Electromagnetic induction. Magnetic Stream - Hypermarket Knowledge

Magnetic flow (magnetic induction lines flow) through the circuit, it is numerically equal to the product of the magnetic induction vector module on the area, limited by the contour, and on the cosine of the angle between the direction of the magnetic induction vector and the normal to the surface limited to this circuit.

The formula for the work of the amper force when moving a direct conductor with a constant current in a uniform magnetic field.

Thus, the work of the amper power can be expressed through current strength in a movable conductor and changing the magnetic flux through the outline, which includes this conductor:

Inductance contour.

Inductance - phys. The value is numerically equal to self-induction EMF arising in the circuit when the current is changed by 1 per 1 second.
Also inductance can be calculated by the formula:

where F is a magnetic flow through the contour, I is the current strength in the circuit.

Units of inductance in the SI system:

Energy magnetic field.

The magnetic field has energy. Just as in the charged capacitor, there is a stock of electrical energy, in the coil, in the turns of which flows current flows, there is a stock of magnetic energy.

Electromagnetic induction.

Electromagnetic induction - The phenomenon of the occurrence of the electric current in the closed circuit when the magnetic flux passing through it is changed.

Faraday experiences. Explanation of electromagnetic induction.

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

By definition of Faraday, the following is common to these experiments: if the induction vector stream, piercing a closed, conductive circuit changes, then an electric current occurs in the circuit.

This phenomenon is called phenomenon electromagnetic induction , and current - induction. At the same time, the phenomenon is completely independent of the method of changing the flow of magnetic induction.

Formula E.D.S. electromagnetic induction.

EMF induction In a closed loop, it is directly proportional to the rate of change of magnetic flux through the area limited to this circuit.

Lenza rule.

Lenza rule

The induction current appears in the closed circuit with its magnetic field opposes the change in the magnetic flux to which it is called.

Self-induction, its explanation.

Self-induction - The phenomenon of the appearance of EDC induction in email as a result of changes in current.

Circuit chain
When closing in the email, the current increases, which causes an increase in magnetic flux in the coil, a vortex email appears, directed against the current, i.e. In the coil, self-induction emfs occurs, which prevents the increase in the current in the chain (the vortex field slows down the electrons).
As a result, L1 lights up later than L2.

Blurring chain
When operating an email deck decreases, a decrease in M.Potok in the coil arises, the vortex email appears, directed as the current (striving to preserve the former current strength), i.e. In the coil there is a self-induction EMF, which maintains the current in the chain.
As a result, when it turns off brightly flashes.

in the electrical engineering, the self-induction phenomenon manifests itself when the chain is closed (email increases gradually) and when the circuit is blurred (email does not disappear).

Formula E.D.S. self-induction.

EMF of self-induction prevents the increase in current force when the circuit is turned on and decreasing the current for the circuit of the chain.

The first and second position of the theory of the electromagnetic field of Maxwell.

1. Any displaced electric field generates a vortex magnetic field. The alternating electric field was called Maxwell, as it is, like an ordinary current, causes a magnetic field. The vortex magnetic field is generated by both the conductivity currents of the IPR (moving electrical charges) and the offset currents (displaced electric field E).

The first equation Maxwell

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

The second equation Maxwell:

Electromagnetic radiation.

Electromagnetic waves, electromagnetic radiation- spreading in the space indignation (change of state) of the electromagnetic field.

3.1. Wave - These are oscillations that spread in space over time.
Mechanical waves can only be distributed in some medium (substance): in gas, in liquid, in a solid. The source of waves are oscillating bodies that create environmental deformation in the surrounding space. A prerequisite for the appearance of elastic waves is the emergence of the forces in particular, in particular, elasticity at the moment of indignation of the medium. They strive to bring the neighboring particles when they diverge, and push them away from each other at the time of rapprochement. The forces of elasticity, acting on the particles distant from the source, begin to withdraw them from equilibrium. Longitudinal waves Characterized only by gaseous and liquid media, but transverse - also and solid bodies: the reason for this is that particles that make up the environment data can move freely, as they are not rigidly fixed, unlike solid tel. Accordingly, transverse oscillations are fundamentally impossible.

Longitudinal waves occur when the medium particles fluctuate, focusing along the distribution vector. Transverse waves apply to perpendicular to the direction of exposure to the direction. In short: if in the medium the deformation caused by perturbation is manifested in the form of shear, stretching and compression, then we are talking A solid body for which both longitudinal and transverse waves are possible. If the appearance of the shift is impossible, then the medium can be any.

