A magnetic flux arises. The nature of magnetism: magnetic flux, definition, properties, general characteristics

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.

The unit of magnetic flux is 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

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 you 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, the larger the size of the circuit, the greater the magnetic flux will pass through it.

Here we can summarize and say that magnetic flux depends on the area of ​​​​space through which it passes. If we, for example, take a fixed frame of a certain size, which is penetrated by a constant magnetic field, then in this case the magnetic flux that passes through this frame will be constant.

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 a compass to malfunction 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.

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.

B is a physical quantity that is a force characteristic of a 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 the International System of Units, the unit of magnetic induction is taken to be the induction of a magnetic field in which a maximum Ampere force of 1 N acts on each meter of conductor length with a current of 1 A. This unit is called tesla (abbreviated as 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- the phenomenon of the occurrence of electric current in a closed conducting circuit with any change in the magnetic flux penetrating 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 the induced current, and this current, in accordance with Lenz’s rule, is directed so that the magnetic flux it creates counteracts the change in the external magnetic flux.

Law of Electromagnetic Induction

The induced emf in a closed loop is equal to the rate of change of the magnetic flux passing through the loop taken with the opposite sign:

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 is a special case of 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-induced 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:

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

The energy of the magnetic field of the coil is W 1 = LI 1 2 /2. By definition, the inductance of the coil is L = Ф/I 1. Hence,

Magnetic flux (flux of magnetic induction lines) through the contour is numerically equal to the product of the magnitude of the magnetic induction vector by the area limited by the contour and by the cosine of the angle between the direction of the magnetic induction vector and the normal to the surface limited by this contour.

Formula for the work of the Ampere force during the movement of a straight conductor with a constant current in a uniform magnetic field.

Thus, the work done by Ampere's force can be expressed in terms of the current in the moved conductor and the change in magnetic flux through the circuit in which this conductor is connected:

Loop 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:

Magnetic field energy.

A magnetic field has energy. Just as there is a reserve of electrical energy in a charged capacitor, there is a reserve of magnetic energy in the coil through which current flows.

Electromagnetic induction.

Electromagnetic induction - the phenomenon of the occurrence of electric current in a closed circuit when the magnetic flux passing through it changes.

Faraday's experiments. Explanation of electromagnetic induction.

If you bring a permanent magnet close to the coil or vice versa (Fig. 3.1), an electric current will arise in the coil. The same thing happens with two closely spaced coils: if an alternating current source is connected to one of the coils, then alternating current will also appear in the other, but this effect is best manifested if the two coils are connected with a core

According to Faraday's definition, these experiments have the following in common: If the flux of the induction vector penetrating a closed, conducting circuit changes, then an electric current arises in the circuit.

This phenomenon is called the phenomenon electromagnetic induction , and the current is induction. In this case, the phenomenon is completely independent of the method of changing the flux of the magnetic induction vector.

Formula e.m.f. electromagnetic induction.

induced emf in a closed loop is directly proportional to the rate of change of magnetic flux through the area limited by this loop.

Lenz's rule.

Lenz's rule

The induced current arising in a closed circuit with its magnetic field counteracts the change in the magnetic flux that causes it.

Self-induction, its explanation.

Self-induction- the phenomenon of the occurrence of induced emf in an electrical circuit as a result of a change in current strength.

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 flashes brightly when turned off.

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).

Formula e.m.f. self-induction.

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.

The first and second provisions of Maxwell's theory of electromagnetic field.

1. Any displaced electric field generates a vortex magnetic field. An alternating electric field was named by Maxwell because, like an ordinary current, it produces a magnetic field. The vortex magnetic field is generated both by conduction currents Ipr (moving electric charges) and displacement currents (moved electric field E).

Maxwell's first equation

2. Any displaced magnetic field generates a vortex electric field (the basic law of electromagnetic induction).

Maxwell's second equation:

Electromagnetic radiation.

