DEFINITION

Flux of magnetic induction vector(or magnetic flux) (dФ) in the general case, through an elementary area, a scalar physical quantity is called, which is equal to:

where is the angle between the direction of the magnetic induction vector () and the direction of the normal vector () to the site dS ().

Based on formula (1), the magnetic flux through an arbitrary surface S is calculated (in the general case) as:

The magnetic flux of a uniform magnetic field through a flat surface can be found as:

For a uniform field, a flat surface located perpendicular to the magnetic induction vector, the magnetic flux is equal to:

The flux of the magnetic induction vector can be negative and positive. This is due to the choice of a positive direction. Very often, the flux of the magnetic induction vector is associated with a circuit through which current flows. In this case, the positive direction of the normal to the contour is related to the direction of current flow by the rule of the right gimlet. Then, the magnetic flux, which is created by a current-carrying circuit, through the surface bounded by this circuit, is always greater than zero.

The unit of measure for the flux of magnetic induction in the international system of units (SI) is the weber (Wb). Formula (4) can be used to determine the unit of magnetic flux. One Weber is called a magnetic flux that passes through a flat surface, an area of ​​​​which is 1 square meter, placed perpendicular to the lines of force of a uniform magnetic field:

Gauss theorem for magnetic field

The Gauss theorem for a magnetic field flux reflects the fact that there are no magnetic charges, which is why the lines of magnetic induction are always closed or go to infinity, they have no beginning and end.

The Gauss theorem for the magnetic flux is formulated as follows: The magnetic flux through any closed surface (S) is equal to zero. In mathematical form, this theorem is written as follows:

It turns out that the Gauss theorems for the fluxes of the magnetic induction vector () and the strength of the electrostatic field (), through a closed surface, differ fundamentally.

Examples of problem solving

EXAMPLE 1

Exercise Calculate the flux of the magnetic induction vector through the solenoid, which has N turns, the length of the core l, the cross-sectional area S, the magnetic permeability of the core. The current flowing through the solenoid is I.
Solution Inside the solenoid, the magnetic field can be considered uniform. Magnetic induction is easy to find using the magnetic field circulation theorem and choosing a rectangular circuit as a closed circuit (the circulation of the vector along which we will consider (L)) a rectangular circuit (it will cover all N turns). Then we write (we take into account that outside the solenoid the magnetic field is zero, in addition, where the contour L is perpendicular to the lines of magnetic induction B = 0):

In this case, the magnetic flux through one turn of the solenoid is ():

The total flux of magnetic induction that goes through all the turns:
Answer

EXAMPLE 2

Exercise What will be the flux of magnetic induction through a square frame, which is in vacuum in the same plane with an infinitely long straight conductor with current (Fig. 1). The two sides of the frame are parallel to the wire. The length of the side of the frame is b, the distance from one of the sides of the frame is c.

Solution The expression by which it is possible to determine the induction of the magnetic field will be considered known (see Example 1 of the section "Magnetic induction unit of measure"):


Electric dipole moment
Electric charge
electrical induction
Electric field
electrostatic potential See also: Portal:Physics

magnetic flux- physical quantity equal to the product of the modulus of the magnetic induction vector \vec B to the area S and the cosine of the angle α between vectors \vec B and normal \mathbf(n). Flow \Phi_B as an integral of the magnetic induction vector \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 forced himself to smile and realized 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 affairs, Prince Vasily had to resolve matters with Pierre, who, it is true, had spent whole days at home, that is, with Prince Vasily, with whom he lived, he was ridiculous, agitated and stupid (as he should being in love) in Helen's presence, but still not proposing.

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 measurement 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 “N”. The opposite one, pointing south, is red and marked with an “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

Right hand or gimlet rule:

The direction of the magnetic field lines and the direction of the current that creates it are interconnected by the well-known rule of the right hand or gimlet, which was introduced by D. Maxwell and is illustrated by the following figures:

Few people know that a gimlet is a tool for drilling holes in a tree. Therefore, it is more understandable to call this rule the rule of a screw, screw or corkscrew. However, grasping the wire as in the figure is sometimes life-threatening!

Magnetic induction B :

Magnetic induction- is the main fundamental characteristic of the magnetic field, similar to the electric field strength vector E . The magnetic induction vector is always directed tangentially to the magnetic line and shows its direction and strength. The unit of magnetic induction in B = 1 T is the magnetic induction of a homogeneous field, in which a section of the conductor with a length of l\u003d 1 m, with a current strength in it in I\u003d 1 A, the maximum Ampere force acts from the side of the field - F\u003d 1 H. The direction of Ampère's force is determined by the rule of the left hand. In the CGS system, the magnetic induction of the field is measured in gauss (Gs), in the SI system - in teslas (Tl).