Each wave applies at some speed. Under wave speed Understand the rate of spread of indignation. Since the speed of the wave is a permanent value (for a given environment), then the distance traveled distance is equal to the product at the time of its propagation. Thus, to find the wavelength, it is necessary to multiply the speed of the wave for the period of oscillations in it:

Wavelength - The distance between the two points closest to each other in space in which oscillations occur in the same phase. The wavelength corresponds to the spatial period of the wave, that is, the distance that the point with the permanent phase "passes" over the time interval equal to the period of oscillations, so

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

Definition: The wave number K is called the rapid growth of the wave phase φ According to the spatial coordinate.

3.2. Flat wave - Wave, the front of which has a plane shape.

The front of a flat wave is unlimited in size, the phase velocity vector is perpendicular to the front. A flat wave is a private solution of the wave equation and a convenient model: such a wave in nature does not exist, since the front of a flat wave begins in and ends in what, obviously, can not be.

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

Where

· - Laplace operator;

· - the desired function;

· - The radius of the vector of the desired point;

· - Wave speed;

· - Time.

Wave surface - geometric location of points experiencing the outrage of the generalized coordinate in the same phase. Private case of a wave surface - a wave front.

BUT) Flat wave - This is a wave, the wave surface of which is a totality of parallel to each other planes.

B) Spherical wave - This is a wave, the wave surface of which is a combination of concentric spheres.

Ray - line, normal and wave surface. Under the direction of propagation, the waves understand the direction of the rays. If the wave spread medium is homogeneous and isotropic, rays straight (and if the wave is flat - parallel straight).

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

3.3. Energy characteristics of the wave

The medium in which the wave is propagated, has a mechanical energy folding from the energies of the oscillatory movement of all its particles. The energy of one particle with a mass M 0 is by the formula: E 0 \u003d M 0 α 2 Ω. 2/2. The amount of medium contains n \u003d p./ m 0 particles (ρ - Medium density). Therefore, the unit of the volume of the medium has the energy w p \u003d n 0 \u003d ρ Α 2 Ω. 2 /2.

Volumetric density of energy (W p) - the energy of the oscillatory movement of the particles of the medium contained in the unit of its volume:

Energy flow (F) - the value equal to the energy carried by the wave through this surface per unit of time:

Wave intensity or energy flow density (I) - the value equal to the stream of energy carried by the wave through a single platform perpendicular to the direction of the wave propagation:

3.4. Electromagnetic wave

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

The condition of emergence electromagnetic waves. The changes in the magnetic field occur when the current is changed in the conductor, and the current power in the conductor changes when the speed of the electric charges changes in it, i.e., when the charges are moving with acceleration. Consequently, electromagnetic waves should occur with the accelerated movement of electrical charges. With a charge rate equal to zero, there is only an electric field. At constant charge speed, an electromagnetic field occurs. With an accelerated charge movement, an electromagnetic wave radiation occurs, which spreads in space with a finite speed.

Electromagnetic waves propagate in a substance with a finite speed. Here ε and μ is the dielectric and magnetic permeability of the substance, ε 0 and μ 0 - electrical and magnetic constant: ε 0 \u003d 8,85419 · 10 -12 f / m, μ 0 \u003d 1,25664 · 10 -6 Gn / m.

Speed \u200b\u200bof electromagnetic waves in vacuum (ε \u003d μ \u003d 1):

Basic characteristics Electromagnetic radiation It is customary to consider the frequency, wavelength and polarization. The wavelength depends on the rate of radiation propagation. The group rate of propagation of electromagnetic radiation in a vacuum is equal to the speed of light, in other media, this speed is less.

The electromagnetic radiation is customary to divide the frequencies to the ranges (see table). There are no sharp transitions between the bands, they sometimes overlap, and the boundaries between them are conditional. Since the rate of radiation propagation is constant, the frequency of its oscillations is rigidly related to the wavelength in vacuo.

Wave interference. Coherent waves. Conditions of coherence of waves.

Optical path length (ODP) light. Communication difference ODP Waves with a phase difference of oscillations caused by waves.

The amplitude of the resulting oscillation during the interference of two waves. The conditions of maxima and minima amplitude in the interference of two waves.

