Magnetic field and its properties. What is the earth's magnetic field

Magnetic field sources

The magnetic field is created (generated) by the current of charged particles, or by a time-varying electric field, or by the intrinsic magnetic moments of the particles (the latter, for the sake of uniformity of the picture, can be formally reduced to electric currents).

calculation

In simple cases, the magnetic field of a current-carrying conductor (including the case of a current distributed arbitrarily over volume or space) can be found from the Biot-Savart-Laplace law or the circulation theorem (it is also Ampère's law). In principle, this method is limited to the case (approximation) of magnetostatics - that is, the case of constant (if we are talking about strict applicability) or rather slowly changing (if we are talking about approximate application) magnetic and electric fields.

In more complex situations, it is sought as a solution to Maxwell's equations.

Manifestation of a magnetic field

The magnetic field manifests itself in the effect on the magnetic moments of particles and bodies, on moving charged particles (or current-carrying conductors). The force acting on an electrically charged particle moving in a magnetic field is called the Lorentz force, which is always directed perpendicular to the vectors v and B. It is proportional to the charge of the particle q, the velocity component v, perpendicular to the direction of the magnetic field vector B, and the magnitude of the magnetic field induction B. In the SI system of units, the Lorentz force is expressed as follows:

in the CGS system of units:

where square brackets denote the vector product.

Also (due to the action of the Lorentz force on charged particles moving along the conductor), the magnetic field acts on the conductor with current. The force acting on a current-carrying conductor is called ampere force. This force is the sum of the forces acting on individual charges moving inside the conductor.

Interaction of two magnets

One of the most common manifestations of a magnetic field in ordinary life is the interaction of two magnets: identical poles repel, opposite ones attract. It seems tempting to describe the interaction between magnets as an interaction between two monopoles, and from a formal point of view, this idea is quite realizable and often very convenient, and therefore practically useful (in calculations); however, a detailed analysis shows that in fact this is not a completely correct description of the phenomenon (the most obvious question that cannot be explained within the framework of such a model is the question of why monopoles can never be separated, that is, why the experiment shows that no isolated the body does not actually have a magnetic charge; in addition, the weakness of the model is that it is not applicable to the magnetic field created by a macroscopic current, which means that, if not considered as a purely formal technique, it only leads to a complication of the theory in a fundamental sense).

It would be more correct to say that a force acts on a magnetic dipole placed in an inhomogeneous field, which tends to rotate it so that the magnetic moment of the dipole is co-directed with the magnetic field. But no magnet experiences a (total) force from a uniform magnetic field. Force acting on a magnetic dipole with a magnetic moment m is expressed by the formula:

The force acting on a magnet (which is not a single point dipole) from an inhomogeneous magnetic field can be determined by summing all the forces (defined by this formula) acting on the elementary dipoles that make up the magnet.

However, an approach is possible that reduces the interaction of magnets to the Ampère force, and the formula itself above for the force acting on a magnetic dipole can also be obtained based on the Ampère force.

The phenomenon of electromagnetic induction

vector field H measured in amperes per meter (A/m) in the SI system and in oersteds in the CGS. Oersteds and gausses are identical quantities, their separation is purely terminological.

Magnetic field energy

The increment in the energy density of the magnetic field is:

H- magnetic field strength, B- magnetic induction

In the linear tensor approximation, the magnetic permeability is a tensor (we denote it ) and the multiplication of a vector by it is a tensor (matrix) multiplication:

or in components.

The energy density in this approximation is equal to:

- components of the magnetic permeability tensor , - tensor represented by a matrix inverse to the matrix of the magnetic permeability tensor, - magnetic constant

When the coordinate axes are chosen to coincide with the principal axes of the magnetic permeability tensor, the formulas in the components are simplified:

are the diagonal components of the magnetic permeability tensor in its own axes (the other components in these special coordinates - and only in them! - are equal to zero).

In an isotropic linear magnet:

- relative magnetic permeability

In vacuum and:

The energy of the magnetic field in the inductor can be found by the formula:

Ф - magnetic flux, I - current, L - inductance of a coil or coil with current.

