What is called magnetic flux. Magnetic induction

Among physical quantities important place occupies magnetic flux. This article explains what it is and how to determine its size.

What is magnetic flux

This is a quantity that determines the level of the magnetic field passing through the surface. It is designated “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 magnitude 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 field of 1 Tesla passing perpendicular to a surface with an area 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 magnetic flux formula is similar to the formula by which illumination is calculated.

Permanent magnets

One of the field sources is permanent magnets. They have been known for many centuries. The compass needle was made from magnetized iron, and in Ancient Greece There was a legend about an island that attracts metal parts of ships.

There are permanent magnets various shapes and are made from different materials:

iron ones are the cheapest, but have less attractive force;
neodymium - made 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 suspended from the middle or placed on a floating piece of wood or foam, 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 designated “N.” The opposite one, pointing south, is red and marked “S”. Magnets with like poles attract, and with opposite poles they repel.

In 1851, Michael Faraday proposed the concept of closed induction lines. These lines come out of the north pole of the magnet, pass through the surrounding space, enter the south and return to the north inside the device. The lines and field strength are closest at the poles. The attractive force is also higher here.

If you put a piece of glass on the device and sprinkle iron filings on top in a thin layer, they will be located along the magnetic field lines. When several devices are placed nearby, the sawdust will show the interaction between them: attraction or repulsion.

Earth's magnetic field

Our planet can be imagined as a magnet, the axis of which is inclined by 12 degrees. The intersection of this axis with the surface is 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 there the compass needle is unreliable, and other methods have to be used.

Particles of the “solar wind” have an electric charge, so when moving around them, a magnetic field appears, interacting with the Earth’s field and directing 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 directed perpendicular to the surface, and charged particles enter the atmosphere, causing the northern lights.

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, Andre-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.

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

In a coil wound with an insulated wire through which 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 is 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), appearing in a contour limited by conductors, is directly proportional to the rate of change of flux passing through the area of this contour.

Important! For an emf to occur, the wire must cross the power lines. When moving along the lines, there is no EMF.

If the coil in which the EMF occurs is connected to an electrical circuit, then a current arises in the winding, creating its own electromagnetic field in the inductor.

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

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

Video

MAGNETIC FLUX

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

Scientific and technical encyclopedic dictionary.

See what "MAGNETIC FLUX" is in other dictionaries:

The flow 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 F through the final... ... Big Encyclopedic Dictionary

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

magnetic flux- A scalar quantity 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 the magnetic induction at a given point by the area... ... Technical Translator's Guide

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

A value characterizing the magnetic effect on a given surface. The magnetic field 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: ELECTRICAL ENGINEERING. TERMS AND DEFINITIONS OF BASIC CONCEPTS. GOST R 52002 2003 (approved by Resolution of the State Standard of the Russian Federation dated 01/09/2003 N 3 art.) ... Official terminology

The flow 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 F through the final... ... Encyclopedic Dictionary

Classical electrodynamics ... Wikipedia

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

Magnetic flux- 12. Magnetic flux Magnetic induction flux 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 we're talking about about magnetic flux, and what has not yet been stated clearly enough or has not been...

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 a field. The field lines intersect the surface.

Determination of magnetic flux:

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:

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

From the magnetic flux formula it is clear that the maximum magnetic flux will be at cos α = 1, and this will happen when vector B is parallel to the normal to the surface S. The minimum magnetic flux will be at cos α = 0, this will happen when vector B is perpendicular to the normal to the surface S, because in this case the lines of vector B will slide along the surface S without intersecting it.

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

Magnetic flux is measured in webers (volt-seconds): 1 wb = 1 v * s. In addition, Maxwell is used to measure magnetic flux: 1 wb = 10 8 μs. Accordingly, 1 μs = 10 -8 vb.

Magnetic flux is a scalar quantity.

ENERGY OF THE MAGNETIC FIELD OF CURRENT

Around a current-carrying conductor there is a magnetic field that has energy. Where does it come from? The current source included in the electrical circuit has a reserve of energy. At the moment of closing the electrical circuit, the current source spends part of its energy to overcome the effect of the self-inductive emf that arises. This part of the energy, called the current’s own energy, goes to the formation of a magnetic field. The energy of the magnetic field is equal to the intrinsic energy of the current. The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction emf in order to create a current in the circuit.

