Magnetic flux formula through tension. Magnetic field 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 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 conductor carrying current 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. Energy magnetic field equal to the current's own energy. The current's own energy is numerically equal to the work that the current source must do to overcome Self-induced emf to create 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 .

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.).

A MAGNETIC FIELD

The magnetic interaction of moving electric charges, according to the concepts of field theory, is explained as follows: every moving electric charge creates a magnetic field in the surrounding space that can act on other moving electric charges.

IN - physical quantity, which is the strength characteristic of the magnetic field. It is called magnetic induction (or magnetic field induction).

Magnetic induction - vector quantity. The magnitude of the magnetic induction vector is equal to the ratio of the maximum value of the Ampere force acting on a straight conductor with current to the current strength in the conductor and its length:

Unit of magnetic induction. IN International system units per unit of magnetic induction is the induction of such a magnetic field in which for each meter of length of the conductor at a current strength of 1 A a maximum Ampere force of 1 N acts. This unit is called tesla (abbreviated: T), in honor of the outstanding Yugoslav physicist N. Tesla:

LORENTZ FORCE

The movement of a current-carrying conductor in a magnetic field shows that the magnetic field acts on moving electric charges. Ampere force acts on the conductor F A = ​​IBlsin a, and the Lorentz force acts on a moving charge:

Where a- angle between vectors B and v.

Movement of charged particles in a magnetic field. In a uniform magnetic field, a charged particle moving at a speed perpendicular to the magnetic field induction lines is acted upon by a force m, constant in magnitude and directed perpendicular to the velocity vector. Under the influence of a magnetic force, the particle acquires acceleration, the modulus of which is equal to:

In a uniform magnetic field, this particle moves in a circle. The radius of curvature of the trajectory along which the particle moves is determined from the condition from which it follows,

The radius of curvature of the trajectory is a constant value, since a force perpendicular to the velocity vector changes only its direction, but not its magnitude. And this means that this trajectory is a circle.

The period of revolution of a particle in a uniform magnetic field is equal to:

The last expression shows that the period of revolution of a particle in a uniform magnetic field does not depend on the speed and radius of its trajectory.

If the electric field strength is zero, then the Lorentz force l is equal to the magnetic force m:

ELECTROMAGNETIC INDUCTION

The phenomenon of electromagnetic induction was discovered by Faraday, who established that an electric current arises in a closed conducting circuit with any change in the magnetic field penetrating the circuit.

MAGNETIC FLUX

Magnetic flux F(flux of magnetic induction) through a surface of area S- a value equal to the product of the magnitude of the magnetic induction vector and the area S and cosine of the angle A between the vector and the normal to the surface:

Ф=BScos

In SI, the unit of magnetic flux is 1 Weber (Wb) - magnetic flux through a surface of 1 m2 located perpendicular to the direction of a uniform magnetic field, the induction of which is 1 T:

Electromagnetic induction-occurrence phenomenon electric current in a closed conducting circuit with any change in the magnetic flux passing through the circuit.

Arising in a closed loop, the induced current has such a direction that its magnetic field counteracts the change in the magnetic flux that causes it (Lenz's rule).

LAW OF ELECTROMAGNETIC INDUCTION

Faraday's experiments showed that the strength of the induced current I i in a conducting circuit is directly proportional to the rate of change in the number of magnetic induction lines penetrating the surface bounded by this circuit.

Therefore, the strength of the induction current is proportional to the rate of change of the magnetic flux through the surface bounded by the contour:

It is known that if a current appears in the circuit, this means that external forces act on the free charges of the conductor. The work done by these forces to move a unit charge along a closed loop is called electromotive force (EMF). Let's find the induced emf ε i.

According to Ohm's law for a closed circuit

Since R does not depend on , then

The induced emf coincides in direction with induced current, and this current, in accordance with Lenz’s rule, is directed so that the magnetic flux created by it counteracts the change in the external magnetic flux.

Law of Electromagnetic Induction

The induced emf in a closed loop is equal to that taken from opposite sign rate of change of magnetic flux penetrating the circuit:

SELF-INDUCTION. INDUCTANCE

Experience shows that magnetic flux F associated with a circuit is directly proportional to the current in that circuit:

Ф = L*I .

Loop inductance L- proportionality coefficient between the current passing through the circuit and the magnetic flux created by it.

The inductance of a conductor depends on its shape, size and properties of the environment.

Self-induction- the phenomenon of the occurrence of induced emf in a circuit when the magnetic flux changes caused by a change in the current passing through the circuit itself.

Self-induction - special case electromagnetic induction.

Inductance is a quantity numerically equal to the self-inductive emf that occurs in a circuit when the current in it changes by one per unit of time.

In SI, the unit of inductance is taken to be the inductance of a conductor in which, when the current strength changes by 1 A in 1 s, a self-inductive emf of 1 V occurs. This unit is called henry (H):

MAGNETIC FIELD ENERGY

The phenomenon of self-induction is similar to the phenomenon of inertia. Inductance plays the same role when changing current as mass does when changing the speed of a body. The analogue of speed is current.

This means that the energy of the magnetic field of the current can be considered a value similar to the kinetic energy of the body:

Let us assume that after disconnecting the coil from the source, the current in the circuit decreases with time according to a linear law.