Magnetic properties of substances

From a fundamental point of view, as mentioned above, a magnetic field can be created (and therefore - in the context of this paragraph - and weakened or strengthened) by an alternating electric field, electric currents in the form of streams of charged particles or magnetic moments of particles.

The specific microscopic structure and properties of various substances (as well as their mixtures, alloys, states of aggregation, crystalline modifications, etc.) lead to the fact that at the macroscopic level they can behave quite differently under the action of an external magnetic field (in particular, weakening or amplifying it to varying degrees).

In this regard, substances (and media in general) in relation to their magnetic properties are divided into the following main groups:

Antiferromagnets are substances in which the antiferromagnetic order of the magnetic moments of atoms or ions is established: the magnetic moments of substances are directed oppositely and are equal in strength.
Diamagnets are substances that are magnetized against the direction of an external magnetic field.
Paramagnets are substances that are magnetized in an external magnetic field in the direction of the external magnetic field.
Ferromagnets are substances in which, below a certain critical temperature (Curie point), a long-range ferromagnetic order of magnetic moments is established.
Ferrimagnets - materials in which the magnetic moments of the substance are directed oppositely and are not equal in strength.
The above groups of substances mainly include ordinary solid or (to some) liquid substances, as well as gases. The interaction with the magnetic field of superconductors and plasma differs significantly.

Toki Foucault

Foucault currents (eddy currents) - closed electric currents in a massive conductorarising from a change in the magnetic flux penetrating it. They are inductive currents formed in a conducting body either due to a change in time of the magnetic field in which it is located, or as a result of the movement of the body in a magnetic field, leading to a change in the magnetic flux through the body or any part of it. According to Lenz's rule, the magnetic field of Foucault currents is directed so as to oppose the change in magnetic flux that induces these currents.

The history of the development of ideas about the magnetic field

Although magnets and magnetism were known much earlier, the study of the magnetic field began in 1269, when the French scientist Peter Peregrine (the knight Pierre of Méricourt) noted the magnetic field on the surface of a spherical magnet using steel needles and determined that the resulting magnetic field lines intersected at two points, which he called "poles" by analogy with the poles of the Earth. Nearly three centuries later, William Gilbert Colchester used the work of Peter Peregrinus and for the first time definitively stated that the earth itself was a magnet. Published in 1600, Gilbert's work De Magnete, laid the foundations of magnetism as a science.

Three discoveries in a row have challenged this "basis of magnetism." First, in 1819, Hans Christian Oersted discovered that an electric current creates a magnetic field around itself. Then, in 1820, André-Marie Ampère showed that parallel wires carrying current in the same direction attract each other. Finally, Jean-Baptiste Biot and Félix Savard discovered a law in 1820 called the Biot-Savart-Laplace law, which correctly predicted the magnetic field around any live wire.

Expanding on these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electric current in magnets, and instead of the dipoles of magnetic charges in the Poisson model, he proposed the idea that magnetism is associated with constantly flowing current loops. This idea explained why the magnetic charge could not be isolated. In addition, Ampère deduced the law named after him, which, like the Biot-Savart-Laplace law, correctly described the magnetic field produced by direct current, and the magnetic field circulation theorem was also introduced. Also in this work, Ampère coined the term "electrodynamics" to describe the relationship between electricity and magnetism.

Although the magnetic field strength of a moving electric charge implied in Ampère's law was not explicitly stated, in 1892 Hendrik Lorentz derived it from Maxwell's equations. At the same time, the classical theory of electrodynamics was basically completed.

The twentieth century expanded views on electrodynamics, thanks to the emergence of the theory of relativity and quantum mechanics. Albert Einstein, in his paper in 1905, where his theory of relativity was substantiated, showed that electric and magnetic fields are part of the same phenomenon, considered in different frames of reference. (See The moving magnet and the conductor problem - the thought experiment that eventually helped Einstein develop special relativity). Finally, quantum mechanics was combined with electrodynamics to form quantum electrodynamics (QED).