Electromagnetic waves, electromagnetic radiation- a disturbance (change in state) of the electromagnetic field propagating in space.

3.1. Wave - These are vibrations that propagate in space over time.
Mechanical waves can propagate only in some medium (substance): in a gas, in a liquid, in a solid. The source of waves are oscillating bodies that create environmental deformation in the surrounding space. A necessary condition for the appearance of elastic waves is the appearance at the moment of disturbance of the medium of forces preventing it, in particular, elasticity. They tend to bring neighboring particles closer together when they move apart, and push them away from each other when they approach each other. Elastic forces, acting on particles remote from the source of disturbance, begin to unbalance them. Longitudinal waves characteristic only of gaseous and liquid media, but transverse– also to solid bodies: the reason for this is that the particles that make up these media can move freely, since they are not rigidly fixed, unlike solid bodies. Accordingly, transverse vibrations are fundamentally impossible.

Longitudinal waves arise when particles of the medium oscillate, oriented along the vector of propagation of the disturbance. Transverse waves propagate in a direction perpendicular to the impact vector. In short: if in a medium the deformation caused by a disturbance manifests itself in the form of shear, stretching and compression, then we are talking about a solid body for which both longitudinal and transverse waves are possible. If the appearance of a shift is impossible, then the environment can be any.

Each wave travels at a certain speed. Under wave speed understand the speed of propagation of the disturbance. Since the speed of a wave is a constant value (for a given medium), the distance traveled by the wave is equal to the product of the speed and the time of its propagation. Thus, to find the wavelength, you need to multiply the speed of the wave by the period of oscillation in it:

Wavelength - the distance between two points closest to each other in space, in which the oscillations occur in the same phase. The wavelength corresponds to the spatial period of the wave, that is, the distance that a point with a constant phase “travels” in a time interval equal to the period of oscillation, therefore

Wave number(also called spatial frequency) is the ratio 2 π radian to wavelength: the spatial analogue of circular frequency.

Definition: wave number k is the rate of growth of the wave phase φ by spatial coordinate.

3.2. Plane wave - a wave whose front has the shape of a plane.

The front of a plane wave is unlimited in size, the phase velocity vector is perpendicular to the front. A plane wave is a particular solution to the wave equation and a convenient model: such a wave does not exist in nature, since the front of a plane wave begins at and ends at , which, obviously, cannot exist.

The equation of any wave is a solution to a differential equation called a wave equation. The wave equation for the function is written as:

Where

· - Laplace operator;

· - the required function;

· - radius of the vector of the desired point;

· - wave speed;

· - time.

wave surface - geometric locus of points experiencing perturbation of the generalized coordinate in the same phase. A special case of a wave surface is a wave front.

A) Plane wave is a wave whose wave surfaces are a collection of planes parallel to each other.

B) Spherical wave is a wave whose wave surfaces are a collection of concentric spheres.

Ray- line, normal and wave surface. The direction of wave propagation refers to the direction of the rays. If the wave propagation medium is homogeneous and isotropic, the rays are straight (and if the wave is plane, they are parallel straight lines).

The concept of a ray in physics is usually used only in geometric optics and acoustics, since when effects that are not studied in these directions occur, the meaning of the concept of a ray is lost.

3.3. Energy characteristics of the wave

The medium in which the wave propagates has mechanical energy, which is the sum of the energies of the vibrational motion of all its particles. The energy of one particle with mass m 0 is found by the formula: E 0 = m 0 Α 2 ω 2 /2. A unit volume of the medium contains n = p/m 0 particles (ρ - density of the medium). Therefore, a unit volume of the medium has energy w р = nЕ 0 = ρ Α 2 ω 2 /2.

Volumetric energy density(W р) - energy of vibrational motion of particles of the medium contained in a unit of its volume:

Energy flow(F) - a value equal to the energy transferred by a wave through a given surface per unit time:

Wave intensity or energy flux density(I) - a value equal to the energy flow transferred by a wave through a unit area perpendicular to the direction of wave propagation:

3.4. Electromagnetic wave

Electromagnetic wave- the process of propagation of an electromagnetic field in space.

