The magnetic field is determined. Permanent magnetic field
Just as an electrical charge at rest acts on another charge through 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 early XIX in. Danish scientist Oersted did important discovery, 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. four ). 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 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 set aside thumb indicates the direction of the force acting on the conductor (rice. 9 ).
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 experiment, magnetic induction vector, vector direction, superposition principle. Graphic representation of magnetic fields, magnetic induction lines. Magnetic flux, energy characteristic of the field. Magnetic forces, Ampere force, Lorentz force. Movement of charged particles in a magnetic field. Magnetic properties of matter, Ampère's hypothesis)
If a hardened steel rod is inserted into a current-carrying coil, then unlike iron rod it does not demagnetize after power off, and long time retains magnetization.
Bodies that retain magnetization for a long time are called permanent magnets or simply magnets.
The French scientist Ampère explained the magnetization of iron and steel by electric currents that circulate inside each molecule of these substances. At the time of Ampere, nothing was known about the structure of the atom, so the nature of molecular currents remained unknown. Now we know that in every atom there are negatively charged particles-electrons, which, during their movement, create magnetic fields, and they cause the magnetization of iron and. become.
Magnets can have a wide variety of shapes. Figure 290 shows arcuate and strip magnets.
Those places of the magnet where the strongest are found magnetic actions are called the poles of a magnet(Fig. 291). Every magnet, like the magnetic needle known to us, necessarily has two poles; northern (N) and southern (S).
By bringing a magnet to objects made of various materials, it can be established that very few of them are attracted to the magnet. Good cast iron, steel, iron are attracted by a magnet and some alloys, much weaker - nickel and cobalt.
Natural magnets are found in nature (Fig. 292) - iron ore (the so-called magnetic iron ore). rich deposits we have magnetic iron ore in the Urals, in Ukraine, in the Karelian Autonomous Soviet Socialist Republic, the Kursk region and in many other places.
Iron, steel, nickel, cobalt and some other alloys acquire magnetic properties in the presence of magnetic iron ore. Magnetic iron ore allowed people to get acquainted for the first time with magnetic properties tel.
If the magnetic needle is brought closer to another similar arrow, then they will turn and be set against each other with opposite poles (Fig. 293). The arrow also interacts with any magnet. Bringing a magnet to the poles of a magnetic needle, you will notice that the north pole of the arrow is repelled from the north pole of the magnet and is attracted to the south pole. The south pole of the arrow is repelled by the south pole of the magnet and is attracted by the north pole.
Based on the experiences described, make the following conclusion; different names Magnetic poles attract and like poles repel.
The interaction of magnets is explained by the fact that around every magnet there is a magnetic field. The magnetic field of one magnet acts on another magnet, and, conversely, the magnetic field of the second magnet acts on the first magnet.
With the help of iron filings, one can get an idea of the magnetic field of permanent magnets. Figure 294 gives an idea of the magnetic field of a bar magnet. Both the magnetic lines of the magnetic field of the current and the magnetic lines of the magnetic field of the magnet are closed lines. Outside the magnet, magnetic lines exit the north pole of the magnet and enter the south pole, closing inside the magnet.
Figure 295, a shows the magnetic magnetic field lines of two magnets, facing each other with the same poles, and in Figure 295, b - two magnets facing each other with opposite poles. Figure 296 shows the magnetic lines of the magnetic field of an arcuate magnet.
All of these pictures are easy to experience.
Questions. 1. What is the difference in magnetization with a current of a piece of iron and a piece of steel? 2, What bodies are called permanent magnets? 3. How did Ampere explain the magnetization of iron? 4. How can we now explain the molecular Ampère currents? 5. What is called the magnetic poles of a magnet? 6. Which of the substances you know are attracted by a magnet? 7. How do the poles of magnets interact with each other? 8. How can you determine the poles of a magnetized steel rod using a magnetic needle? 9. How can one get an idea of the magnetic field of a magnet? 10. What are the magnetic lines of the magnetic field of a magnet?
Sources permanent magnetic fields (PMF) workplaces are permanent magnets, electromagnets, high-current DC systems (DC transmission lines, electrolyte baths, etc.).
Permanent magnets and electromagnets are widely used in instrumentation, magnetic washers for cranes, magnetic separators, magnetic water treatment devices, magnetohydrodynamic generators (MHD), nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), as well as in physiotherapy practice.
