Gauss (unit of magnetic induction). The traditional problem of induction and the failure of all principles or rules of induction

April 30th 236 (2*3=6) years since the birth of the great mathematician Carl Friedrich Gauss.

Wikipedia
Johann Carl Friedrich Gauss(German Johann Carl Friedrich Gauß; April 30, 1777, Braunschweig - February 23, 1855, Göttingen) - German mathematician, mechanic, physicist and astronomer. Considered one of the greatest mathematicians of all time, "the king of mathematicians." Laureate of the Copley medal (1838), foreign member of the Swedish (1821) and Russian (1824) Academies of Sciences, of the English Royal Society.

Biography
I won't copy my entire biography here. It is long and divided into three periods. I will limit myself to a textbook story about calculating the sum of an arithmetic progression.
Gauss's grandfather was a poor peasant, his father was a gardener, a bricklayer, and a canal keeper in the Duchy of Brunswick. Already at the age of two, the boy showed himself to be a child prodigy. At the age of three, he could read and write, even correcting his father's counting errors. According to legend, school teacher math to keep the kids busy for a long time, invited them to calculate the sum of numbers from 1 to 100. Young Gauss noticed that the pairwise sums from opposite ends are the same: 1+100=101, 2+99=101, etc., and instantly got the result: 50*101=5050 .
Until old age, he was accustomed most make calculations in your mind.
Well, one more excerpt:
1839: The 62-year-old Gauss mastered the Russian language and in letters to the St. Petersburg Academy asked to send him Russian magazines and books, in particular “ captain's daughter» Pushkin. It is assumed that this is due to Gauss's interest in the works of Lobachevsky, who in 1842, on the recommendation of Gauss, was elected a foreign corresponding member of the Göttingen Royal Society.

I don’t know how it is for anyone, but up to this moment it seemed to me that Pushkin and Gauss were in some kind of parallel universes... More precisely, I never thought about both at the same time ... However, here ...
I recommend everyone to read the full biography. Such rich life that a few centuries would not have been enough for another person to accomplish all this.

Scientific activity
Associated with the name Gauss fundamental research in almost all major areas of mathematics: in algebra, number theory, differential and non-Euclidean geometry, mathematical analysis, the theory of functions of a complex variable, probability theory, as well as in analytical and celestial mechanics, astronomy, physics and geodesy. “In every field, the depth of penetration into the material, the boldness of thought and the significance of the result were amazing. Gauss was called "the king of mathematicians" (lat. Princeps mathematicorum).
Gauss was extremely strict about his published works and never published even outstanding results if he considered his work on this topic to be incomplete. His personal seal showed a tree with several fruits, under the motto: "Pauca sed matura" (few, but ripe). A study of Gauss's archive showed that he was slow to publish a number of his discoveries, and as a result, other mathematicians were ahead of him. Here is an incomplete list of priorities he missed.

  • Non-Euclidean geometry, where Lobachevsky and Bolyai were ahead of him.
  • Elliptic functions, where he also advanced far, but did not have time to print anything, and after the work of Jacobi and Abel, the need for publication disappeared.
  • A meaningful outline of the theory of quaternions, independently discovered by Hamilton 20 years later.
  • Method least squares, rediscovered later by Legendre.
  • The law of distribution of prime numbers, with which Legendre's publication also outstripped him.
Several students, students of Gauss, became eminent mathematicians, for example: Riemann, Dedekind, Bessel, Möbius.

I will not write about the achievements of Gauss in algebra, geometry, mathematical analysis, analytical mechanics and astronomy either. Wikipedia has a separate section dedicated to each area. I will quote only a little bit from "geometry".

<...>A letter from Gauss to Lobachevsky has been preserved in which his sense of solidarity is clearly expressed, and in personal letters published after his death, Gauss admires Lobachevsky's work. In 1817 he wrote to the astronomer W. Olbers:

I am becoming more and more convinced that the necessity of our geometry cannot be proved at least by the human mind and for the human mind. Perhaps in another life we ​​will come to views on the nature of space that are now inaccessible to us. So far, geometry has had to be placed not on the same level with arithmetic, which exists purely a priori, but rather with mechanics.


It's great, right?

The name of Gauss is associated with many theorems and scientific terms in mathematics, astronomy and physics.

  • Gaussian algorithm for calculating the date of Easter
  • Gaussian discriminants
  • Gaussian curvature
  • Gaussian integers
  • Gauss interpolation formula
  • Gaussian tape
  • Gauss method (solutions of systems of linear equations)
  • Gauss-Jordan method
  • Gauss-Seidel method
  • Normal or Gaussian distribution
  • Direct Gaussian
  • Gauss gun
  • Gauss series
  • Gauss-Wanzel theorem
  • Gaussian filter
  • Gauss formula - Bonnet
I will focus on some of the items on this list. There are a lot of them, and therefore everything is quite fluent.
For some items there will be only illustrations. We will start with them.

1. Gauss gun
Gauss gun (Eng. Gauss gun, Coil gun, Gauss cannon) is one of the varieties of electromagnetic mass accelerator. Named after the German scientist Carl Gauss, who laid the foundations mathematical theory electromagnetism.

2. Gaussian curvature
Gaussian curvature is a measure of the curvature of a surface in the vicinity of any of its points.

3. Direct Gauss
If no sides of the quadrilateral are parallel, then the midpoint of the segment connecting the points of intersection of opposite sides lies on the line connecting the midpoints of the diagonals. This line is called the Gauss line.

