Electric dipole moment
Electric charge
electrical induction
Electric field
electrostatic potential

magnetostatics
Biot-Savart-Laplace law Ampère's law Magnetic moment A magnetic field magnetic flux Magnetic induction

Electrodynamics
vector potential Dipole Potentials of Lienar - Wiechert Lorentz force Bias current Unipolar induction Maxwell's equations Electricity Electromotive force Electromagnetic induction Electromagnetic radiation Electromagnetic field

Electrical circuit
Ohm's law Kirchhoff's laws Inductance radio waveguide Resonator Electric capacity electrical conductivity Electrical resistance Electrical impedance

Notable scientists
Henry Cavendish Michael Faraday Nikola Tesla André-Marie Ampère Gustav Robert Kirchhoff James Clerk (Clark) Maxwell Henry Rudolf Hertz Albert Abraham Michelson Robert Andrews Milliken

See also: Portal:Physics

magnetic flux - physical quantity equal to the product of the modulus of the magnetic induction vector $\backslash vec\; B$ to the area S and the cosine of the angle α between vectors $\backslash vec\; B$ and normal $\backslash mathbf(n)$. Flow $\backslash Phi\_B$ as an integral of the magnetic induction vector $\backslash vec\; B$ through the end surface S is defined via the integral over the surface:

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In this case, the vector element d S surface area S defined as

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Magnetic flux quantization

The values ​​of the magnetic flux Φ passing through

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An excerpt characterizing the Magnetic flux

- C "est bien, mais ne demenagez pas de chez le prince Basile. Il est bon d" avoir un ami comme le prince, she said, smiling at Prince Vasily. - J "en sais quelque chose. N" est ce pas? [That's good, but don't move away from Prince Vasily. It's good to have such a friend. I know something about it. Isn't it?] And you're still so young. You need advice. You are not angry with me that I use the rights of old women. - She fell silent, as women are always silent, waiting for something after they say about their years. - If you marry, then another matter. And she put them together in one look. Pierre did not look at Helen, and she at him. But she was still terribly close to him. He mumbled something and blushed.
Returning home, Pierre could not sleep for a long time, thinking about what had happened to him. What happened to him? Nothing. He only realized that the woman he knew as a child, about whom he absentmindedly said: “Yes, good,” when he was told that Helen was beautiful, he realized that this woman could belong to him.
“But she is stupid, I myself said she was stupid,” he thought. - There is something nasty in the feeling that she aroused in me, something forbidden. I was told that her brother Anatole was in love with her, and she was in love with him, that there was a whole story, and that Anatole was expelled from this. Her brother is Ippolit... Her father is Prince Vasily... This is not good, he thought; and at the same time as he was reasoning like this (these reasonings were still unfinished), he found himself smiling and realizing that another series of reasonings had surfaced because of the first ones, that at the same time he was thinking about her insignificance and dreaming about how she would be his wife, how she could love him, how she could be completely different, and how everything he thought and heard about her could be untrue. And he again saw her not as some kind of daughter of Prince Vasily, but saw her whole body, only covered with a gray dress. “But no, why didn’t this thought occur to me before?” And again he told himself that it was impossible; that something nasty, unnatural, as it seemed to him, dishonest would be in this marriage. He remembered her former words, looks, and the words and looks of those who had seen them together. He remembered the words and looks of Anna Pavlovna when she told him about the house, remembered thousands of such hints from Prince Vasily and others, and he was horrified that he had not bound himself in any way in the performance of such a thing, which, obviously, was not good. and which he must not do. But at the same time as he was expressing this decision to himself, from the other side of his soul her image surfaced with all its feminine beauty.

In November 1805, Prince Vasily had to go to four provinces for an audit. He arranged this appointment for himself in order to visit his ruined estates at the same time, and taking with him (at the location of his regiment) his son Anatole, together with him to call on Prince Nikolai Andreevich Bolkonsky in order to marry his son to the daughter of this rich old man. But before leaving and these new cases, Prince Vasily had to resolve matters with Pierre, who, however, recent times spent whole days at home, that is, at Prince Vasily, with whom he lived, he was ridiculous, excited and stupid (as a lover should be) in the presence of Helen, but still did not make an offer.

