will show the direction of deflection of the north pole of the magnetic needle placed under the conductor. Using this rule and knowing the polarity of the arrow, you can also determine the direction of the current in the conductor.
Magnetic field of a straight conductor has the shape of concentric circles. If you place your right hand over the conductor, palm down, so that the current seems to come out of the fingers, then the bent thumb will point to the north pole of the magnetic needle.Such a field is called a circular magnetic field.
The direction of the circular field lines of force depends on the conductor and is determined by the so-called gimlet rule. If you mentally screw the gimlet in the direction of the current, then the direction of rotation of its handle will coincide with the direction of the magnetic field lines. By applying this rule, you can find out the direction of the current in a conductor if you know the direction of the field lines created by this current.
Returning to the experiment with the magnetic needle, we can be convinced that it is always located with its northern end in the direction of the magnetic field lines.
So, A magnetic field arises around a straight conductor through which electric current passes. It has the shape of concentric circles and is called a circular magnetic field.
Pickles d. Magnetic field of the solenoid
A magnetic field arises around any conductor, regardless of its shape, provided that an electric current passes through the conductor.
In electrical engineering we deal with ones consisting of a number of turns. To study the magnetic field of the coil that interests us, let us first consider what shape the magnetic field of one turn has.
Let's imagine a coil of thick wire piercing a sheet of cardboard and connected to a current source. When an electric current passes through a coil, a circular magnetic field is formed around each individual part of the coil. According to the “gimlet” rule, it is not difficult to determine that the magnetic lines of force inside the coil have the same direction (towards us or away from us, depending on the direction of the current in the coil), and they exit from one side of the coil and enter the other side. A series of such turns, shaped like a spiral, is the so-called solenoid (coil).
Around the solenoid, when current passes through it, a magnetic field is formed. It is obtained as a result of the addition of the magnetic fields of each turn and is shaped like the magnetic field of a rectilinear magnet. The lines of force of the magnetic field of the solenoid, as in a rectilinear magnet, leave one end of the solenoid and return to the other. Inside the solenoid they have the same direction. Thus, the ends of the solenoid have polarity. The end from which the lines of force emerge is north pole solenoid, and the end into which the power lines enter is its south pole.
Solenoid Poles can be determined by right hand rule, but for this you need to know the direction of the current in its turns. If you place your right hand on the solenoid, palm down, so that the current seems to come out of the fingers, then the bent thumb will point to the north pole of the solenoid. From this rule it follows that the polarity of the solenoid depends on the direction of the current in it. It is not difficult to verify this practically by bringing a magnetic needle to one of the poles of the solenoid and then changing the direction of the current in the solenoid. The arrow will instantly rotate 180°, i.e. it will indicate that the poles of the solenoid have changed.
The solenoid has the property of drawing in light iron objects. If a steel bar is placed inside the solenoid, then after some time, under the influence of the magnetic field of the solenoid, the bar will become magnetized. This method is used in manufacturing.
Electromagnets
It is a coil (solenoid) with an iron core placed inside it. The shapes and sizes of electromagnets are varied, but the general structure of all of them is the same.
The electromagnet coil is a frame, most often made of pressed wood or fiber and has various shapes depending on the purpose of the electromagnet. Insulated copper wire is wound on the frame in several layers - the winding of the electromagnet. It has a different number of turns and is made of wire of different diameters, depending on the purpose of the electromagnet.
To protect the winding insulation from mechanical damage, the winding is covered with one or several layers of paper or some other insulating material. The beginning and end of the winding are brought out and connected to output terminals mounted on the frame, or to flexible conductors with lugs at the ends.
The electromagnet coil is mounted on a core made of soft, annealed iron or alloys of iron with silicon, nickel, etc. Such iron has the smallest residual. Cores are most often made of composite thin sheets insulated from each other. The shapes of the cores can be different, depending on the purpose of the electromagnet.
