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.
The magnetic line of force is drawn in a plane perpendicular to the movement of current 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, which acts with a force of 1 newton on each 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 -
The magnetic field can be created by the current of charged particles and/or by the magnetic moments of electrons in atoms (and by the magnetic moments of other particles, although to a much lesser extent) (permanent magnets).
In addition, it appears in the presence of a time-varying electric field.
The main power characteristic of the magnetic field is magnetic induction vector (magnetic field induction vector) . From a mathematical point of view, it is a vector field that defines and specifies the physical concept of a magnetic field. Often the vector of magnetic induction is called simply a magnetic field for brevity (although this is probably not the most strict use of the term).
Another fundamental characteristic of the magnetic field (alternative magnetic induction and closely related to it, practically equal to it in physical value) is vector potential .
A magnetic field can be called a special kind of matter, through which interaction is carried out between moving charged particles or bodies that have a magnetic moment.
Magnetic fields are a necessary (in context) consequence of the existence of electric fields.
- From the point of view of quantum field theory, magnetic interaction - as a special case of electromagnetic interaction is transferred by a fundamental massless boson - a photon (a particle that can be represented as a quantum excitation of an electromagnetic field), often (for example, in all cases of static fields) - virtual.
Magnetic field sources
The magnetic field is created (generated) by the current of charged particles, or by the 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 (not being 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 inductionIn 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 constantWhen 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 permeabilityIn 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 groups of substances listed above 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).
see also
- Magnetic Film Visualizer
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 method of measurement 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.
A magnetic field is a special form of matter that is created by magnets, conductors with current (moving charged particles) and which can be detected by the interaction of magnets, conductors with current (moving charged particles).
Oersted's experience
The first experiments (carried out in 1820), which showed that there is a deep connection between electrical and magnetic phenomena, were the experiments of the Danish physicist H. Oersted.
A magnetic needle located near the conductor rotates through a certain angle when the current is turned on in the conductor. When the circuit is opened, the arrow returns to its original position.
It follows from the experience of G. Oersted that there is a magnetic field around this conductor.
Ampère experience
Two parallel conductors, through which an electric current flows, interact with each other: they attract if the currents are in the same direction, and repel if the currents are in the opposite direction. This is due to the interaction of the magnetic fields that arise around the conductors.
Magnetic field properties
1. Materially, i.e. exists independently of us and our knowledge of it.
2. Created by magnets, conductors with current (moving charged particles)
3. Detected by the interaction of magnets, conductors with current (moving charged particles)
4. Acts on magnets, conductors with current (moving charged particles) with some force
5. There are no magnetic charges in nature. You cannot separate the north and south poles and get a body with one pole.
6. The reason why bodies have magnetic properties was found by the French scientist Ampère. Ampere put forward the conclusion that the magnetic properties of any body are determined by closed electric currents inside it.
These currents represent the movement of electrons in orbits in the atom.
If the planes in which these currents circulate are located randomly with respect to each other due to the thermal motion of the molecules that make up the body, then their interactions are mutually compensated and the body does not exhibit any magnetic properties.
And vice versa: if the planes in which the electrons rotate are parallel to each other and the directions of the normals to these planes coincide, then such substances enhance the external magnetic field.
7. Magnetic forces act in a magnetic field in certain directions, which are called magnetic lines of force. With their help, you can conveniently and clearly show the magnetic field in a particular case.
In order to depict the magnetic field more accurately, we agreed in those places where the field is stronger, to show the lines of force located more densely, i.e. closer to each other. And vice versa, in places where the field is weaker, field lines are shown in a smaller number, i.e. less frequently located.
8. The magnetic field characterizes the vector of magnetic induction.
The magnetic induction vector is a vector quantity that characterizes the magnetic field.
The direction of the magnetic induction vector coincides with the direction of the north pole of a free magnetic needle at a given point.
The direction of the field induction vector and the current strength I are related by the “rule of the right screw (gimlet)”:
if you screw the gimlet in the direction of the current in the conductor, then the direction of the speed of movement of the end of its handle at a given point will coincide with the direction of the magnetic induction vector at this point.
In the last century, various scientists have put forward several assumptions about the Earth's magnetic field. According to one of them, the field appears as a result of the rotation of the planet around its axis.
It is based on the curious Barnet-Einstein effect, which lies in the fact that when any body rotates, a magnetic field arises. The atoms in this effect have their own magnetic moment, as they rotate around their own axis. This is how the Earth's magnetic field appears. However, this hypothesis did not withstand experimental tests. It turned out that the magnetic field obtained in such a non-trivial way is several million times weaker than the real one.
Another hypothesis is based on the appearance of a magnetic field due to the circular motion of charged particles (electrons) on the surface of the planet. She, too, was incompetent. The movement of electrons can cause the appearance of a very weak field, moreover, this hypothesis does not explain the reversal of the Earth's magnetic field. It is known that the north magnetic pole does not coincide with the north geographical.
Solar wind and mantle currents
The mechanism of formation of the magnetic field of the Earth and other planets of the solar system is not fully understood and so far remains a mystery to scientists. However, one proposed hypothesis does a pretty good job of explaining the inversion and magnitude of the real field induction. It is based on the work of the internal currents of the Earth and the solar wind.
The internal currents of the Earth flow in the mantle, which consists of substances with very good conductivity. The core is the current source. Energy from the core to the earth's surface is transferred by convection. Thus, in the mantle there is a constant movement of matter, which forms a magnetic field according to the well-known law of motion of charged particles. If we associate its appearance only with internal currents, it turns out that all planets whose direction of rotation coincides with the direction of rotation of the Earth must have an identical magnetic field. However, it is not. Jupiter's north geographic pole coincides with the north magnetic.
Not only internal currents are involved in the formation of the Earth's magnetic field. It has long been known that it reacts to the solar wind, a stream of high-energy particles coming from the Sun as a result of reactions occurring on its surface.
The solar wind by its nature is an electric current (the movement of charged particles). Entrained by the rotation of the Earth, it creates a circular current, which leads to the appearance of the Earth's magnetic field.