Notes

TSB. 1973, "Soviet Encyclopedia".
In particular cases, a magnetic field can exist even in the absence of an electric field, but generally speaking, a magnetic field is deeply interconnected with an electric field, both dynamically (mutual generation of each other by alternating electric and magnetic fields), and in the sense that, upon transition to a new frame of reference, the magnetic and the electric field are expressed through each other, that is, generally speaking, they cannot be unconditionally separated.
Yavorsky B. M., Detlaf A. A. Handbook of Physics: 2nd ed., Revised. - M .: Science, Main edition of physical and mathematical literature, 1985, - 512 p.
In SI, magnetic induction is measured in teslas (T), in the cgs system in gauss.
Exactly coincide in the CGS system of units, in SI they differ by a constant coefficient, which, of course, does not change the fact of their practical physical identity.
The most important and superficial difference here is that the force acting on a moving particle (or on a magnetic dipole) is calculated in terms of and not in terms of . Any other physically correct and meaningful measurement method will also make it possible to measure it, although sometimes it turns out to be more convenient for a formal calculation - what, in fact, is the point of introducing this auxiliary quantity (otherwise, we would do without it at all, using only
However, it should be well understood that a number of fundamental properties of this "matter" are fundamentally different from the properties of the usual type of "matter", which could be designated by the term "substance".
See Ampère's theorem.
For a homogeneous field, this expression gives zero force, since all derivatives are equal to zero B by coordinates.
Sivukhin D.V. General course of physics. - Ed. 4th, stereotypical. - M .: Fizmatlit; MIPT Publishing House, 2004. - Vol. III. Electricity. - 656 p. - ISBN 5-9221-0227-3; ISBN 5-89155-086-5.

A magnetic field this is the matter that arises around sources of electric current, as well as around permanent magnets. In space, the magnetic field is displayed as a combination of forces that can affect magnetized bodies. This action is explained by the presence of driving discharges at the molecular level.

The magnetic field is formed only around electric charges that are in motion. That is why the magnetic and electric fields are integral and together form electromagnetic field. The components of the magnetic field are interconnected and act on each other, changing their properties.

Magnetic field properties:
1. The magnetic field arises under the influence of driving charges of electric current.
2. At any of its points, the magnetic field is characterized by a vector of physical quantity called magnetic induction, which is the force characteristic of the magnetic field.
3. The magnetic field can only affect magnets, conductive conductors and moving charges.
4. The magnetic field can be of constant and variable type
5. The magnetic field is measured only by special devices and cannot be perceived by the human senses.
6. The magnetic field is electrodynamic, as it is generated only during the movement of charged particles and affects only the charges that are in motion.
7. Charged particles move along a perpendicular trajectory.

The size of the magnetic field depends on the rate of change of the magnetic field. Accordingly, there are two types of magnetic field: dynamic magnetic field and gravitational magnetic field. Gravitational magnetic field arises only near elementary particles and is formed depending on the structural features of these particles.

Magnetic moment occurs when a magnetic field acts on a conductive frame. In other words, the magnetic moment is a vector that is located on the line that runs perpendicular to the frame.

The magnetic field can be represented graphically using magnetic lines of force. These lines are drawn in such a direction that the direction of the field forces coincides with the direction of the field line itself. Magnetic field lines are continuous and closed at the same time.

The direction of the magnetic field is determined using a magnetic needle. The lines of force also determine the polarity of the magnet, the end with the exit of the lines of force is the north pole, and the end with the entrance of these lines is the south pole.

It is very convenient to visually assess the magnetic field using ordinary iron filings and a piece of paper.
If we put a sheet of paper on a permanent magnet, and sprinkle sawdust on top, then the iron particles will line up according to the magnetic field lines.

The direction of the lines of force for the conductor is conveniently determined by the famous gimlet rule or right hand rule. If we grab the conductor with our hand so that the thumb looks in the direction of the current (from minus to plus), then the 4 remaining fingers will show us the direction of the magnetic field lines.