The energy of the magnetic field created by the current is directly proportional to the square of the current. Where does the magnetic field energy go after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)

4.1. Law of electromagnetic induction. Self-induction. Inductance

Basic formulas

· Law electromagnetic induction(Faraday's law):

, (39)

where is the induction emf; is the total magnetic flux (flux linkage).

· Magnetic flux created by current in the circuit,

where is the inductance of the circuit; is the current strength.

· Faraday's law as applied to self-induction

· Induction emf, which occurs when the frame rotates with current in a magnetic field,

where is the magnetic field induction; is the area of the frame; is the angular velocity of rotation.

Solenoid inductance

, (43)

where is the magnetic constant; is the magnetic permeability of the substance; is the number of turns of the solenoid; is the cross-sectional area of the turn; is the length of the solenoid.

Current strength when opening the circuit

where is the current established in the circuit; is the inductance of the circuit; is the resistance of the circuit; is the opening time.

Current strength when closing the circuit

. (45)

Relaxation time

Examples of problem solving

Example 1.

The magnetic field changes according to the law , where = 15 mT,. A circular conducting coil with a radius = 20 cm is placed in a magnetic field at an angle to the direction of the field (at the initial moment of time). Find the induced emf arising in the coil at time = 5 s.

Solution

According to the law of electromagnetic induction, the inductive emf arising in a coil is , where is the magnetic flux coupled in the coil.

where is the area of the turn; is the angle between the direction of the magnetic induction vector and the normal to the contour:.

Let's substitute the numerical values: = 15 mT,, = 20 cm = = 0.2 m,.

Calculations give .

Example 2

In a uniform magnetic field with induction = 0.2 T, there is a rectangular frame, the moving side of which, length = 0.2 m, moves at a speed = 25 m/s perpendicular to the field induction lines (Fig. 42). Determine the induced emf arising in the circuit.

Solution

When conductor AB moves in a magnetic field, the area of the frame increases, therefore, the magnetic flux through the frame increases and an induced emf occurs.

According to Faraday's law, where, then, but, therefore.

The “–” sign indicates that the induced emf and induced current are directed counterclockwise.

SELF-INDUCTION

Each conductor through which electric current flows is in its own magnetic field.

When the current strength changes in the conductor, the m.field changes, i.e. the magnetic flux created by this current changes. A change in magnetic flux leads to the emergence of a vortex electric field and an induced emf appears in the circuit. This phenomenon is called self-induction. Self-induction is the phenomenon of the occurrence of induced emf in an electrical circuit as a result of a change in current strength. The resulting emf is called self-induced emf

Manifestation of the phenomenon of self-induction

Circuit closure When there is a short circuit in the electrical circuit, the current increases, which causes an increase in the magnetic flux in the coil, and a vortex electric field appears, directed against the current, i.e. a self-induction emf arises in the coil, preventing the increase in current in the circuit (the vortex field inhibits the electrons). As a result L1 lights up later, than L2.

Open circuit When the electrical circuit is opened, the current decreases, a decrease in the flux in the coil occurs, and a vortex electrical field appears, directed like a current (trying to maintain the same current strength), i.e. A self-induced emf arises in the coil, maintaining the current in the circuit. As a result, L when turned off flashes brightly. Conclusion in electrical engineering, the phenomenon of self-induction manifests itself when the circuit is closed (the electric current increases gradually) and when the circuit is opened (the electric current does not disappear immediately).

INDUCTANCE

What does self-induced emf depend on? Electric current creates its own magnetic field. The magnetic flux through the circuit is proportional to the magnetic field induction (Ф ~ B), the induction is proportional to the current strength in the conductor (B ~ I), therefore the magnetic flux is proportional to the current strength (Ф ~ I). The self-induction emf depends on the rate of change of current in the electrical circuit, on the properties of the conductor (size and shape) and on the relative magnetic permeability of the medium in which the conductor is located. A physical quantity showing the dependence of the self-induction emf on the size and shape of the conductor and on the environment in which the conductor is located is called the self-induction coefficient or inductance. Inductance - physical. a value numerically equal to the self-inductive emf that occurs in the circuit when the current changes by 1 Ampere in 1 second. Inductance can also be calculated using the formula:

where Ф is the magnetic flux through the circuit, I is the current strength in the circuit.

