magnetic induction - is the magnetic flux density at a given point in the field. The unit of magnetic induction is the tesla.(1 T \u003d 1 Wb / m 2).

Returning to the previously obtained expression (1), we can quantify magnetic flux through a certain surface as the product of the magnitude of the charge flowing through a conductor aligned with the boundary of this surface with the complete disappearance of the magnetic field, by the resistance of the electrical circuit through which these charges flow

.

In the experiments described above with a test coil (ring), it was removed to a distance at which all manifestations of the magnetic field disappeared. But you can simply move this coil within the field and at the same time electric charges will also move in it. Let us pass in expression (1) to increments

Ф + Δ Ф = r(q - Δ q) => Δ Ф = - rΔq => Δ q\u003d -Δ F / r

where Δ Ф and Δ q- increments of the flow and the number of charges. Different signs of the increments are explained by the fact that the positive charge in the experiments with the removal of the coil corresponded to the disappearance of the field, i.e. negative increment of the magnetic flux.

With the help of a test turn, you can explore the entire space around a magnet or current coil and build lines, the direction of the tangents to which at each point will correspond to the direction of the magnetic induction vector B(Fig. 3)

These lines are called magnetic induction vector lines or magnetic lines .

The space of the magnetic field can be mentally divided by tubular surfaces formed by magnetic lines, and the surfaces can be chosen in such a way that the magnetic flux inside each such surface (tube) is numerically equal to one and graphically depict the axial lines of these tubes. Such tubes are called single, and the lines of their axes are called single magnetic lines . The picture of the magnetic field depicted with the help of single lines gives not only a qualitative, but also a quantitative idea of ​​it, because. in this case, the value of the magnetic induction vector turns out to be equal to the number of lines passing through a unit surface normal to the vector B, a the number of lines passing through any surface is equal to the value of the magnetic flux .

Magnetic lines are continuous and this principle can be mathematically represented as

those. the magnetic flux passing through any closed surface is zero .

Expression (4) is valid for the surface s any form. If we consider the magnetic flux passing through the surface formed by the turns of a cylindrical coil (Fig. 4), then it can be divided into surfaces formed by individual turns, i.e. s=s 1 +s 2 +...+s eight . Moreover, in the general case, different magnetic fluxes will pass through the surfaces of different turns. So in fig. 4, eight single magnetic lines pass through the surfaces of the central turns of the coil, and only four through the surfaces of the outer turns.

In order to determine the total magnetic flux passing through the surface of all turns, it is necessary to add up the fluxes passing through the surfaces of individual turns, or, in other words, interlocking with individual turns. For example, the magnetic fluxes interlocking with the four upper turns of the coil in Fig. 4 will be equal to: F 1 =4; F 2 =4; F 3 =6; F 4 \u003d 8. Also, mirror-symmetrical with the bottom.

Flux linkage - the virtual (imaginary total) magnetic flux Ψ, interlocking with all turns of the coil, is numerically equal to the sum of the fluxes interlocking with individual turns: Ψ = w e F m, where F m- the magnetic flux created by the current passing through the coil, and w e is the equivalent or effective number of turns of the coil. The physical meaning of flux linkage is the coupling of magnetic fields of coil turns, which can be expressed by the coefficient (multiplicity) of flux linkage k= Ψ/Ф = w e.

That is, for the case shown in the figure, two mirror-symmetrical halves of the coil:

Ψ \u003d 2 (Ф 1 + Ф 2 + Ф 3 + Ф 4) \u003d 48

The virtuality, that is, the imaginary flux linkage, manifests itself in the fact that it does not represent a real magnetic flux, which no inductance can multiply, but the behavior of the coil impedance is such that it seems that the magnetic flux increases by a multiple of the effective number of turns, although in reality it is simply interaction of turns in the same field. If the coil increased the magnetic flux by its flux linkage, then it would be possible to create magnetic field multipliers on the coil even without current, because the flux linkage does not imply the closed circuit of the coil, but only the joint geometry of the proximity of the turns.

Often the actual distribution of the flux linkage over the turns of the coil is unknown, but it can be assumed to be uniform and the same for all turns if the real coil is replaced with an equivalent one with a different number of turns. w e, while maintaining the magnitude of the flux linkage Ψ = w e F m, where F m is the flux interlocking with the internal turns of the coil, and w e is the equivalent or effective number of turns of the coil. For the one considered in Fig. 4 cases w e \u003d Ψ / F 4 \u003d 48 / 8 \u003d 6.