The self-induction emf in this case has a constant value:

where I is the initial value of the current, t is the time period during which the current strength decreases from I to 0. During time t, an electric charge passes through the circuit q = I cp t . Because, I cp = (I + 0)/2 = I/2 then q=It/2

. Therefore, the work of electric current is:

This work is done due to the energy of the magnetic field of the coil. Thus we again get: Example.

Determine the energy of the magnetic field of the coil in which, at a current of 7.5 A, the magnetic flux is 2.3 * 10 -3 Wb. How will the field energy change if the current strength is halved?

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. Magnetic flux through small area dS, within which 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. M.p. is measured by the number of magnetic power lines passing through this 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 equal to 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

• , Mitkevich V.F.. This book contains a lot that is not always paid due attention when we're talking about O magnetic flux, and what has not been stated clearly enough so far or has not been...
• Magnetic flux and its transformation, Mitkevich V.F.. This book will be produced in accordance with your order using Print-on-Demand technology.

This book contains a lot that is not always given due attention when it comes to...

What is magnetic flux?

In order to give an accurate quantitative formulation of Faraday's law of electromagnetic induction, it is necessary to introduce a new quantity - magnetic induction vector flux.

The magnetic induction vector characterizes the magnetic field at each point in space. You can introduce another quantity that depends on the values ​​of the vector not at one point, but at all points of the surface bounded by a flat closed contour.

To do this, consider a flat closed conductor (circuit) bounding a surface of area S and placed in a uniform magnetic field (Fig. 2.4). The normal (vector whose modulus is equal to unity) to the plane of the conductor makes an angle with the direction of the magnetic induction vector. Magnetic flux Ф (flux of the magnetic induction vector) through a surface of area S is a value equal to the product of the magnitude of the magnetic induction vector by the area S and the cosine of the angle between the vectors and:

The product is a projection of the magnetic induction vector onto the normal to the contour plane. That's why

The greater the value of B n and S, the greater the magnetic flux. The value of F is called “magnetic flux” by analogy with the flow of water, which is greater the greater the speed of water flow and the cross-sectional area of ​​the pipe.

Magnetic flux can be interpreted graphically as a value proportional to the number of magnetic induction lines penetrating a surface of area S. Weber.

1 weber (1 Wb) is created by a uniform magnetic field with an induction of 1 T through a surface with an area of ​​1 m 2 located perpendicular to the magnetic induction vector.

Magnetic flux depends on the orientation of the surface that the magnetic field penetrates.

General information about magnetic flux

Today's physics lesson is devoted to the topic of magnetic flux. In order to give an accurate quantitative formulation of Faraday's law of electromagnetic induction, we will need to introduce a new quantity, which is actually called magnetic flux or flux of the magnetic induction vector.

From previous classes you already know that the magnetic field is described by the magnetic induction vector B. Based on the concept of induction vector B, we can find the magnetic flux. To do this, we will consider a closed conductor or circuit with area S. Let us assume that a uniform magnetic field with induction B passes through it. Then the magnetic flux F, the vector of magnetic induction through a surface of area S, is the value of the product of the module of the magnetic induction vector B by the area of ​​the circuit S and on the cos of the angle between vector B and the normal cos alpha:

In general, we have come to the conclusion that if we place a current-carrying circuit in a magnetic field, then all the induction lines of this magnetic field will pass through the circuit. That is, we can safely say that the magnetic induction line is this very magnetic induction, which is located at every point of this line. Or we can say that magnetic induction lines are the flow of the induction vector along the space limited and described by these lines, i.e. magnetic flux.

Now let's remember what a unit of magnetic flux is equal to:

Direction and amount of magnetic flux But you also need to know that each magnetic flux has its own direction and quantitative value. In this case, we can say that the circuit penetrates a certain magnetic flux. And also, it should be noted that the magnitude of the magnetic flux depends on the size of the circuit, that is, what larger size

circuit, the greater the magnetic flux will pass through it.

As the strength of the magnetic field increases, the magnetic induction will naturally increase. In addition, the magnitude of the magnetic flux will increase proportionally depending on the increased magnitude of induction.

Practical task

1. Look carefully at this figure and answer the question: How can the magnetic flux change if the circuit rotates around the OO axis?

2. How do you think the magnetic flux can change if we take a closed loop, which is located at a certain angle to the lines of magnetic induction and its area is reduced by half, and the vector module is increased by four times?
3. Look at the answer options and tell me how the frame should be oriented in a uniform magnetic field so that the flux through this frame is zero? Which answer is correct?

4. Look carefully at the drawing of the depicted circuits I and II and give an answer, how can the magnetic flux change when they rotate?

5. What do you think determines the direction of the induction current?
6. What is the difference between magnetic induction and magnetic flux? Name these differences.
7. Name the formula for magnetic flux and the quantities included in this formula.
8. What methods of measuring magnetic flux do you know?

It's interesting to know

Did you know that increased solar Activity affects the Earth's magnetic field and approximately every eleven and a half years it increases so much that it can disrupt radio communications, cause compass failure and negatively affect human well-being. Such processes are called magnetic storms.

Myakishev G. Ya., Physics. 11th grade: educational. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; edited by V. I. Nikolaeva, N. A. Parfentieva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

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 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- 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- (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- 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

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- 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

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

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

• , 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... Buy for 2252 UAH (Ukraine only)
• Magnetic flux and its transformation, Mitkevich V.F.. This book will be produced in accordance with your order using Print-on-Demand technology.