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

1) Wave Interference - Such an overlap of waves, in which their mutual strengthening occurs in time at one points of space and weakening in others, depending on the relationship between the phases of these waves.

The necessary conditions To observe interference:

1) waves must have the same (or close) frequencies so that the picture, resulting from the overlay of the waves, has not changed over time (or changed not very quickly, whatever it could be to register);

2) waves must be unidirectional (or have a close direction); Two perpendicular waves will never give interference (try folding two perpendicular sinusoids!). In other words, the folded waves must have the same wave vectors (or close-directed).

Waves for which these two conditions are performed are called Coherent. The first condition is sometimes called temporary coherencesecond - spatial coherence.

Consider as an example the result of the addition of two identical unidirectional sinusoids. We will only vary their relative shift. In other words, we fold two coherent waves, which differ only on the initial phases (or their sources are shifted relative to each other, or even more together).

If the sinusoids are located so that their maxima (and minima) coincide in space, their mutual strengthening will occur.

If the sinusoids are shifted relative to each other on the singer period, the maxima of one will come to the minimum of another; Sinusoids will destroy each other, that is, their mutual weakening will occur.

Mathematically, it looks like this. We fold two waves:

here x 1 and x 2 - distances from the sources of the waves to the point of space in which we observe the overlay result. The square amplitude of the resulting wave (proportional intensity of the wave) is given by the expression:

The maximum of this expression is 4A 2.minimum - 0; It all depends on the difference in the initial phases and on the so-called difference of the waves :

At this point of space, the interference maximum will be observed, when interference minimum.

In our simple example, the sources of the waves and the point of space, where we observe the interference, are on one straight line; Along this direct interference picture for all points is the same. If we slide the observation point aside from a straight line connecting sources, we will fall into the area of \u200b\u200bspace, where the interference pattern changes from the point to the point. In this case, we will observe the interference of waves with equal frequencies and close wave vectors.

2) 1. The optical length of the path is called the product of the geometric length D of the light wave path in this medium to the absolute refractive index of this medium N.

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

where, λ is the wavelength of light in vacuum.

3) the amplitude of the resulting oscillation depends on the value called difference of travel waves.

If the movement difference is equal to an integer number of waves, then the waves come to the point of syphase. Folding on the waves enhance each other and give oscillation with a twin amplitude.

If the movement difference is equal to an odd number of half-breaves, then the waves come to the point A in antiphase. In this case, they quit each other, the amplitude of the resulting oscillation is zero.

At other points of space, partial amplification or weakening of the resulting wave is observed.

4) Jung's experience

In 1802, English scientist Thomas Jung Put the experience in which the interference of light was observed. Light from a narrow gap S., fell on the screen with two close sluts S 1 and S 2.. Passing through each of the slots, the light beam expanded, and on the white screen, the light beams pasted through the gaps S 1 and S 2., overlap. In the area of \u200b\u200boverlapping light beams, an interference pattern was observed in the form of alternating light and dark strips.

Implementation of light interference from conventional light sources.

Light interference on a thin film. The conditions of maxima and minima of the interference of light on the film in the reflected and in the transmitted light.

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

1) the interference phenomenon is observed in a thin layer of unsuccessful liquids (kerosene or oil on the surface of the water), in soap bubbles, gasoline, on the wings of butterflies, in the colors of running, and so on.

2) Interference occurs when the initial beam of light is separated by two beam when it passes through a thin film, for example, the film applied to the surface of the lenses in enlightened lens. The beam of light, passing through the film thickness, will reflect twice - from the inner and outer surfaces. The reflected rays will have a constant phase difference equal to the twin thickness of the film, why the rays become coherent and interfer. Full quenching of the rays will occur when where the wavelength is. If a nm, then the thickness of the film is 550: 4 \u003d 137.5 nm.

Thread of magnetic induction vector IN (magnetic flow) through a small surface area ds. called a scalar physical value equal

Here - a single vector of normal to the area of \u200b\u200bthe square ds., In N. - Projection of the vector IN On the direction of normal, - the angle between vectors IN and n. (Fig. 6.28).