It is also possible to replace a real coil with an equivalent one while maintaining the number of turns Ψ = w F n. Then, in order to maintain the flux linkage, it is necessary to accept that the magnetic flux f n = Ψ/ w .

The first option of replacing the coil with an equivalent one preserves the pattern of the magnetic field by changing the parameters of the coil, the second - saves the parameters of the coil by changing the picture of the magnetic field.

Among the physical quantities, an important place is occupied by the magnetic flux. This article explains what it is and how to determine its value.

What is magnetic flux

This is a quantity that determines the level of the magnetic field passing through the surface. Denoted "FF" and depends on the strength of the field and the angle of passage of the field through this surface.

It is calculated according to the formula:

FF=B⋅S⋅cosα, where:

• FF - magnetic flux;
• B is the value of magnetic induction;
• S is the surface area through which this field passes;
• cosα is the cosine of the angle between the perpendicular to the surface and the flow.

The SI unit of measure is "weber" (Wb). 1 weber is created by a 1 T field passing perpendicular to a surface of 1 m².

Thus, the flow is maximum when its direction coincides with the vertical and is equal to "0" if it is parallel to the surface.

Interesting. The formula for the magnetic flux is similar to the formula by which the illumination is calculated.

permanent magnets

One of the sources of the field are permanent magnets. They have been known for centuries. A compass needle was made of magnetized iron, and in ancient Greece there was a legend about an island that attracted the metal parts of ships to itself.

Permanent magnets come in various shapes and are made from different materials:

• iron - the cheapest, but have less attractive power;
• neodymium - from an alloy of neodymium, iron and boron;
• Alnico is an alloy of iron, aluminum, nickel and cobalt.

All magnets are bipolar. This is most noticeable in rod and horseshoe devices.

If the rod is hung in the middle or placed on a floating piece of wood or foam, then it will turn in the north-south direction. The pole pointing north is called the north pole and is painted blue on laboratory instruments and denoted by "N". The opposite one, pointing south, is red and marked "S". Like poles attract magnets, while opposite poles repel.

In 1851, Michael Faraday proposed the concept of closed lines of induction. These lines leave the north pole of the magnet, pass through the surrounding space, enter the south and inside the device return to the north. The closest lines and field strengths are near the poles. Here, too, the attraction force is higher.

If a piece of glass is placed on the device, and iron filings are poured on top in a thin layer, then they will be located along the lines of the magnetic field. When several devices are located next to each other, the sawdust will show the interaction between them: attraction or repulsion.

Earth's magnetic field

Our planet can be represented as a magnet, the axis of which is tilted by 12 degrees. The intersections of this axis with the surface are called magnetic poles. Like any magnet, the Earth's lines of force run from the north pole to the south. Near the poles, they run perpendicular to the surface, so the compass needle is unreliable there, and other methods have to be used.

The particles of the "solar wind" have an electric charge, so when moving around them, a magnetic field appears that interacts with the Earth's field and directs these particles along the lines of force. Thus, this field protects the earth's surface from cosmic radiation. However, near the poles, these lines are perpendicular to the surface, and charged particles enter the atmosphere, causing the aurora borealis.

In 1820, Hans Oersted, while conducting experiments, saw the effect of a conductor through which an electric current flows on a compass needle. A few days later, André-Marie Ampere discovered the mutual attraction of two wires, through which a current flowed in the same direction.

Interesting. During electric welding, nearby cables move when the current changes.

Ampère later suggested that this was due to the magnetic induction of the current flowing through the wires.

In a coil wound with an insulated wire through which an electric current flows, the fields of the individual conductors reinforce each other. To increase the attractive force, the coil is wound on an open steel core. This core becomes magnetized and attracts iron parts or the other half of the core in relays and contactors.

Electromagnetic induction

When the magnetic flux changes, an electric current is induced in the wire. This fact does not depend on what causes this change: the movement of a permanent magnet, the movement of a wire, or a change in the current strength in a nearby conductor.

This phenomenon was discovered by Michael Faraday on August 29, 1831. His experiments showed that the EMF (electromotive force) that appears in a circuit limited by conductors is directly proportional to the rate of change of the flow passing through the area of ​​\u200b\u200bthis circuit.

Important! For the occurrence of EMF, the wire must cross the lines of force. When moving along the lines, there is no EMF.

If the coil in which the EMF occurs is included in the electrical circuit, then a current appears in the winding, which creates its own electromagnetic field in the inductor.

When a conductor moves in a magnetic field, an EMF is induced in it. Its directionality depends on the direction of wire movement. The method by which the direction of magnetic induction is determined is called the “right hand method”.