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 a product of the amount of charge flowing through a conductor aligned with the boundary of this surface with complete disappearance magnetic field, on 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 it will also move electric charges. 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. Miscellaneous signs 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 depict graphically 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, through the surfaces of different turns in general case different magnetic fluxes will pass through. So in fig. 4, eight single coils pass through the surfaces of the central turns of the coil. magnetic lines, and only four through the surfaces of the extreme turns.

In order to determine the total magnetic flux passing through the surface of all turns, it is necessary to add 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 - virtual (imaginary total) magnetic flux Ψ, interlocking with all turns of the coil, numerically is equal to the sum flows interlocking with individual coils: 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. physical meaning flux linkage - 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 for replacing the coil with an equivalent one preserves the magnetic field pattern by changing the coil parameters, the second option preserves the coil parameters by changing the magnetic field pattern.

The relationship between electric and magnetic fields has been noticed for a very long time. This connection was discovered in the 19th century by the English physicist Faraday and gave it a name. It appears at the moment when the magnetic flux penetrates the surface of a closed circuit. After a change in the magnetic flux occurs for a certain time, an electric current appears in this circuit.

The relationship of electromagnetic induction and magnetic flux

The essence of the magnetic flux is displayed by the well-known formula: Ф = BS cos α. In it, F is a magnetic flux, S is the surface of the contour (area), B is the vector of magnetic induction. The angle α is formed due to the direction of the magnetic induction vector and the normal to the contour surface. It follows that the magnetic flux will reach the maximum threshold at cos α = 1, and the minimum threshold at cos α = 0.

In the second variant, the vector B will be perpendicular to the normal. It turns out that the flow lines do not cross the contour, but only slide along its plane. Therefore, the characteristics will be determined by the lines of the vector B that intersect the surface of the contour. For calculation, Weber is used as a unit of measurement: 1 wb \u003d 1v x 1s (volt-second). Another, smaller unit of measure is the maxwell (µs). It is: 1 wb \u003d 108 μs, that is, 1 μs \u003d 10-8 wb.

For research by Faraday, two wire spirals were used, isolated from each other and placed on a wooden coil. One of them was connected to an energy source, and the other to a galvanometer designed to record small currents. At that moment, when the circuit of the original spiral closed and opened, in the other circuit the arrow of the measuring device deviated.

Conducting research on the phenomenon of induction

In the first series of experiments, Michael Faraday inserted a magnetized metal bar into a coil connected to a current, and then pulled it out (Fig. 1, 2).

1 2

If a magnet is placed in a coil connected to measuring instrument, an inductive current begins to flow in the circuit. If the magnetic bar is removed from the coil, the induction current still appears, but its direction is already reversed. Consequently, the parameters of the induction current will be changed in the direction of the bar and depending on the pole with which it is placed in the coil. The strength of the current is affected by the speed of movement of the magnet.

In the second series of experiments, a phenomenon is confirmed in which a changing current in one coil causes an induction current in another coil (Fig. 3, 4, 5). This happens at the moments of closing and opening the circuit. Whether it closes or opens electrical circuit, the direction of the current will also depend. In addition, these actions are nothing more than ways to change the magnetic flux. When the circuit is closed, it will increase, and when it is opened, it will decrease, simultaneously penetrating the first coil.

3 4

5

As a result of the experiments, it was found that the occurrence of an electric current inside a closed conducting circuit is possible only when they are placed in an alternating magnetic field. At the same time, the flow can change in time by any means.

The electric current that appears under the influence of electromagnetic induction is called induction, although this will not be a current in the conventional sense. When a closed circuit is in a magnetic field, an EMF is generated with an exact value, and not a current depending on different resistances.

This phenomenon is called the EMF of induction, which is reflected by the formula: Eind = - ∆F / ∆t. Its value coincides with the rate of change in the magnetic flux penetrating the surface of a closed loop, taken from negative value. The minus present in given expression, is a reflection of Lenz's rule.

Lenz's rule for magnetic flux

A well-known rule was derived after a series of studies in the 30s of the 19th century. It is formulated in the following way:

The direction of the induction current, excited in a closed circuit by a changing magnetic flux, affects the magnetic field created by it in such a way that it, in turn, creates an obstacle to the magnetic flux that causes the appearance of the inductive current.