The main physical parameters characterizing the PMF are field strength (N), magnetic flux (F) and magnetic induction (V). In the SI system, the unit of measurement of the magnetic field strength is ampere per meter (A/m), magnetic flux - Weber (Wb ), magnetic flux density (magnetic induction) - tesla (Tl ).
Changes in the state of health of persons working with PMF sources were revealed. Most often, these changes manifest themselves in the form of vegetative dystonia, asthenovegetative and peripheral vasovegetative syndromes, or a combination thereof.
According to the standard in force in our country (“Maximum Permissible Levels of Exposure to Permanent Magnetic Fields When Working with Magnetic Devices and Magnetic Materials” No. 1742-77), the PMF intensity at workplaces should not exceed 8 kA / m (10 mT). Permissible levels of PMF recommended by the International Committee on Non-Ionizing Radiation (1991) are differentiated by the contingent, the place of exposure and the time of work. For professionals: 0.2 Tl - when exposed to a full working day (8 hours); 2 Tl - with a short-term effect on the body; 5 Tl - with a short-term impact on the hands. For the population, the level of continuous exposure to PMF should not exceed 0.01 T.
RF EMP sources are widely used in a wide variety of industries National economy. They are used to transmit information at a distance (broadcasting, radiotelephone communications, television, radar, etc.). In industry, electromagnetic radiation of the radio wave range is used for induction and dielectric heating of materials (hardening, melting, soldering, welding, metal spraying, heating of the internal metal parts of electrovacuum devices during pumping, drying wood, heating plastics, gluing plastic compounds, heat treatment food products and etc.). EMR is widely used in scientific research(radiospectroscopy, radio astronomy) and medicine (physiotherapy, surgery, oncology). In a number of cases, electromagnetic radiation occurs as a side unused factor, for example, near overhead power lines (OL), transformer substations, electrical appliances, including household ones. The main sources of EMF RF radiation in environment serve as antenna systems of radar stations (RLS), radio and television and radio stations, including mobile radio systems and overhead power lines.
The human and animal body is very sensitive to the effects of RF EMF.
Critical organs and systems include: central nervous system, eyes, gonads, and according to some authors, the hematopoietic system. The biological effect of these radiations depends on the wavelength (or radiation frequency), the generation mode (continuous, pulsed) and the conditions of exposure to the body (constant, intermittent; general, local; intensity; duration). It is noted that biological activity decreases with increasing wavelength (or decreasing frequency) of radiation. The most active are centi-, deci-, and meter-wave bands. Injuries caused by RF EMR can be acute or chronic. Acute ones arise under the action of significant thermal radiation intensities. They are extremely rare - in case of accidents or gross violations of safety regulations at the radar. For professional conditions more characteristic are chronic lesions, which are detected, as a rule, after several years of work with microwave EMR sources.
Main normative documents that regulate the permissible levels of exposure to RF EMR are: GOST 12.1.006 - 84 “SSBT. Electromagnetic fields of radio frequencies.
Permissible levels "and SanPiN 2.2.4 / 2.1.8.055-96" electromagnetic radiation radio frequency band". They normalize the energy exposure (EE) for electric (E) and magnetic (H) fields, as well as the energy flux density (PEF) for a working day (Table 5.11).
Table 5.11.
Maximum Permissible Levels (MPL) per working day for employees
With EMI RF
| Parameter | Frequency bands, MHz | ||||
| Name | unit of measurement | 0,003-3 | 3-30 | 30-300 | 300-300000 |
| EE E | (W/m) 2 *h | - | |||
| uh n | (A/m) 2 *h | - | - | - | |
| ppe | (μW / cm 2) * h | - | - | - |
For the entire population under continuous exposure, the following MPs for electric field strength, V/m, have been established:
Frequency range MHz
0,03-0,30........................................................... 25
0,3-3,0.............................................................. 15
3-30.................................................................. 10
30-300............................................................... 3*
300-300000...................................................... 10
* Except for TV stations, the remote controls for which are differentiated according to
depending on the frequency from 2.5 to 5 V/m.
The number of devices operating in the radio frequency range includes video displays of personal computer terminals. Today, personal computers (PCs) are wide application in production, in scientific research, in medical institutions, at home, in universities, schools and even kindergartens. When used in the production of PCs, depending on technological tasks, they can affect the human body for a long time (within a working day). In domestic conditions, the time of using a PC is not at all controllable.
For PC video display terminals (VDT), the following EMI remote controls are installed (SanPiN 2.2.2.542-96 “Hygienic requirements for video display terminals, personal electronic computers and organization of work”) - table. 5.12.