Fig. 6.28. Magnetic induction vector stream through the playground

Magnetic flow F. B. through an arbitrary closed surface S. Raven

The absence of magnetic charges in nature leads to the fact that the vector lines IN Do not have any beginning, no end. Therefore, the flow of the vector IN Through a closed surface should be zero. Thus, for any magnetic field and an arbitrary closed surface S. Condition is fulfilled

Formula 6.28 expresses theorem of Ostrogradsky - Gauss for vector :

We emphasize again: this theorem is a mathematical expression of the fact that there are no magnetic charges in nature, on which the magnetic induction lines would have ended, as was the case in the case of electric field strength E. Spot charges.

This property significantly distinguishes the magnetic field from electric. The magnetic induction lines are closed, therefore the number of lines included in some space is equal to the number of lines overlooking this volume. If incoming streams take with one sign, and the emerging - with the other, the total flow of the magnetic induction vector through the closed surface will be zero.

Fig. 6.29. V. Weber (1804-1891) - German physicist

The difference between the magnetic field from the electrostatic is also manifested in the value of the value that we call circulation - integral from the vector field along the closed path. In electrostatics is zero integral

taken on an arbitrary closed contour. This is due to the potential of the electrostatic field, that is, with the fact that the work on the movement of the charge in the electrostatic field does not depend on the path, but only on the position of the initial and endpoints.

Let's see what is the case with a similar magnitude for the magnetic field. Take a closed circuit covering a direct current, and calculate the vector circulation for it IN , i.e

As it was obtained above, magnetic induction, created by a straight-line conductor with a current at a distance R. from the conductor is equal

Consider the case when the contour covering the direct current lies in the plane perpendicular to the current, and is a circle with a radius R. With the center on the conductor. In this case, the circulation of the vector IN on this circle is equal

It can be shown that the result for circulation of the magnetic induction vector does not change at a continuous deformation of the contour, if, with this deformation, the circuit does not cross the current lines. Then, by the principle of superposition, the circulation of the magnetic induction vector along the path covering several currents is proportional to their algebraic amount (Fig. 6.30)

Fig. 6.30. Closed circuit (L) with a given bypass direction.
The currents I 1, I 2 and I 3 are depicted, creating a magnetic field.
Contribution to the circulation of the magnetic field along the circuit (L) give only currents I 2 and I 3

If the selected circuit does not cover currents, then the circulation is zero.

When calculating the algebraic amount of currents, a current sign should be taken into account: we will consider a positive current, the direction of which is associated with the direction of bypass by contour by the rule of the right screw. For example, current contribution I. 2 in circulation - negative, and current contribution I. 3 - positive (Fig. 6.18). Taking advantage of the ratio

between the power of current I. through any closed surface S. and current density for vector circulation IN can be recorded

where S. - any closed surface based on this circuit L..

Such fields are called vortex. Therefore, for a magnetic field, it is impossible to introduce the potential, as was done for the electric field of point charges. The most clearly difference of potential and vortex fields can be represented by the picture of the power lines. The power lines of the electrostatic field are similar to heroes: they begin and end on charges (or go into infinity). The magnetic field power lines never resemble "hedgehogs": they are always closed and covered current currents.

To illustrate the use of the circulation theorem, we find another method already known to us the magnetic field of an infinite solenoid. Take a rectangular outline 1-2-3-4 (Fig. 6.31) and calculate the circulation of the vector IN By this contour

Fig. 6.31. The use of the circulation theorem in to the determination of the magnetic field of the solenoid

The second and fourth integrals are zero due to the perpendicularity of vectors and

We reproduced the result (6.20) without integrating magnetic fields from individual turns.

The resulting result (6.35) can be used to find the magnetic field of a thin toroidal solenoid (Fig.6.32).

Fig. 6.32. Toroidal coil: Magnetic induction lines are closed inside the coil and are concentric circles. They are sent in such a way that looking along them, we would see the current in the turns circulating clockwise. One of the induction lines of some radius R 1 ≤ R< r 2 изображена на рисунке

Magnetic materials are those that are subject to the influence of special power fields, in turn, non-magnetic materials are not subject to or poorly subject to the magnetic field forces, which is taken to represent with the help of power lines (magnetic flow) with certain properties. In addition, they always form closed loops, they behave as if they are elastic, that is, during distortion, they are trying to return to the old distance and in their natural shape.

Invisible power

Magnets have property to attract some metals, especially iron and steel, as well as nickel, nickel alloys, chromium and cobalt. Materials that create attraction forces are magnets. There are different types of them. Materials that can be easily magnetized are called ferromagnetic. They can be rigid or soft. Soft ferromagnetic materials such as iron, quickly lose their properties. Magnets made of these materials are called temporary. Hard materials, such as steel, keep their properties much longer and used as permanent.