Occurrence condition electromagnetic waves. Changes in the magnetic field occur when the current strength in the conductor changes, and the current strength in the conductor changes when the speed of movement of electric charges in it changes, i.e. when charges move with acceleration. Consequently, electromagnetic waves should arise from the accelerated movement of electric charges. When the charge speed is zero, there is only an electric field. At a constant charge speed, an electromagnetic field arises. With the accelerated movement of a charge, an electromagnetic wave is emitted, which propagates in space at a finite speed.

Electromagnetic waves propagate in matter at a finite speed. Here ε and μ are the dielectric and magnetic permeabilities of the substance, ε 0 and μ 0 are the electric and magnetic constants: ε 0 = 8.85419·10 –12 F/m, μ 0 = 1.25664·10 –6 H/m.

Speed ​​of electromagnetic waves in vacuum (ε = μ = 1):

Main characteristics Electromagnetic radiation is generally considered to be frequency, wavelength and polarization. The wavelength depends on the speed of propagation of radiation. The group speed of propagation of electromagnetic radiation in a vacuum is equal to the speed of light; in other media this speed is less.

Electromagnetic radiation is usually divided into frequency ranges (see table). There are no sharp transitions between the ranges; they sometimes overlap, and the boundaries between them are arbitrary. Since the speed of radiation propagation is constant, the frequency of its oscillations is strictly related to the wavelength in vacuum.

Wave interference. Coherent waves. Conditions for wave coherence.

Optical path length (OPL) of light. Relationship between the difference o.d.p. waves with a difference in the phases of the oscillations caused by the waves.

The amplitude of the resulting oscillation when two waves interfere. Conditions for maxima and minima of amplitude during interference of two waves.

Interference fringes and interference pattern on a flat screen when illuminated by two narrow long parallel slits: a) red light, b) white light.

1) WAVE INTERFERENCE- such a superposition of waves in which their mutual amplification, stable over time, occurs at some points in space and weakening at others, depending on the relationship between the phases of these waves.

The necessary conditions to observe interference:

1) the waves must have the same (or close) frequencies so that the picture resulting from the superposition of waves does not change over time (or does not change very quickly so that it can be recorded in time);

2) the waves must be unidirectional (or have a similar direction); two perpendicular waves will never interfere (try adding two perpendicular sine waves!). In other words, the waves being added must have identical wave vectors (or closely directed ones).

Waves for which these two conditions are met are called COHERENT. The first condition is sometimes called temporal coherence, second - spatial coherence.

Let us consider as an example the result of adding two identical unidirectional sinusoids. We will only vary their relative shift. In other words, we add two coherent waves that differ only in their initial phases (either their sources are shifted relative to each other, or both).

If the sinusoids are located so that their maxima (and minima) coincide in space, they will be mutually amplified.

If the sinusoids are shifted relative to each other by half a period, the maxima of one will fall on the minima of the other; the sinusoids will destroy each other, that is, their mutual weakening will occur.

Mathematically it looks like this. Add two waves:

Here x 1 And x 2- the distance from the wave sources to the point in space at which we observe the result of the superposition. The squared amplitude of the resulting wave (proportional to the intensity of the wave) is given by:

The maximum of this expression is 4A 2, minimum - 0; everything depends on the difference in the initial phases and on the so-called wave path difference :

When at a given point in space an interference maximum will be observed, and when - an interference minimum.

In our simple example, the wave sources and the point in space where we observe interference are on the same straight line; along this line the interference pattern is the same for all points. If we move the observation point away from the straight line connecting the sources, we will find ourselves in a region of space where the interference pattern changes from point to point. In this case, we will observe the interference of waves with equal frequencies and close wave vectors.