Table 5.12. Maximum allowable levels of EMP generated by VDT
1This article presents the results of studies of vector and scalar magnetic fields of permanent magnets and the definition of their propagation.
permanent magnet
electromagnet
vector magnetic field
scalar magnetic field.
2. Borisenko A.I., Tarapov I.E. Vector analysis and the beginnings of tensor calculus. - M .: Higher school, 1966.
3. Kumpyak D.E. Vector and tensor analysis: tutorial. - Tver: Tver State University, 2007. - 158 p.
4. McConnell A.J. Introduction to tensor analysis with applications to geometry, mechanics and physics. – M.: Fizmatlit, 1963. – 411 p.
5. Borisenko A.I., Tarapov I.E. Vector analysis and the beginnings of tensor calculus. - 3rd ed. - M .: Higher School, 1966.
permanent magnets. Permanent magnetic field.
Magnet- these are bodies that have the ability to attract iron and steel objects and repel some others due to the action of their magnetic field. The magnetic field lines pass from the south pole of the magnet, and exit from the north pole (Fig. 1).
Rice. 1. Magnet and magnetic field lines
A permanent magnet is a product made of a hard magnetic material with a high residual magnetic induction that retains the state of magnetization for a long time. Permanent magnets are manufactured in various shapes and are used as autonomous (not consuming energy) sources of a magnetic field (Fig. 2).
An electromagnet is a device that creates a magnetic field when an electric current is passed through. Typically, an electromagnet consists of a winding of an inferromagnetic core, which acquires the properties of a magnet when an electric current passes through the winding.
Rice. 2. Permanent magnet
In electromagnets designed primarily to create mechanical force, there is also an armature (moving part of the magnetic circuit) that transmits force.
Permanent magnets made of magnetite have been used in medicine since ancient times. Queen Cleopatra of Egypt wore a magnetic amulet.
In ancient China, in the Imperial Book of internal medicine"The question of the use of magnetic stones for the correction of Qi energy in the body - "living force" was touched upon.
The theory of magnetism was first developed by the French physicist André Marie Ampère. According to his theory, the magnetization of iron is explained by the existence of electric currents that circulate inside the substance. Ampere made his first reports on the results of experiments at a meeting of the Paris Academy of Sciences in the autumn of 1820. The concept of “magnetic field” was introduced into physics by English physicist Michael Faraday. Magnets interact through a magnetic field, he also introduced the concept of magnetic lines of force.
Vector magnetic field
A vector field is a mapping that associates each point of the space under consideration with a vector with the beginning at that point. For example, the wind speed vector in this moment time varies from point to point and can be described by a vector field (Fig. 3).
Scalar magnetic field
If each point M of a given region of space (most often of dimension 2 or 3) is associated with some (usually real) number u, then we say that a scalar field is given in this region. In other words, a scalar field is a function that maps Rn to R (a scalar function of a point in space).
Gennady Vasilyevich Nikolaev tells in a simple way, shows and proves on simple experiments the existence of the second type of magnetic field, which science, for a strange reason, has not found. Since the time of Ampère, there has been an assumption that it exists. He called the field discovered by Nikolaev a scalar field, but it is still often called by his name. Nikolaev brought electromagnetic waves to a complete analogy with ordinary mechanical waves. Now physics considers electromagnetic waves as exclusively transverse, but Nikolaev is sure and proves that they are also longitudinal or scalar, and this is logical, as a wave can propagate forward without direct pressure, it is simply absurd. According to the scientist, the longitudinal field was hidden by science on purpose, perhaps in the process of editing theories and textbooks. This was done with simple intent and consistent with other cuts.
Rice. 3. Vector magnetic field
The first cut that was made was the lack of ether. Why?! Because the ether is energy, or a medium that is under pressure. And this pressure, if the process is properly organized, can be used as a free source of energy!!! The second cutback was the removal of the longitudinal wave, as a result of the fact that if the ether is a source of pressure, that is, energy, then if only transverse waves are added in it, then no free or free energy can be obtained, a longitudinal wave is required.
Then the counter imposition of waves makes it possible to pump out the pressure of the ether. Often this technology is called the zero point, which is generally correct. It is on the border of the connection of plus and minus (increased and reduced pressure), with the oncoming movement of waves, you can get the so-called Bloch zone or a simple dip of the medium (ether), where additional energy of the medium will be attracted.