Magnetic field strength H:

Another characteristic of the magnetic field is tension, which is analogous to the electric displacement vector D in electrostatics. Determined by the formula:

The magnetic field strength is a vector quantity, it is a quantitative characteristic of the magnetic field and does not depend on the magnetic properties of the medium. In the CGS system, the magnetic field strength is measured in oersteds (Oe), in the SI system - in amperes per meter (A / m).

Magnetic flux F:

Magnetic flux Ф is a scalar physical quantity that characterizes the number of magnetic induction lines penetrating a closed loop. Let's consider a special case. IN uniform magnetic field, whose induction vector modulus is equal to ∣В ∣, is placed flat closed loop area S. The normal n to the contour plane makes an angle α with the direction of the magnetic induction vector B . The magnetic flux through the surface is the value Ф, determined by the relation:

In the general case, the magnetic flux is defined as the integral of the magnetic induction vector B through the finite surface S.

It is worth noting that the magnetic flux through any closed surface is zero (Gauss's theorem for magnetic fields). This means that the lines of force of the magnetic field do not break anywhere, i.e. the magnetic field has a vortex nature, and also that it is impossible for the existence of magnetic charges that would create a magnetic field in the same way that electric charges create an electric field. In SI, the unit of magnetic flux is Weber (Wb), in the CGS system - maxwell (Mks); 1 Wb = 10 8 µs.

Definition of inductance:

Inductance is the coefficient of proportionality between the electric current flowing in any closed circuit and the magnetic flux created by this current through the surface, the edge of which is this circuit.

Otherwise, inductance is the proportionality factor in the self-induction formula.

In the SI system of units, inductance is measured in henries (H). A circuit has an inductance of one henry if, when the current changes by one ampere per second, a self-induction emf of one volt occurs at the circuit terminals.

The term "inductance" was proposed by Oliver Heaviside, an English self-taught scientist in 1886. Simply put, inductance is the property of a current-carrying conductor to store energy in a magnetic field, equivalent to capacitance for an electric field. It does not depend on the magnitude of the current, but only on the shape and size of the current-carrying conductor. To increase the inductance, the conductor is wound in coils, the calculation of which is the program

MAGNETIC FLUX

MAGNETIC FLUX(symbol F), a measure of the strength and extent of the MAGNETIC FIELD. The flow through area A at right angles to the same magnetic field is Ф=mNA, where m is the magnetic PERMEABILITY of the medium, and H is the intensity of the magnetic field. The magnetic flux density is the flux per unit area (symbol B), which is equal to H. A change in the magnetic flux through an electrical conductor induces an ELECTRIC DRIVE FORCE.


Scientific and technical encyclopedic dictionary.

See what "MAGNETIC FLOW" is in other dictionaries:

    The flux of the magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = ВndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux Ф through the final ... ... Big Encyclopedic Dictionary

    - (flux of magnetic induction), flux Ф of the magnetic vector. induction B through c.l. surface. M. p. dФ through a small area dS, within which the vector B can be considered unchanged, is expressed by the product of the size of the area and the projection Bn of the vector onto ... ... Physical Encyclopedia

    magnetic flux- A scalar value equal to the flux of magnetic induction. [GOST R 52002 2003] magnetic flux The flux of magnetic induction through a surface perpendicular to the magnetic field, defined as the product of magnetic induction at a given point and the area ... ... Technical Translator's Handbook

    MAGNETIC FLUX- flux Ф of the magnetic induction vector (see (5)) В through the surface S, normal to the vector В in a uniform magnetic field. The unit of magnetic flux in SI (see) ... Great Polytechnic Encyclopedia

    A value that characterizes the magnetic effect on a given surface. M. p. is measured by the number of magnetic lines of force passing through a given surface. Technical railway dictionary. M .: State transport ... ... Technical railway dictionary

    magnetic flux- a scalar quantity equal to the flux of magnetic induction... Source: ELEKTROTEHNIKA. TERMS AND DEFINITIONS OF BASIC CONCEPTS. GOST R 52002 2003 (approved by the Decree of the State Standard of the Russian Federation of 01/09/2003 N 3 st) ... Official terminology

    The flux of the magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = BndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux Ф through the final ... ... encyclopedic Dictionary

    Classical electrodynamics ... Wikipedia

    magnetic flux- , flux of magnetic induction flux of the vector of magnetic induction through any surface. For a closed surface, the total magnetic flux is zero, which reflects the solenoid nature of the magnetic field, i.e., the absence in nature of ... Encyclopedic Dictionary of Metallurgy

    magnetic flux- 12. Magnetic flux Flux of magnetic induction Source: GOST 19880 74: Electrical engineering. Basic concepts. Terms and definitions original document 12 magnetic on ... Dictionary-reference book of terms of normative and technical documentation

Books

  • Magnetic flux and its transformation, Mitkevich V. F. This book contains a lot that is not always paid due attention when it comes to magnetic flux, and that has not been sufficiently clearly expressed or has not been so far ...