And the direction of the Lorentz force - the force with which the magnetic field acts on a charged particle or conductor with current, according to left hand rule.
If we place the left hand in a magnetic field so that 4 fingers look in the direction of the current in the conductor, and the lines of force enter the palm, then the thumb will indicate the direction of the Lorentz force, the force acting on the conductor placed in the magnetic field.

That's about it. Be sure to ask any questions in the comments.

Subject: Magnetic field

Prepared by: Baigarashev D.M.

Checked by: Gabdullina A.T.

A magnetic field

If two parallel conductors are connected to a current source so that an electric current passes through them, then, depending on the direction of the current in them, the conductors either repel or attract.

The explanation of this phenomenon is possible from the standpoint of the appearance around the conductors of a special type of matter - a magnetic field.

The forces with which current-carrying conductors interact are called magnetic.

A magnetic field- this is a special kind of matter, a specific feature of which is the action on a moving electric charge, conductors with current, bodies with a magnetic moment, with a force depending on the charge velocity vector, the direction of the current strength in the conductor and on the direction of the magnetic moment of the body.

The history of magnetism goes back to ancient times, to the ancient civilizations of Asia Minor. It was on the territory of Asia Minor, in Magnesia, that a rock was found, samples of which were attracted to each other. According to the name of the area, such samples began to be called "magnets". Any magnet in the form of a rod or a horseshoe has two ends, which are called poles; it is in this place that its magnetic properties are most pronounced. If you hang a magnet on a string, one pole will always point north. The compass is based on this principle. The north-facing pole of a free-hanging magnet is called the magnet's north pole (N). The opposite pole is called the south pole (S).

Magnetic poles interact with each other: like poles repel, and unlike poles attract. Similarly, the concept of an electric field surrounding an electric charge introduces the concept of a magnetic field around a magnet.

In 1820, Oersted (1777-1851) discovered that a magnetic needle located next to an electrical conductor deviates when current flows through the conductor, that is, a magnetic field is created around the current-carrying conductor. If we take a frame with current, then the external magnetic field interacts with the magnetic field of the frame and has an orienting effect on it, i.e., there is a position of the frame at which the external magnetic field has a maximum rotating effect on it, and there is a position when the torque force is zero.

The magnetic field at any point can be characterized by the vector B, which is called magnetic induction vector or magnetic induction at the point.

Magnetic induction B is a vector physical quantity, which is a force characteristic of the magnetic field at a point. It is equal to the ratio of the maximum mechanical moment of forces acting on a loop with current placed in a uniform field to the product of the current strength in the loop and its area:

The direction of the magnetic induction vector B is taken to be the direction of the positive normal to the frame, which is related to the current in the frame by the rule of the right screw, with a mechanical moment equal to zero.

In the same way as the lines of electric field strength are depicted, the lines of magnetic field induction are depicted. The line of induction of the magnetic field is an imaginary line, the tangent to which coincides with the direction B at the point.

The directions of the magnetic field at a given point can also be defined as the direction that indicates

the north pole of the compass needle placed at that point. It is believed that the lines of induction of the magnetic field are directed from the north pole to the south.

The direction of the lines of magnetic induction of the magnetic field created by an electric current that flows through a straight conductor is determined by the rule of a gimlet or a right screw. The direction of rotation of the screw head is taken as the direction of the lines of magnetic induction, which would ensure its translational movement in the direction of the electric current (Fig. 59).

where n 01 = 4 Pi 10 -7 V s / (A m). - magnetic constant, R - distance, I - current strength in the conductor.

Unlike electrostatic field lines, which start at a positive charge and end at a negative one, magnetic field lines are always closed. No magnetic charge similar to electric charge was found.

One tesla (1 T) is taken as a unit of induction - the induction of such a uniform magnetic field in which a maximum torque of 1 N m acts on a frame with an area of 1 m 2, through which a current of 1 A flows.

The induction of a magnetic field can also be determined by the force acting on a current-carrying conductor in a magnetic field.

A conductor with current placed in a magnetic field is subjected to the Ampère force, the value of which is determined by the following expression:

where I is the current strength in the conductor, l- the length of the conductor, B is the modulus of the magnetic induction vector, and is the angle between the vector and the direction of the current.