The work is an attempt to practically repeat some of the experiments described in the book by G.V. Nikolaev “Modern electrodynamics and the reasons for its paradoxicality” and to reproduce the generator and motor of Stefan Marinov, as far as possible at home.
The experience of G.V. Nikolaev with magnets: We used two round magnets from the speakers
Two flat magnets located on a plane with opposite poles. They are attracted to each other (Fig. 4), meanwhile, when they are perpendicular (regardless of the orientation of the poles), there is no attractive force (only torque is present) (Fig. 5).
Now let's cut the magnets in the middle and connect them in pairs with different poles, forming magnets of the original size (Fig. 6).
When these magnets are located in the same plane (Fig. 7), they will again, for example, be attracted to each other, while with a perpendicular arrangement they will already be repelled (Fig. 8). In the latter case, the longitudinal forces acting along the cut line of one magnet are a reaction to the transverse forces acting on side surfaces another magnet and vice versa. The existence of a longitudinal force contradicts the laws of electrodynamics. This force is the result of the action of a scalar magnetic field present at the place where the magnets are cut. Such a composite magnet is called siberian colia.
A magnetic well is a phenomenon when a vector magnetic field repels, and a scalar magnetic field attracts, and a distance is born between them.
Bibliographic link
Zhangisina G.D., Syzdykbekov N.T., Zhanbirov Zh.G., Sagyntai M., Mukhtarbek E.K. PERMANENT MAGNETS AND PERMANENT MAGNETIC FIELDS // Successes of modern natural sciences. - 2015. - No. 1-8. - S. 1355-1357;URL: http://natural-sciences.ru/ru/article/view?id=35401 (date of access: 04/05/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"
What is a permanent magnet
A ferromagnetic product capable of retaining a significant residual magnetization after the removal of an external magnetic field is called a permanent magnet. Permanent magnets are made from various metals, such as: cobalt, iron, nickel, rare earth metal alloys (for neodymium magnets), as well as from natural minerals such as magnetites.
The scope of permanent magnets today is very wide, but their purpose is fundamentally the same everywhere - as a source of a constant magnetic field without power supply. Thus, a magnet is a body that has its own.
The very word “magnet” comes from the Greek phrase, which translates as “stone from Magnesia”, after the name of the Asian city, where deposits of magnetite, magnetic iron ore, were discovered in ancient times. From a physical point of view, an elementary magnet is an electron, and the magnetic properties of magnets are generally determined by the magnetic moments of the electrons that make up the magnetized material.
The characteristics of the demagnetizing section of the material from which the permanent magnet is made determine the properties of a permanent magnet: the higher the coercive force Hc, and the higher the residual magnetic induction Br, the stronger and more stable the magnet.
Coercive force (literally translated from Latin - "holding force") - this is necessary for the complete demagnetization of a ferro- or ferrimagnetic substance. Thus, the greater the coercive force a particular magnet has, the more resistant it is to demagnetizing factors.
The unit of measure for the coercive force is Ampere/meter. And, as you know, is a vector quantity, which is the power characteristic of the magnetic field. The characteristic value of the residual magnetic induction of permanent magnets is about 1 Tesla.
Types and properties of permanent magnets
ferrite
Ferrite magnets, although fragile, have good corrosion resistance, which, at a low price, makes them the most common. Such magnets are made from an alloy of iron oxide with barium or strontium ferrite. This composition allows the material to retain its magnetic properties over a wide temperature range - from -30°C to +270°C.
Magnetic products in the form of ferrite rings, bars and horseshoes are widely used both in industry and in everyday life, in technology and electronics. They are used in acoustic systems, in generators, in. In the automotive industry, ferrite magnets are installed in starters, power windows, cooling systems and fans.
Ferrite magnets are characterized by a coercive force of about 200 kA/m and a residual magnetic induction of about 0.4 Tesla. On average, a ferrite magnet can last from 10 to 30 years.
Alnico (aluminium-nickel-cobalt)
Permanent magnets based on an alloy of aluminum, nickel and cobalt are characterized by unsurpassed temperature resistance and stability: they are able to maintain their magnetic properties at temperatures up to +550 ° C, although the coercive force characteristic of them is relatively small. Under the action of a relatively small magnetic field, such magnets will lose their original magnetic properties.
Judge for yourself: a typical coercive force is about 50 kA/m with a residual magnetization of about 0.7 Tesla. However, despite this feature, Alnico magnets are indispensable for some scientific research.
The typical contents of highly magnetic alnico alloys range from 7 to 10% aluminum, 12 to 15% nickel, 18 to 40% cobalt, and 3 to 4% copper.