Magnetic Stream: Definition and Characteristics

There is a specific power field around the magnet, and this creates the possibility of energy. The magnetic flux is equal to the product of the average power fields of the perpendicular surface in which it penetrates. It is depicted using the symbol "φ", it is measured in units called Webers (WB). The magnitude of the flow passing through the specified area will vary from one point to another around the item. Thus, the magnetic flux is the so-called measure of the power of a magnetic field or an electric current based on the total number of charged power lines passing through a certain area.

Revealing the mystery of magnetic streams

All magnets, regardless of their shape, have two areas, which are called poles capable of producing a certain chain of an organized and balanced system of invisible power lines. These lines from the stream form a special field, the form of which manifests itself more intensively in some parts compared to others. Areas with the greatest attraction are called poles. Vector field lines cannot be detected by the naked eye. Visually, they are always displayed in the form of power lines with unambiguous poles at each end of the material, where the lines are denser and concentrated. Magnetic flow are lines that create vibrations of attraction or repulsion, showing their direction and intensity.

Lines of magnetic flux

Magnetic power lines are defined as curves moving along a certain trajectory in a magnetic field. Tanner to these curves at any point shows the direction of the magnetic field in it. Characteristics:

Each stream line forms a closed outline.

These induction lines never intersect, but tend to shrink or stretch, changing their sizes in one direction or another.

As a rule, the power lines have the beginning and end on the surface.

There is also a certain direction from north to south.

Power lines that are close to each other, forming a strong magnetic field.

• When the neighboring pole is the same (north-north or south-south), they are repelled from each other. When the neighboring poles do not coincide (north-south or south-north), they attract each other. This effect resembles the famous expression that opposites are attracted.

Magnetic Molecules and Weber Theory

Weber Theory relies on the fact that all atoms have magnetic properties due to the connection between electrons in atoms. The groups of atoms are connected together in such a way that their surrounding fields rotate in the same direction. This kind of materials consist of groups of tiny magnetics (if we consider them on molecular level) Around the atoms, this means that the ferromagnetic material consists of molecules that are characteristic of the force of attraction. They are known as dipoles and are grouped into domains. When the material is magnetized, all domains become one. The material loses its ability to attract and repel in the event that its domains are disconnected. Diples together form a magnet, but individually, each of them is trying to push off from unipolar, thus the opposite poles are attracted.

Fields and poles

The force and direction of the magnetic field determine the lines of the magnetic flux. The area of \u200b\u200battraction is stronger where the lines are close to each other. The lines are closest in the pole of the rod base, the strongest is the strongest. Planet Earth itself is in this powerful power field. It acts as if the gigantic strip magnetized plate passes through the middle of the planet. The North Pole of the Compass Arrow is directed toward the point, called the Northern Magnetic Pole, the South Pole, indicates a magnetic south. However, these directions differ from the geographical northern and southern poles.

Nature magnetism

Magnetism plays an important role in electrical engineering and electronics, because without its components, such as relays, solenoids, inductors, chokes, coils, loudspeakers, electric motors, generators, transformers, electricity meters, etc. Magnets can be found in Natural natural state in the form of magnetic ores. There are two main types, it is magnetite (it is also called iron oxide) and magnetic Zheleznyak. The molecular structure of this material in a non-magnetic state is represented in the form of a free magnetic chain or individual tiny particles that are freely located in random order. When the material is magnetized, this random arrangement of molecules changes, and tiny random molecular particles are built up in such a way that they produce a whole series of agreements. This idea of \u200b\u200bmolecular alignment of ferromagnetic materials is called Weber's theory.

Measurement and practical application

The most common generators use a magnetic flow for electricity production. His power is widely used in electrical generators. The device that serves to measure this interesting phenomenon is called a fluux, it consists of a coil and electronic equipment, which evaluates the change in the voltage in the coil. In physics, the flow rate is indicator of the number of power lines passing through a certain area. Magnetic stream is a measure of magnetic power lines.

Sometimes even non-magnetic material may also have diamagnetic and paramagnetic properties. Interesting fact It is that attraction forces can be destroyed when heated or hit by a hammer from the same material, but they cannot be destroyed or insulated if you simply break a large instance into two parts. Each broken piece will have its own northern and southern pole, and it doesn't matter how small these pieces will be.