The direction of the Ampere force can be determined by the rule of the left hand: the palm of the left hand is positioned so that the lines of magnetic induction enter the palm, four fingers are placed in the direction of the current in the conductor, then the bent thumb shows the direction of the Ampere force.

Considering that I = q 0 nSv and substituting this expression into (3.21), we obtain F = q 0 nSh/B sin a. The number of particles (N) in a given volume of the conductor is N = nSl, then F = q 0 NvB sin a.

Let us determine the force acting from the side of the magnetic field on a separate charged particle moving in a magnetic field:

This force is called the Lorentz force (1853-1928). The direction of the Lorentz force can be determined by the rule of the left hand: the palm of the left hand is positioned so that the lines of magnetic induction enter the palm, four fingers show the direction of movement of the positive charge, the thumb bent shows the direction of the Lorentz force.

The force of interaction between two parallel conductors, through which currents I 1 and I 2 flow, is equal to:

where l- the part of a conductor that is in a magnetic field. If the currents are in the same direction, then the conductors are attracted (Fig. 60), if the opposite direction, they are repelled. The forces acting on each conductor are equal in magnitude, opposite in direction. Formula (3.22) is the main one for determining the unit of current strength 1 ampere (1 A).

The magnetic properties of a substance are characterized by a scalar physical quantity - magnetic permeability, which shows how many times the induction B of a magnetic field in a substance that completely fills the field differs in absolute value from the induction B 0 of a magnetic field in vacuum:

According to their magnetic properties, all substances are divided into diamagnetic, paramagnetic and ferromagnetic.

Consider the nature of the magnetic properties of substances.

Electrons in the shell of atoms of matter move in different orbits. For simplicity, we consider these orbits to be circular, and each electron revolving around the atomic nucleus can be considered as a circular electric current. Each electron, like a circular current, creates a magnetic field, which we will call orbital. In addition, an electron in an atom has its own magnetic field, called the spin field.

If, when introduced into an external magnetic field with induction B 0, induction B is created inside the substance< В 0 , то такие вещества называются диамагнитными (n< 1).

AT diamagnetic In materials in the absence of an external magnetic field, the magnetic fields of electrons are compensated, and when they are introduced into a magnetic field, the induction of the magnetic field of an atom becomes directed against the external field. The diamagnet is pushed out of the external magnetic field.

At paramagnetic materials, the magnetic induction of electrons in atoms is not fully compensated, and the atom as a whole turns out to be like a small permanent magnet. Usually in matter all these small magnets are oriented arbitrarily, and the total magnetic induction of all their fields is equal to zero. If you place a paramagnet in an external magnetic field, then all small magnets - atoms will turn in the external magnetic field like compass needles and the magnetic field in the substance increases ( n >= 1).

ferromagnetic are materials that are n"1. So-called domains, macroscopic regions of spontaneous magnetization, are created in ferromagnetic materials.

In different domains, the induction of magnetic fields has different directions (Fig. 61) and in a large crystal

mutually compensate each other. When a ferromagnetic sample is introduced into an external magnetic field, the boundaries of individual domains are shifted so that the volume of domains oriented along the external field increases.

With an increase in the induction of the external field B 0, the magnetic induction of the magnetized substance increases. For some values of B 0, the induction stops its sharp growth. This phenomenon is called magnetic saturation.

A characteristic feature of ferromagnetic materials is the phenomenon of hysteresis, which consists in the ambiguous dependence of the induction in the material on the induction of the external magnetic field as it changes.

The magnetic hysteresis loop is a closed curve (cdc`d`c), expressing the dependence of the induction in the material on the amplitude of the induction of the external field with a periodic rather slow change in the latter (Fig. 62).

The hysteresis loop is characterized by the following values B s , B r , B c . B s - the maximum value of the induction of the material at B 0s ; B r - residual induction, equal to the value of the induction in the material when the induction of the external magnetic field decreases from B 0s to zero; -B c and B c - coercive force - a value equal to the induction of the external magnetic field necessary to change the induction in the material from residual to zero.