The calculation of the magnitude of the magnetic field is important for the design of electrical machines and transformers.

Video

Among the many definitions and concepts associated with a magnetic field, one should highlight the magnetic flux, which has a certain direction. This property is widely used in electronics and electrical engineering, in the design of instruments and devices, as well as in the calculation of various circuits.

The concept of magnetic flux

First of all, it is necessary to establish exactly what is called magnetic flux. This value should be considered in combination with a uniform magnetic field. It is homogeneous at every point of the designated space. A certain surface, which has some fixed area, denoted by the symbol S, falls under the action of a magnetic field. The field lines act on this surface and cross it.

Thus, the magnetic flux Ф, crossing the surface with area S, consists of a certain number of lines coinciding with the vector B and passing through this surface.

This parameter can be found and displayed in the form of the formula Ф = BS cos α, in which α is the angle between the normal direction to the surface S and the magnetic induction vector B. Based on this formula, one can determine the magnetic flux with a maximum value at which cos α = 1 , and the position of the vector B will become parallel to the normal perpendicular to the surface S. Conversely, the magnetic flux will be minimal if the vector B is located perpendicular to the normal.

In this version, the vector lines simply slide along the plane and do not cross it. That is, the flux is taken into account only along the lines of the magnetic induction vector crossing a specific surface.

To find this value, weber or volt-seconds are used (1 Wb \u003d 1 V x 1 s). This parameter can be measured in other units. The smaller value is the maxwell, which is 1 Wb = 10 8 µs or 1 µs = 10 -8 Wb.

Magnetic field energy and magnetic induction flux

If an electric current is passed through a conductor, then a magnetic field is formed around it, which has energy. Its origin is associated with the electric power of the current source, which is partially consumed to overcome the EMF of self-induction that occurs in the circuit. This is the so-called self-energy of the current, due to which it is formed. That is, the energies of the field and current will be equal to each other.

The value of the self-energy of the current is expressed by the formula W \u003d (L x I 2) / 2. This definition is considered equal to the work that is done by a current source that overcomes the inductance, that is, the self-induction EMF and creates a current in the electrical circuit. When the current stops acting, the energy of the magnetic field does not disappear without a trace, but is released, for example, in the form of an arc or spark.

The magnetic flux that occurs in the field is also known as the flux of magnetic induction with a positive or negative value, the direction of which is conventionally indicated by a vector. As a rule, this flow passes through a circuit through which an electric current flows. With a positive direction of the normal relative to the contour, the direction of current movement is a value determined in accordance with . In this case, the magnetic flux created by the circuit with electric current, and passing through this circuit, will always have a value greater than zero. Practical measurements also point to this.

The magnetic flux is usually measured in units established by the international SI system. This is the already known Weber, which is the magnitude of the flow passing through a plane with an area of ​​1 m2. This surface is placed perpendicular to the magnetic field lines with a uniform structure.

This concept is well described by the Gauss theorem. It reflects the absence of magnetic charges, so the induction lines are always represented as closed or going to infinity without beginning or end. That is, the magnetic flux passing through any kind of closed surfaces is always zero.

What is magnetic flux?

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 the field. Field lines intersect the surface.

Magnetic flux definition

Definition of magnetic flux:

The 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

Magnetic flux formula:

here α is the angle between the direction of the magnetic induction vector B and the normal to the surface S.

It can be seen from the magnetic flux formula that the maximum magnetic flux will be at cos α = 1, and this will happen when the vector B is parallel to the normal to the surface S. The minimum magnetic flux will be at cos α = 0, this will be when the vector B is perpendicular to the normal to the surface S, because in this case the lines of the vector B will slide over the surface S without crossing it.

And according to the definition of magnetic flux, only those lines of the magnetic induction vector that intersect a given surface are taken into account.

Magnetic flux is a scalar quantity.

The magnetic flux is measured

The magnetic flux is measured in webers (volt-seconds): 1 wb \u003d 1 v * s.

In addition, Maxwell is used to measure the magnetic flux: 1 wb \u003d 10 8 μs. Accordingly, 1 μs = 10 -8 wb.

Magnetic materials are those that are subject to the influence of special force fields, while non-magnetic materials are not subject to or weakly subject to the forces of a magnetic field, which is usually represented by lines of force (magnetic flux) that have certain properties. In addition to always forming closed loops, they behave as if they are elastic, that is, during the distortion, they try to return to their previous distance and to their natural shape.

invisible force

Magnets tend to attract certain metals, especially iron and steel, as well as nickel, nickel, chromium and cobalt alloys. Materials that create attractive forces are magnets. There are various types. Materials that can be easily magnetized are called ferromagnetic. They can be hard or soft. Soft ferromagnetic materials such as iron lose their properties quickly. Magnets made from these materials are called temporary. Rigid materials such as steel hold their properties much longer and are used as permanent materials.