Among physical quantities An important place occupies a magnetic flux. This article tells about what it is, and how to determine its magnitude.

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Magnetic flux formula

What is a magnetic stream

This is a value that determines the level of the magnetic field passing through the surface. It is denoted by "FF" and depends on the force force and the field of field passage through this surface.

It is calculated by the formula:

FF \u003d B⋅s⋅cosα, where:

• FF - magnetic stream;
• 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.

Unit of measurement in the SI system is "Weber" (WB). 1 Weber is created by a field of 1 TL, passing perpendicular to the surface with an area of \u200b\u200b1 m².

Thus, the flow is maximum in the coincidence of its direction with a vertical and equal to "0", if it is parallel with the surface.

Interesting.The formula of the magnetic flux is similar to the formula for which illumination is calculated.

Permanent magnets

One of the sources of the field are permanent magnets. They are known many centuries. From the magnetized iron, the compass arrow was manufactured, and in Ancient Greece There was a legend about the island that attracts the metal parts of the ships to themselves.

Permanent magnets are various shapes and made from different materials:

• iron - the cheapest, but have a smaller attracting force;
• neodymium - from alloy neodymium, iron and boron;
• alnico - alloy of iron, aluminum, nickel and cobalt.

All magnets are bipoly. This is more visible in rod and horseshoe devices.

If the rod is suspended behind the middle or put on a floating piece of wood or foam, it will unfold in the direction of North-South. The pole showing north is called the northern and on laboratory devices paint in blue and denote "n". The opposite, showing south, is red and designated "S". The magnets of the same name are attracted, and opposite - repel.

In 1851, Michael Faraday proposed the concept of closed lines induction. These lines come out of the north pole of the magnet, pass through the surrounding space, enter the southern and inside the device are returned to the North. The closest line and the intensity of the field in the poles. Here is also the above attracting force.

If you put a piece of glass on the device, and on top of a thin layer pour iron sawders, then they will be located along the magnetic field lines. When there is a number of multiple sawdust devices, the interaction between them will show: attraction or repulsion.

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Magnet and iron sawdust

Magnetic field of land

Our planet can be represented as a magnet whose axis is tilted by 12 degrees. The intersection of this axis is called magnetic poles with the surface. As with any magnet, the power lines of the Earth go from the North Pole to the South. Near the poles, they pass perpendicular to the surface, so there is an arrow of the compass is unreliable, and you have to use other ways.

The solar wind particles have an electrical charge, so when moving around them a magnetic field appears, interacting with the land field and guides these particles along the power lines. Thus, this field protects ground surface from cosmic radiation. However, near the poles, these lines are sent perpendicular to the surface, and the charged particles fall into the atmosphere, causing the northern lights.

Electromagnets

In 1820, Hans Ersted, conducting experiments, saw the impact of the conductor, through which the electric current flows, on the compass arrow. A few days later, Andre-Marie Ampere discovered the mutual attraction of two wires, which flowed a current of one direction.

Interesting. During the electric welding work, nearby cables are moving when the current is changed.

Later, the ampere suggested that this is due to the magnetic induction of the current flowing through the wires.

In the coil, wound by insulated wire, which flows electric current, the fields of individual conductors enhance each other. To increase the strength of attraction, the coil is wound on an open steel core. This core is magnetized and attracts iron parts or the second half of the core in the relay and contactors.

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Electromagnets

Electromagnetic induction

When changing the magnetic flux in the wire, an electric current is guided. This fact does not depend on what reasons this change was caused: the movement of a permanent magnet, the movement of the wire or a change in the current force in a nearby conductor.

This phenomenon was opened by Michael Faraday on August 29, 1831. Its experiments have shown that the EMF (electromotive force) appears in the circuit bounded by the conductors, directly moving the flow rate passing through the area of \u200b\u200bthis circuit.

Important! For the emergence of EMF, the wire must cross the power lines. When moving along the emf lines is missing.

If the coil in which the EMF occurs is included in the electrical chain, then the winding occurs a current that creates its electromagnetic field in the inducement coil.

Rule rule

When the conductor moves in the magnetic field in it, the EMF is guided. Its orientation depends on the direction of movement of the wire. The method, with which the direction of magnetic induction is determined, is called "Method right hand».

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Rule rule

Calculation of the magnetic field value is important for the design of electrical machines and transformers.