For each ferromagnet, there is such a temperature (Curie point (J. Curie, 1859-1906), above which the ferromagnet loses its ferromagnetic properties.

There are two ways to bring a magnetized ferromagnet into a demagnetized state: a) heat above the Curie point and cool; b) magnetize the material with an alternating magnetic field with a slowly decreasing amplitude.

Ferromagnets with low residual induction and coercive force are called soft magnetic. They find application in devices where a ferromagnet has to be frequently remagnetized (cores of transformers, generators, etc.).

Magnetically hard ferromagnets, which have a large coercive force, are used for the manufacture of permanent magnets.

Just as an electric charge at rest acts on another charge through an electric field, an electric current acts on another current through magnetic field. The action of a magnetic field on permanent magnets is reduced to its action on charges moving in the atoms of a substance and creating microscopic circular currents.

Doctrine of electromagnetism based on two assumptions:

the magnetic field acts on moving charges and currents;
a magnetic field arises around currents and moving charges.

Interaction of magnets

Permanent magnet(or magnetic needle) is oriented along the magnetic meridian of the Earth. The end pointing north is called north pole(N) and the opposite end is south pole(S). Approaching two magnets to each other, we note that their like poles repel, and opposite ones attract ( rice. one ).

If we separate the poles by cutting the permanent magnet into two parts, then we will find that each of them will also have two poles, i.e. will be a permanent magnet ( rice. 2 ). Both poles - north and south - are inseparable from each other, equal.

The magnetic field created by the Earth or permanent magnets is depicted, like the electric field, by magnetic lines of force. A picture of the magnetic field lines of any magnet can be obtained by placing a sheet of paper over it, on which iron filings are poured in a uniform layer. Getting into a magnetic field, the sawdust is magnetized - each of them has a north and south poles. Opposite poles tend to approach each other, but this is prevented by the friction of sawdust on paper. If you tap the paper with your finger, the friction will decrease and the filings will be attracted to each other, forming chains that represent the lines of a magnetic field.

On the rice. 3 shows the location in the field of a direct magnet of sawdust and small magnetic arrows indicating the direction of the magnetic field lines. For this direction, the direction of the north pole of the magnetic needle is taken.

Oersted's experience. Magnetic field current

At the beginning of the XIX century. Danish scientist Oersted made an important discovery by discovering action of electric current on permanent magnets . He placed a long wire near the magnetic needle. When a current was passed through the wire, the arrow turned, trying to be perpendicular to it ( rice. 4 ). This could be explained by the appearance of a magnetic field around the conductor.

The magnetic lines of force of the field created by a direct conductor with current are concentric circles located in a plane perpendicular to it, with centers at the point through which the current passes ( rice. 5 ). The direction of the lines is determined by the right screw rule:

If the screw is rotated in the direction of the field lines, it will move in the direction of the current in the conductor .

The force characteristic of the magnetic field is magnetic induction vector B . At each point, it is directed tangentially to the field line. Electric field lines start on positive charges and end on negative ones, and the force acting in this field on a charge is directed tangentially to the line at each of its points. Unlike the electric field, the lines of the magnetic field are closed, which is due to the absence of "magnetic charges" in nature.

The magnetic field of the current is fundamentally no different from the field created by a permanent magnet. In this sense, an analogue of a flat magnet is a long solenoid - a coil of wire, the length of which is much greater than its diameter. The diagram of the lines of the magnetic field he created, depicted in rice. 6 , similar to that for a flat magnet ( rice. 3 ). The circles indicate the sections of the wire forming the solenoid winding. The currents flowing through the wire from the observer are indicated by crosses, and the currents in the opposite direction - towards the observer - are indicated by dots. The same designations are accepted for magnetic field lines when they are perpendicular to the plane of the drawing ( rice. 7 a, b).

The direction of the current in the solenoid winding and the direction of the magnetic field lines inside it are also related by the right screw rule, which in this case is formulated as follows:

If you look along the axis of the solenoid, then the current flowing in the clockwise direction creates a magnetic field in it, the direction of which coincides with the direction of movement of the right screw ( rice. eight )

Based on this rule, it is easy to figure out that the solenoid shown in rice. 6 , its right end is the north pole, and its left end is the south pole.