If an electric current is passed through the winding of an electromagnet, a magnetic field is formed around the winding, which magnetizes the core. Since the core is made of soft iron, it will be magnetized instantly. If you then turn off the current, the magnetic properties of the core will also quickly disappear, and it will cease to be a magnet. The poles of an electromagnet, like a solenoid, are determined by the right-hand rule. If you change in the winding of an electromagnet, then the polarity of the electromagnet will change in accordance with this.
The action of an electromagnet is similar to the action of a permanent magnet. However, there is a big difference between them. A permanent magnet always has magnetic properties, and an electromagnet only when an electric current passes through its winding.
In addition, the attractive force of a permanent magnet is constant, since the magnetic flux of a permanent magnet is constant. The force of attraction of an electromagnet is not a constant value. The same electromagnet can have different attractive forces. The attractive force of any magnet depends on the magnitude of its magnetic flux.
The force of attraction, and therefore its magnetic flux, depends on the magnitude of the current passing through the winding of this electromagnet. The greater the current, the greater the attractive force of the electromagnet, and, conversely, the less current in the winding of the electromagnet, the less force it attracts magnetic bodies to itself.
But for electromagnets that are different in structure and size, their strength of attraction depends not only on the magnitude of the current in the winding. If, for example, we take two electromagnets of the same design and size, but one with a small number of winding turns, and the other with a much larger number, then it is easy to see that at the same current the attractive force of the latter will be much greater. Indeed, the greater the number of turns of a winding, the greater the magnetic field created around this winding at a given current, since it is composed of the magnetic fields of each turn. This means that the magnetic flux of the electromagnet, and therefore the force of its attraction, will be greater, the greater the number of turns the winding has.
There is another reason that affects the magnitude of the magnetic flux of an electromagnet. This is the quality of its magnetic circuit. A magnetic circuit is the path along which the magnetic flux is closed. The magnetic circuit has a certain magnetic resistance. Magnetic reluctance depends on the magnetic permeability of the medium through which the magnetic flux passes. The greater the magnetic permeability of this medium, the lower its magnetic resistance.
Since m The magnetic permeability of ferromagnetic bodies (iron, steel) is many times greater than the magnetic permeability of air, so it is more profitable to make electromagnets so that their magnetic circuit does not contain air sections. The product of the current strength and the number of turns of the electromagnet winding is called magnetomotive force. Magnetomotive force is measured in the number of ampere-turns.
For example, a current of 50 mA passes through the winding of an electromagnet with 1200 turns. M magnetomotive force such an electromagnet equals 0.05 x 1200 = 60 ampere-turns.
The action of magnetomotive force is similar to the action of electromotive force in an electrical circuit. Just as EMF causes electric current, magnetomotive force creates magnetic flux in an electromagnet. Just as in an electric circuit, with an increase in emf, the current value increases, so in a magnetic circuit, with an increase in magnetomotive force, the magnetic flux increases.
Action magnetic resistance similar to the action of electrical resistance in a circuit. Just as the current decreases as the resistance of an electrical circuit increases, so does the current in a magnetic circuit. An increase in magnetic resistance causes a decrease in magnetic flux.
The dependence of the magnetic flux of an electromagnet on the magnetomotive force and its magnetic resistance can be expressed by a formula similar to the formula of Ohm's law: magnetomotive force = (magnetic flux / magnetic resistance)
Magnetic flux is equal to magnetomotive force divided by magnetic reluctance.
The number of turns of the winding and the magnetic resistance for each electromagnet is a constant value. Therefore, the magnetic flux of a given electromagnet changes only with a change in the current passing through the winding. Since the force of attraction of an electromagnet is determined by its magnetic flux, in order to increase (or decrease) the force of attraction of the electromagnet, it is necessary to correspondingly increase (or decrease) the current in its winding.
Polarized electromagnet
A polarized electromagnet is a connection between a permanent magnet and an electromagnet. It's designed this way. So-called soft iron pole extensions are attached to the poles of a permanent magnet. Each pole extension serves as the core of an electromagnet; a coil with a winding is mounted on it. Both windings are connected to each other in series.