2)1. The optical path length is the product of the geometric length d of the path of a light wave in a given medium and the absolute refractive index of this medium n.

2. The phase difference of two coherent waves from one source, one of which travels the path length in a medium with an absolute refractive index, and the other - the path length in a medium with an absolute refractive index:

where , , λ is the wavelength of light in vacuum.

3) The amplitude of the resulting oscillation depends on a quantity called stroke difference waves

If the path difference is equal to an integer number of waves, then the waves arrive at the point in phase. When added, the waves reinforce each other and produce an oscillation with double the amplitude.

If the path difference is equal to an odd number of half-waves, then the waves arrive at point A in antiphase. In this case, they cancel each other, the amplitude of the resulting oscillation is zero.

At other points in space, a partial strengthening or weakening of the resulting wave is observed.

4) Jung's experience

In 1802, an English scientist Thomas Young conducted an experiment in which he observed the interference of light. Light from a narrow gap S, fell on a screen with two closely spaced slits S 1 And S 2. Passing through each of the slits, the light beam expanded, and on the white screen the light beams passing through the slits S 1 And S 2, overlapped. In the region where the light beams overlapped, an interference pattern was observed in the form of alternating light and dark stripes.

Implementation of light interference from conventional light sources.

Interference of light on thin film. Conditions for maximum and minimum interference of light on film in reflected and transmitted light.

Interference fringes of equal thickness and interference fringes of equal inclination.

1) The phenomenon of interference is observed in a thin layer of immiscible liquids (kerosene or oil on the surface of water), in soap bubbles, gasoline, on the wings of butterflies, in tarnished colors, etc.

2) Interference occurs when an initial beam of light splits into two beams as it passes through a thin film, such as the film applied to the surface of the lenses of coated lenses. A ray of light passing through a film of thickness will be reflected twice - from its inner and outer surfaces. The reflected rays will have a constant phase difference equal to twice the thickness of the film, causing the rays to become coherent and interfere. Complete quenching of the rays will occur at , where is the wavelength. If nm, then the film thickness is 550:4 = 137.5 nm.

DEFINITION

Magnetic induction vector flux(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 area 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 the circuit through which the current flows. In this case, the positive direction of the normal to the contour is related to the direction of current flow by the right gimlet rule. Then, the magnetic flux that is created by the current-carrying circuit through the surface bounded by this circuit is always greater than zero.

The unit of magnetic flux in the International System of Units (SI) is the Weber (Wb). Formula (4) can be used to determine the unit of measurement of magnetic flux. One Weber is a magnetic flux that passes through a flat surface with an area of ​​1 square meter, placed perpendicular to the lines of force of a uniform magnetic field:

Gauss's theorem for magnetic field

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

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

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

Examples of problem solving

EXAMPLE 1

Exercise	Calculate the flux of the magnetic induction vector through a solenoid that has N turns, core length l, cross-sectional area S, core magnetic permeability. The current flowing through the solenoid is equal to I.
Solution	Inside the solenoid, the magnetic field can be considered uniform. Magnetic induction can be easily found using the theorem on the circulation of a magnetic field and choosing a rectangular contour as a closed loop (circulation of the vector along which we will consider (L)) (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 equal to (): The total flux of magnetic induction that goes through all turns:
Answer

EXAMPLE 2

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

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

Magnetic flux quantization

Values ​​of magnetic flux Φ passing through

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Excerpt characterizing Magnetic Flux

In November 1805, Prince Vasily was supposed to go to an audit in four provinces. 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 Anatoly, he and he would go to Prince Nikolai Andreevich Bolkonsky in order to marry his son to the daughter of this rich man old man. But before leaving and these new affairs, Prince Vasily needed to resolve matters with Pierre, who, however, had recently been spending whole days at home, that is, with Prince Vasily, with whom he lived, he was funny, excited and stupid (as he should to be in love) in the presence of Helen, but still did not propose.