The magnetic field inside the solenoid is homogeneous - the magnetic induction vector has a constant value there (B = const). In this respect, the solenoid is similar to a flat capacitor, inside which a uniform electric field is created.

The force acting in a magnetic field on a conductor with current

It was experimentally established that a force acts on a current-carrying conductor in a magnetic field. In a uniform field, a rectilinear conductor of length l, through which current I flows, located perpendicular to the field vector B, experiences the force: F = I l B .

The direction of the force is determined left hand rule:

If the four outstretched fingers of the left hand are placed in the direction of the current in the conductor, and the palm is perpendicular to the vector B, then the retracted thumb will indicate the direction of the force acting on the conductor (rice. nine ).

It should be noted that the force acting on a conductor with current in a magnetic field is not directed tangentially to its lines of force, like an electric force, but perpendicular to them. A conductor located along the lines of force is not affected by the magnetic force.

The equation F = IlB allows to give a quantitative characteristic of the magnetic field induction.

Attitude does not depend on the properties of the conductor and characterizes the magnetic field itself.

The module of the magnetic induction vector B is numerically equal to the force acting on a conductor of unit length located perpendicular to it, through which a current of one ampere flows.

In the SI system, the unit of magnetic field induction is tesla (T):

A magnetic field. Tables, diagrams, formulas

(Interaction of magnets, Oersted's experiment, magnetic induction vector, vector direction, superposition principle. Graphic representation of magnetic fields, lines of magnetic induction. Magnetic flux, energy characteristic of the field. Magnetic forces, Ampère force, Lorentz force. Movement of charged particles in a magnetic field. Magnetic properties of matter, Ampère's hypothesis)

The term "magnetic field" usually means a certain energy space in which the forces of magnetic interaction are manifested. They affect:

individual substances: ferrimagnets (metals - mainly cast iron, iron and alloys thereof) and their class of ferrites, regardless of state;

moving charges of electricity.

Physical bodies that have a total magnetic moment of electrons or other particles are called permanent magnets. Their interaction is shown in the picture. power magnetic lines.

They were formed after bringing a permanent magnet to the reverse side of a cardboard sheet with an even layer of iron filings. The picture shows a clear marking of the north (N) and south (S) poles with the direction of the lines of force relative to their orientation: the exit from the north pole and the entrance to the south.

How a magnetic field is created

The sources of the magnetic field are:

permanent magnets;

mobile charges;

time-varying electric field.

Every kindergarten child is familiar with the action of permanent magnets. After all, he already had to sculpt pictures-magnets on the refrigerator, taken from packages with all sorts of goodies.

Electric charges in motion usually have a much higher magnetic field energy than. It is also indicated by lines of force. Let us analyze the rules for their design for a rectilinear conductor with current I.

A magnetic field line is drawn in a plane perpendicular to the current flow so that at each point the force acting on the north pole of the magnetic needle is directed tangentially to this line. This creates concentric circles around the moving charge.

The direction of these forces is determined by the well-known rule of a screw or gimlet with right-handed thread winding.

gimlet rule

It is necessary to position the gimlet coaxially with the current vector and rotate the handle so that the translational movement of the gimlet coincides with its direction. Then the orientation of the magnetic lines of force will be shown by turning the handle.

In the ring conductor, the rotational movement of the handle coincides with the direction of the current, and the translational movement indicates the orientation of the induction.

Magnetic field lines always exit the north pole and enter the south. They continue inside the magnet and are never open.

Rules for the interaction of magnetic fields

Magnetic fields from different sources are added to each other, forming the resulting field.

In this case, magnets with opposite poles (N - S) are attracted to each other, and with the same poles (N - N, S - S) they are repelled. The forces of interaction between the poles depend on the distance between them. The closer the poles are shifted, the greater the force generated.

Main characteristics of the magnetic field

These include:

magnetic induction vector (B);

magnetic flux (F);

flux linkage (Ψ).