Since the pole extensions are directly connected to the poles of a permanent magnet, they have magnetic properties even in the absence of current in the windings; At the same time, their force of attraction is constant and is determined by the magnetic flux of a permanent magnet.
The action of a polarized electromagnet is that when current passes through its windings, the attractive force of its poles increases or decreases depending on the magnitude and direction of the current in the windings. The action of other electromagnets is based on this property of a polarized electromagnet. electrical devices.
The effect of a magnetic field on a current-carrying conductor
If you place a conductor in a magnetic field so that it is located perpendicular to the field lines, and pass an electric current through this conductor, the conductor will begin to move and will be pushed out of the magnetic field.
As a result of the interaction of a magnetic field with an electric current, the conductor begins to move, i.e., electrical energy is converted into mechanical energy.
The force with which a conductor is pushed out of a magnetic field depends on the magnitude of the magnetic flux of the magnet, the strength of the current in the conductor, and the length of the part of the conductor that the field lines intersect. The direction of action of this force, i.e. the direction of movement of the conductor, depends on the direction of the current in the conductor and is determined by left hand rule.
If you hold the palm of your left hand so that the magnetic field lines enter it, and the extended four fingers face the direction of the current in the conductor, then the bent thumb will indicate the direction of movement of the conductor. When applying this rule, we must remember that the field lines come out from the north pole of the magnet.
They are closed, which indicates that there are no magnetic charges in nature. Fields whose field lines are closed are called vortex fields. That is, the magnetic field is a vortex field. This differs from the electric field created by charges.
Solenoid.
Solenoid- This is a wire spiral with current.
The solenoid is characterized by the number of turns per unit length n, length l and diameter d. The thickness of the wire in the solenoid and the pitch of the helix (helical line) are small compared to its diameter d and length l. The term “solenoid” is also used in a broader sense - this is the name given to coils with an arbitrary cross-section (square solenoid, rectangular solenoid), and not necessarily cylindrical in shape (toroidal solenoid). Distinguish long solenoid (l ≫ d) And short solenoid (l ≪ d). In cases where the relationship between d And l not specifically stated, a long solenoid is implied.
The solenoid was invented in 1820 by A. Ampere to enhance the magnetic action of current discovered by X. Oersted and used by D. Arago in experiments on the magnetization of steel rods. The magnetic properties of a solenoid were experimentally studied by Ampere in 1822 (at the same time he introduced the term “solenoid”). The equivalence of the solenoid to permanent natural magnets was established, which was a confirmation of Ampere’s electrodynamic theory, which explained magnetism by the interaction of ring molecular currents hidden in bodies.
Solenoid magnetic field lines:
The direction of these lines is determined using second rule of the right hand.
If you clasp the solenoid with the palm of your right hand, directing four fingers along the current in the turns, then the extended thumb will indicate the direction of the magnetic lines inside the solenoid.
Comparing the magnetic field of a solenoid with the field of a permanent magnet (Fig. below), you can see that they are very similar.
Like a magnet, the solenoid has two poles - north ( N) and southern ( S). The North Pole is the one from which magnetic lines emerge; the south pole is the one they enter. The north pole of the solenoid is always located on the side that the thumb of the palm points to when it is positioned in accordance with the second rule of the right hand.
A solenoid in the form of a coil with a large number of turns is used as a magnet.
Studies of the magnetic field of a solenoid show that the magnetic effect of a solenoid increases with increasing current and the number of turns in the solenoid. In addition, the magnetic action of a solenoid or current-carrying coil is enhanced by introducing an iron rod into it, which is called core.
Electromagnets.
Modern electromagnets can lift loads weighing several tens of tons. They are used in factories when moving heavy iron and steel products. Electromagnets are also used in agriculture to clean the grains of a number of plants from weeds and in other industries.