The more cobalt, the higher the saturation induction and the magnetic energy of the alloy. Additives in the form of 2 to 8% titanium and only 1% niobium contribute to obtaining a greater coercive force - up to 145 kA/m. The addition of 0.5 to 1% silicon ensures the isotropy of the magnetic properties.
Samariaceae
If you need exceptional resistance to corrosion, oxidation and temperatures up to +350 ° C, then the magnetic alloy of samarium and cobalt is what you need.
In terms of cost, samarium-cobalt magnets are more expensive than neodymium ones due to the more scarce and expensive metal- cobalt. However, it is advisable to use them in case of need to have minimum dimensions and weight of final products.
This is most expedient in spacecraft, aviation and computer technology, miniature electric motors and magnetic couplings, in wearable devices and devices (watches, headphones, mobile phones etc.)
Due to its special corrosion resistance, it is samarium magnets that are used in strategic development and military applications. Electric motors, generators, lifting systems, motor vehicles – the strong samarium-cobalt alloy magnet is ideal for aggressive environments and difficult operating conditions. The coercive force is about 700 kA/m with a residual magnetic induction of about 1 Tesla.
neodymium
Neodymium magnets are very much in demand today and seem to be the most promising. Neodymium-iron-boron alloy allows you to create super magnets for various areas from latches and toys to powerful lifting machines.
The high coercive force of the order of 1000 kA/m and the residual magnetization of the order of 1.1 Tesla allow the magnet to persist for many years; for 10 years, a neodymium magnet loses only 1% of its magnetization if its temperature under operating conditions does not exceed +80°C ( for some grades up to +200°C). Thus, neodymium magnets have only two disadvantages - brittleness and low operating temperature.
The magnetic powder together with the binding component forms a soft, flexible and lightweight magnet. Binders such as vinyl, rubber, plastic or acrylic make magnets possible various forms and sizes.
The magnetic force, of course, is inferior to a pure magnetic material, but sometimes such solutions are necessary to achieve certain unusual goals for magnets: in the production of advertising products, in the manufacture of removable stickers on cars, as well as in the manufacture of various stationery and souvenirs.
Like poles of magnets repel, and opposite poles attract. The interaction of magnets is explained by the fact that any magnet has a magnetic field, and these magnetic fields interact with each other. What, for example, is the reason for the magnetization of iron?
According to the hypothesis of the French scientist Ampère, there are elementary elements inside the substance. electric currents(Ampere currents), which are formed due to the movement of electrons around the nuclei of atoms and around their own axis.
When electrons move, elementary magnetic fields arise. And if a piece of iron is introduced into an external magnetic field, then all elementary magnetic fields in this iron are oriented in the same way in the external magnetic field, forming their own magnetic field of a piece of iron. So, if the applied external magnetic field was strong enough, then after it is turned off, a piece of iron will become a permanent magnet.
Knowing the shape and magnetization of a permanent magnet allows for calculations to replace it with an equivalent system of electric magnetization currents. Such a replacement is possible both when calculating the characteristics of the magnetic field, and when calculating the forces acting on the magnet from the external field. For example, we will calculate the interaction force of two permanent magnets.
Let the magnets have the shape of thin cylinders, let's denote their radii as r1 and r2, thicknesses h1, h2, magnet axes coincide, denote the distance between the magnets z, we will assume that it is significant more sizes magnets.
The emergence of an interaction force between magnets is explained traditional way: one magnet creates a magnetic field that affects the second magnet.
To calculate the interaction force, let us mentally replace the magnets with uniform magnetization J1 and J2 with circular currents flowing along the side surface of the cylinders. The strength of these currents will be expressed in terms of the magnetization of the magnets, and their radii will be considered equal to the radii of the magnets.
Let us decompose the induction vector B of the magnetic field created by the first magnet at the location of the second one into two components: axial, directed along the axis of the magnet, and radial, perpendicular to it.
To calculate the total force acting on the ring, it is necessary to mentally divide it into small elements IΔl and sum up acting on each such element.
Using the left-hand rule, it is easy to show that the axial component of the magnetic field leads to the appearance of Ampère forces that tend to stretch (or compress) the ring - the vector sum of these forces is zero.
The presence of the radial component of the field leads to the emergence of Ampere forces directed along the axis of the magnets, that is, to their attraction or repulsion. It remains to calculate the Ampere forces - these will be the forces of interaction between the two magnets.