When the magnetic flux increases, that is, it becomes Ф > 0, and the induction EMF decreases and becomes Eind< 0, в результате этого появляется электроток с такой направленностью, при которой под влиянием его магнитного поля происходит изменение потока в сторону уменьшения при его прохождении через плоскость замкнутого контура.

If the flow decreases, then the reverse process occurs when F< 0 и Еинд >0, that is, the action of the magnetic field of the induction current, there is an increase in the magnetic flux passing through the circuit.

The physical meaning of Lenz's rule is to reflect the law of conservation of energy, when when one quantity decreases, the other increases, and, conversely, when one quantity increases, the other will decrease. Various factors also affect the induction emf. When a strong and weak magnet is alternately inserted into the coil, the device will respectively show a higher value in the first case, and a lower value in the second. The same thing happens when the speed of the magnet changes.

The figure below shows how the direction of the induction current is determined using the Lenz rule. Blue color corresponds to the lines of force of the magnetic fields of the induction current and the permanent magnet. They are located in the direction of the north-south poles that are present in every magnet.

The changing magnetic flux leads to the emergence of an inductive electric current, the direction of which causes opposition from its magnetic field, which prevents changes in the magnetic flux. Concerning, lines of force of the magnetic field of the coil are directed in the direction opposite to the lines of force of the permanent magnet, since its movement occurs in the direction of this coil.

To determine the direction of the current, it is used with a right-hand thread. It must be screwed in such a way that its direction forward movement coincided with the direction of the induction lines of the coil. In this case, the directions of the induction current and the rotation of the gimlet handle will coincide.

Using lines of force, one can not only show the direction of the magnetic field, but also characterize the magnitude of its induction.

We agreed to draw lines of force in such a way that through 1 cm² of the area, perpendicular to the induction vector at a certain point, the number of lines equal to the field induction at this point passed.

In the place where the field induction is greater, the lines of force will be thicker. And, conversely, where the field induction is less, the lines of force are rarer.

A magnetic field with the same induction at all points is called a uniform field. Graphically, a uniform magnetic field is represented by lines of force, which are equally spaced from each other.

An example of a uniform field is the field inside a long solenoid, as well as the field between closely spaced parallel flat pole pieces of an electromagnet.

The product of the induction of a magnetic field penetrating a given circuit by the area of ​​\u200b\u200bthe circuit is called the magnetic flux of magnetic induction, or simply magnetic flux.

The English physicist Faraday gave him a definition and studied his properties. He discovered that this concept allows a deeper consideration of the unified nature of magnetic and electrical phenomena.

Denoting the magnetic flux with the letter F, the area of ​​the circuit S and the angle between the direction of the induction vector B and the normal n to the area of ​​the circuit α, we can write the following equality:

Ф = В S cos α.

Magnetic flux is a scalar quantity.

Since the density of the lines of force of an arbitrary magnetic field is equal to its induction, the magnetic flux is equal to the entire number of lines of force that permeate this circuit.

With a change in the field, the magnetic flux that permeates the circuit also changes: when the field is strengthened, it increases, and when the field is weakened, it decreases.

The unit of magnetic flux in is taken to be the flux that permeates an area of ​​1 m², located in a magnetic uniform field, with an induction of 1 Wb / m², and located perpendicular to the induction vector. Such a unit is called a weber:

1 Wb \u003d 1 Wb / m² ˖ 1 m².

The changing magnetic flux generates an electric field with closed lines of force (vortex electric field). Such a field manifests itself in the conductor as the action of extraneous forces. This phenomenon is called electromagnetic induction, and the electromotive force that arises in this case is the induction EMF.

In addition, it should be noted that the magnetic flux makes it possible to characterize the entire magnet as a whole (or any other sources of the magnetic field). Therefore, if it makes it possible to characterize its action at any single point, then the magnetic flux is entirely. That is, we can say that this is the second most important And, therefore, if magnetic induction acts as a force characteristic of a magnetic field, then magnetic flux is its energy characteristic.

Returning to the experiments, we can also say that each coil coil can be imagined as a single closed coil. The same circuit through which the magnetic flux of the magnetic induction vector will pass. In this case, there will be an induction electricity. Thus, it is under the influence of a magnetic flux that an electric field is formed in a closed conductor. And then this electric field forms an electric current.

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.