Video

magnetic induction - It is a magnetic flux density at this point point. A unit of magnetic induction is Tesla (1 TL \u003d 1 WB / m 2).

Returning to the expression obtained earlier (1), you can quantify magnetic flux through some surface as a product of the charge flowing through the conductor combined with the boundary of this surface with the full disappearance of the magnetic field, on the resistance of the electrical circuit in which these charges occur

.

In the experiments described above, it was removed on such a distance at which all sorts of manifestations of the magnetic field disappeared. But you can simply move this turn within the field and at the same time electrical charges will also move. Let us turn into expression (1) to increments

F + Δ F \u003d r.(q. - Δ q.) \u003d\u003e Δ f \u003d - rΔ Q. => Δ q. \u003d -Δ F / r.

where Δ f and δ q. - the increment of the flow and number of charges. Different signs increments are explained by the fact that a positive charge in experiments with the removal of the turn corresponded to the disappearance of the field, i.e. negative increment of magnetic flux.

With the help of a test turn, you can explore all the space around the magnet or coil with current and build lines, the direction of tangents to which at each point will correspond to the direction of the magnetic induction vector B. (Fig. 3)

These lines are called magnetic induction vector lines or magnetic lines .

The magnetic field space is mentally divided by tubular surfaces formed by magnetic lines, and the surface can be selected in such a way that the magnetic flux within each such surface (tube) is numerically equal to one and depict graphically axial lines of these tubes. Such tubes are called single, and their axes are single magnetic lines . The picture of the magnetic field depicted using single lines gives not only quality, but also a quantitative idea of \u200b\u200bit, because In this case, the magnitude of the magnetic induction vector turns out to be equal to the number of lines passing through the unit of the surface, the normal vector B., but the number of lines passing through any surface equal to the value of the magnetic flux .

Magnetic lines are continuous and this principle can be mathematically present in the form

those. magnetic stream passing through any closed surface is zero .

Expression (4) is valid for the surface s. Any shape. If we consider the magnetic stream passing through the surface formed by the coils of the cylindrical coil (Fig. 4), then it can be divided into surfaces formed by individual wips, i.e. s.=s. 1 +s. 2 +...+s. eight . Moreover, through the surfaces of different turns in the general case, different magnetic flows will be held. So in fig. 4, eight single connections pass through the surfaces of the central turns magnetic lines, and through the surfaces of extreme turns only four.

In order to determine the full magnetic flux passing through the surface of all turns, you need to fold the streams passing through the surfaces of individual turns, or, in other words, covering with separate turns. For example, magnetic fluxes, covering with four topwood coils rice. 4, will be equal: F 1 \u003d 4; F 2 \u003d 4; F 3 \u003d 6; F 4 \u003d 8. Also, mirror-symmetrically with the bottom.

Flow - Virtual (imaginary total) Magnetic flow ψ, adhesive with all coils, is numerically equal to the amount of streams covering with separate tips: ψ \u003d w. EF M. where F. m. - magnetic flow created by a current passing by the coil, and w. E is an equivalent or effective number of coil turns. Physical meaning streaming - the grip of magnetic fields of turns of the coil, which can be expressed by the coefficient (multiplicity) of the stream k. \u003d Ψ / f \u003d w. e.

That is, for the case shown in the figure, two mirror-symmetric halves of the coil:

Ψ \u003d 2 (F 1 + F 2 + F 3 + F 4) \u003d 48

Virtuality, that is, the imaginary streaming is manifested in the fact that it is not a real magnetic flux that no inductance can be increased to magnify, but the behavior of the reel's impedance is that it seems that the magnetic flux increases to a multiple efficient number of turns, although it is really really The interaction of turns in the same field. If the coil increased the magnetic flow with its streaming, then it would be possible to create magnetic field multipliers on the coil even without current, for the streaming does not imply closets of the chain of the coil, but only a joint proximity of the proximity of turns.

Often the real distribution of streams in coil coils is unknown, but it can be taken uniform and the same for all turns, if the real coil is replaced with an equivalent to another number of turns w. e, while maintaining the value of the stream ψ \u003d w. EF M. where F. m. - stream adhesive with internal coils coils, and w. E is an equivalent or effective number of coil turns. For reviewed in Fig. 4 cases w. e \u003d ψ / f 4 \u003d 48/8 \u003d 6.