SI units of inductance:

The inductance of the coil depends on: the number of turns, the size and shape of the coil and the relative magnetic permeability of the medium (possibly a core).

SELF-INDUCTION EMF

The self-inductive emf prevents the current from increasing when the circuit is turned on and the current from decreasing when the circuit is opened.

To characterize the magnetization of a substance in a magnetic field, it is used magnetic moment (P m ). It is numerically equal to the mechanical torque experienced by a substance in a magnetic field with an induction of 1 Tesla.

The magnetic moment of a unit volume of a substance characterizes it magnetization - I , is determined by the formula:

I=R m /V , (2.4)

Where V - volume of the substance.

Magnetization in the SI system is measured, like intensity, in Vehicle, a vector quantity.

The magnetic properties of substances are characterized volumetric magnetic susceptibility - c O , dimensionless quantity.

If any body is placed in a magnetic field with induction IN 0 , then its magnetization occurs. As a result, the body creates its own magnetic field with induction IN " , which interacts with the magnetizing field.

In this case, the induction vector in the medium (IN) will be composed of vectors:

B = B 0 + B " (vector sign omitted), (2.5)

Where IN " - induction of the own magnetic field of a magnetized substance.

The induction of its own field is determined by the magnetic properties of the substance, which are characterized by volumetric magnetic susceptibility - c O , the following expression is true: IN " = c O IN 0 (2.6)

Divide by m 0 expression (2.6):

IN " /m O = c O IN 0 /m 0

We get: N " = c O N 0 , (2.7)

But N " determines the magnetization of a substance I , i.e. N " = I , then from (2.7):

I = c O N 0 . (2.8)

Thus, if a substance is in an external magnetic field with a strength N 0 , then the induction inside it is determined by the expression:

B=B 0 + B " = m 0 N 0 +m 0 N " = m 0 (N 0 +I)(2.9)

The last expression is strictly true when the core (substance) is completely in an external uniform magnetic field (closed torus, infinitely long solenoid, etc.).

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

MAGNETIC FLUX- (symbol F), a measure of the strength and extent of the MAGNETIC FIELD. The flux through area A at right angles to the same magnetic field is Ф = mHA, where m is the magnetic PERMEABILITY of the medium, and H is the intensity of the magnetic field. Magnetic flux density is the flux... ... Scientific and technical encyclopedic dictionary

MAGNETIC FLUX- a value characterizing the magnetic effect on a given surface. The magnetic field 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- flux of 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 F through the final... ... Encyclopedic Dictionary

Books

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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 yet been stated clearly enough or has not been...

Right hand or gimlet rule:

The direction of the magnetic field lines and the direction of the current creating 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 drawings:

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

Magnetic induction B:

Magnetic induction- is the main fundamental characteristic of the magnetic field, similar to the intensity vector electric field 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 = 1T is taken to be magnetic induction uniform field, in which for a section of conductor with a length of l= 1 m, with a current strength in it in I= 1 A, acts from the side of the field maximum force Ampere - F= 1 H. The direction of the Ampere force is determined by the left-hand rule. In the CGS system, magnetic field induction is measured in gauss (G), in the SI system - in tesla (T).

Magnetic field strength H:

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

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

Magnetic flux F:

Magnetic flux F - scalar physical quantity, characterizing the number of magnetic induction lines penetrating a closed circuit. Let's consider special case. IN uniform magnetic field, the magnitude of the induction vector of which is equal to ∣B ∣, 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 quantity Ф, determined by the relation:

In general, magnetic flux is defined as the integral of the magnetic induction vector B through a 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 magnetic field lines do not break off 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 as electric charges create an electric field. In the SI, the unit of magnetic flux is Weber (Wb), in the CGS system it is Maxwell (Mx); 1 Wb = 10 8 μs.

Definition of inductance:

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

Otherwise, inductance is a coefficient of proportionality in the self-induction formula.

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

The term “inductance” was coined by Oliver Heaviside, a self-taught English scientist, in 1886. Simply put, inductance is the property of a current-carrying conductor to accumulate 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 conductor carrying the current. To increase the inductance, the conductor is wound in coils, the calculation of which is what the program is dedicated to