The intensity or force of the impact of the field is estimated by the value magnetic induction vector. It is determined by the value of the force "F" created by the passing current "I" through a conductor of length "l". B \u003d F / (I ∙ l)

The unit of measurement of magnetic induction in the SI system is Tesla (in memory of the scientist physicist who studied these phenomena and described them using mathematical methods). In Russian technical literature, it is designated "Tl", and in international documentation the symbol "T" is adopted.

1 T is the induction of such a uniform magnetic flux that acts with a force of 1 newton per meter of the length of a straight conductor perpendicular to the direction of the field when a current of 1 ampere passes through this conductor.

1Tl=1∙N/(A∙m)

The direction of the vector B is determined by left hand rule.

If you place the palm of your left hand in a magnetic field so that the lines of force from the north pole enter the palm at a right angle, and place four fingers in the direction of the current in the conductor, then the protruding thumb will indicate the direction of the force on this conductor.

In the case when the conductor with electric current is not located at right angles to the magnetic field lines, then the force acting on it will be proportional to the magnitude of the flowing current and the component part of the projection of the length of the conductor with current onto a plane located in the perpendicular direction.

The force acting on the electric current does not depend on the materials from which the conductor is made and its cross-sectional area. Even if this conductor does not exist at all, and the moving charges begin to move in another medium between the magnetic poles, then this force will not change in any way.

If inside the magnetic field at all points the vector B has the same direction and magnitude, then such a field is considered uniform.

Any environment that has , affects the value of the induction vector B .

Magnetic Flux (F)

If we consider the passage of magnetic induction through a certain area S, then the induction limited by its limits will be called magnetic flux.

When the area is inclined at some angle α to the direction of magnetic induction, then the magnetic flux decreases by the value of the cosine of the angle of inclination of the area. Its maximum value is created when the area is perpendicular to its penetrating induction. Ф=В·S

The unit of measurement for magnetic flux is 1 weber, which is determined by the passage of 1 tesla induction through an area of 1 square meter.

Flux linkage

This term is used to obtain the total amount of magnetic flux created from a certain number of current-carrying conductors located between the poles of a magnet.

For the case when the same current I passes through the winding of the coil with the number of turns n, then the total (linked) magnetic flux from all turns is called flux linkage Ψ.

Ψ=n F . The unit of flux linkage is 1 weber.

How is a magnetic field formed from an alternating electric

The electromagnetic field interacting with electric charges and bodies with magnetic moments is a combination of two fields:

electric;

magnetic.

They are interrelated, represent a combination of each other, and when one changes over time, certain deviations occur in the other. For example, when creating an alternating sinusoidal electric field in a three-phase generator, the same magnetic field is simultaneously formed with the characteristics of similar alternating harmonics.

Magnetic properties of substances

In relation to interaction with an external magnetic field, substances are divided into:

antiferromagnets with balanced magnetic moments, due to which a very small degree of magnetization of the body is created;

diamagnets with the property of magnetizing the internal field against the action of the external one. When there is no external field, then they do not exhibit magnetic properties;

paramagnets with the properties of magnetization of the internal field in the direction of the external field, which have a small degree;

ferromagnets, which have magnetic properties without an applied external field at temperatures below the Curie point value;

ferrimagnets with magnetic moments that are unbalanced in magnitude and direction.

All these properties of substances have found various applications in modern technology.

Magnetic circuits

All transformers, inductances, electrical machines and many other devices work on the basis.

For example, in a working electromagnet, the magnetic flux passes through a magnetic circuit made of ferromagnetic steels and air with pronounced non-ferromagnetic properties. The combination of these elements makes up the magnetic circuit.

Most electrical devices have magnetic circuits in their design. Read more about it in this article -

Magnetic field sources

calculation

Manifestation of a magnetic field

Interaction of two magnets

The phenomenon of electromagnetic induction

Magnetic field energy

Magnetic properties of substances

Toki Foucault

The history of the development of ideas about the magnetic field

see also

Notes

Interaction of magnets

Oersted's experience. Magnetic field current

The force acting in a magnetic field on a conductor with current

A magnetic field. Tables, diagrams, formulas

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