Magnetic Flux: Definition and Characterization

Around the magnet there is a certain force field, and this creates the possibility of energy. The magnetic flux is equal to the product of the average force fields of the perpendicular surface into which it penetrates. It is depicted using the symbol "Φ", it is measured in units called Webers (WB). The amount of flow passing through a given area will vary from one point to another around the object. Thus, magnetic flux is a so-called measure of the strength of a magnetic field or electric current, based on the total number of charged lines of force passing through a certain area.

Revealing the mystery of magnetic fluxes

All magnets, regardless of their shape, have two areas, called poles, capable of producing a certain chain of organized and balanced system of invisible lines of force. These lines from the stream form a special field, the form of which is more intense in some parts than in others. The areas with the greatest attraction are called poles. Vector field lines cannot be detected with the naked eye. Visually, they always appear as lines of force with unambiguous poles at each end of the material, where the lines are denser and more concentrated. Magnetic flux is lines that create vibrations of attraction or repulsion, showing their direction and intensity.

Magnetic flux lines

Magnetic lines of force are defined as curves that move along a certain path in a magnetic field. The tangent to these curves at any point shows the direction of the magnetic field in it. Characteristics:

Each flow line forms a closed loop.

These induction lines never intersect, but tend to shrink or stretch, changing their dimensions in one direction or another.

As a rule, lines of force have a beginning and an end on the surface.

There is also a certain direction from north to south.

Field lines that are close to each other, forming a strong magnetic field.

• When adjacent poles are the same (north-north or south-south), they repel each other. When neighboring poles are not aligned (north-south or south-north), they are attracted to each other. This effect is reminiscent of the famous expression that opposites attract.

Magnetic molecules and Weber's theory

Weber's theory relies on the fact that all atoms are magnetic due to the bonds between the electrons in the atoms. Groups of atoms join together in such a way that the fields surrounding them rotate in the same direction. These kinds of materials are made up of groups of tiny magnets (when viewed at the molecular level) around atoms, which means that the ferromagnetic material is made up of molecules that have attractive forces. They are known as dipoles and are grouped into domains. When the material is magnetized, all the domains become one. A material loses its ability to attract and repel when its domains are separated. The dipoles together form a magnet, but individually, each of them tries to repel the unipolar one, thus attracting opposite poles.

Fields and poles

The strength and direction of the magnetic field is determined by the magnetic flux lines. The area of ​​attraction is stronger where the lines are close to each other. The lines are closest to the pole of the rod base, where the attraction is strongest. The planet Earth itself is in this powerful force field. It acts as if a giant striped magnetized plate is running through the middle of the planet. The north pole of the compass needle is directed towards a point called the North magnetic pole, the south pole it points to the magnetic south. However, these directions differ from the geographic North and South Poles.

The nature of magnetism

Magnetism plays an important role in electrical and electronic engineering, because without its components such as relays, solenoids, inductors, chokes, coils, loudspeakers, electric motors, generators, transformers, electricity meters, etc. will not work. Magnets can be found in natural state in the form of magnetic ores. There are two main types, these are magnetite (also called iron oxide) and magnetic ironstone. The molecular structure of this material in a non-magnetic state is presented as a loose magnetic circuit or individual tiny particles that are freely arranged in a random order. When a material is magnetized, this random arrangement of molecules changes, and tiny random molecular particles line up in such a way that they produce a whole series of arrangements. This idea of ​​molecular alignment of ferromagnetic materials is called Weber's theory.

Measurement and practical application

The most common generators use magnetic flux to generate electricity. Its strength is widely used in electrical generators. The device that measures this interesting phenomenon is called a fluxmeter, it consists of a coil and electronic equipment that evaluates the change in voltage in the coil. In physics, a flow is an indicator of the number of lines of force passing through a certain area. Magnetic flux is a measure of the number of magnetic lines of force.

Sometimes even a non-magnetic material can also have diamagnetic and paramagnetic properties. An interesting fact is that attractive forces can be destroyed by heat or by being struck with a hammer of the same material, but they cannot be destroyed or isolated by simply breaking a large specimen in two. Each broken piece will have its own north and south pole, no matter how small the pieces are.