4. Gaussian integers
Gaussian integers (Gaussian numbers, integers complex numbers) are complex numbers whose real and imaginary parts are integers. Introduced by Gauss in 1825.
See what a beauty


This is the distribution of Gaussian primes on complex plane (prime numbers highlighted in red)

5. Gauss (unit)
Gauss ( Russian designation Gs, international - G) - a unit of measurement of magnetic induction in the CGS system.
It is named after the German physicist and mathematician Carl Friedrich Gauss.
1 Gs = 100 μT;
1 T = 10 4 Gs.

And finally
6. Normal distribution or Gaussian distribution
The normal distribution, also called the Gaussian distribution, is a probability distribution, which in the one-dimensional case is given by the distribution density function:

where the parameter μ is the mathematical expectation, median and mode of distribution, and the parameter σ is standard deviation(σ² - variance) distributions.
Probability Density.

Gauss (unit of magnetic induction) Gauss, unit of magnetic induction in cgs system of units(Gaussian and CGSM). Named after K. Gaussian. Abbreviated designation: Russian gs, international Gs. 1 gs is equal to the induction of a homogeneous magnetic field, in which a straight conductor 1 cm long, located perpendicular to the field induction vector, experiences a force of 1 dyne, if a current of 1 CGSM current flows through this conductor. G. can also be defined as magnetic induction, in which a magnetic flux of 1 maxwell passes through a cross section of 1 cm, normal to the direction of the induction lines. The ratio between the CGS and SI units of magnetic induction: 1 t = 10 4 gs. In practice, another unit of kilogauss = 1000 gauss is used. Until 1930, the unit of magnetic field strength, equal to 79.577 a/m, was also called. In 1930, by decision of the International Electrotechnical Commission for the magnetic field strength was adopted special unit oersted .

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Gauss (unit of magnetic induction)" is in other dictionaries:

    GAUSS, a unit of magnetic induction (see MAGNETIC INDUCTION) in the CGS system of units (see CGS SYSTEM OF UNITS). Named after K. Gauss, designated Gs. 1 Gs \u003d 10 4 tesla (see TESLA (unit of magnetic induction)) ... encyclopedic Dictionary

    - ... Wikipedia

    TESLA, a unit of magnetic induction (see MAGNETIC INDUCTION) (B) in the SI system, is named after the physicist N. Tesla. Designated Tl. 1 T \u003d 1 N / (A.m) 1 T (tesla) magnetic induction of such a uniform magnetic field that acts with a force of 1 N ... ... encyclopedic Dictionary

    Tesla, a unit of magnetic induction of the International System of Units, equal to the magnetic induction at which the magnetic flux through transverse section an area of ​​1 m2 is equal to 1 weber. Named after N. Tesla. Designations: Russian tl, international T. 1 ... ... Great Soviet Encyclopedia

    This term has other meanings, see Gauss. Gauss (Russian designation Gs, international G) is a unit of measurement of magnetic induction in the CGS system. It is named after the German physicist and mathematician Carl Friedrich Gauss. 1 Gs = ... ... Wikipedia

Gauss, unit of magnetic induction in cgs system of units(Gaussian and CGSM). Named after K. Gaussian. Abbreviated designation: Russian gs, international Gs. 1 gauss is equal to the induction of a uniform magnetic field in which a straight conductor 1 cm long, located perpendicular to the field induction vector, experiences a force of 1 dyne if a current of 1 CGSM current flows through this conductor. G. can also be defined as magnetic induction, in which a magnetic flux of 1 maxwell passes through a cross section of 1 cm, normal to the direction of the induction lines. The ratio between the CGS and SI units of magnetic induction: 1 t = 10 4 gs. In practice, another unit of kilogauss = 1000 gauss is used. Until 1930, the unit of magnetic field strength, equal to 79.577 a/m, was also called. In 1930, by decision of the International Electrotechnical Commission, a special unit of oersted was adopted for the strength of the magnetic field.

  • - parameters characterizing el.-mag. interaction in a system of closed unbranched electric. circuits in which quasi-stationary currents flow ...

    Physical Encyclopedia

  • - a unit of magnetic induction in the CGS system of units. Named after K. Gauss, denoted Gs: 1 Gs \u003d 10-4 Tesla ...

    Natural science. encyclopedic Dictionary

  • - Motivational induction method - verbal technique, author J. Nutten - . It is carried out in two stages...

    Psychological Dictionary

  • - a method of electrical prospecting with alternating current, based on the study electric currents induction excited in the G.P. by a generator of an alternating electromagnetic field of high frequency ...

    Geological Encyclopedia

  • - named after L. D. Shevyakov Min-va ferrous metallurgy USSR - located in Gubkin, Belgorod region. Created in 1951 as Mining-geol. station of the Academy of Sciences of the USSR, reorganized in 1958 into a branch of the Institute of Gorn. affairs to them. A.A....

    Geological Encyclopedia

  • - Karl Friedrich, German mathematician. As a child, he was an unusually gifted child, from a poor family. His education was paid for by a wealthy aristocrat, the Duke of Brunswick, who learned about him from his teacher...

    Scientific and technical encyclopedic dictionary

  • - a drive in which the information carrier is a 1/2 inch wide magnetic tape in a reel or a 1/4 inch wide magnetic tape in a cassette ...

    Brief dictionary for printing

  • - methods of establishing causation between phenomena. Formulated by English. logician D. S. Mill. He relied on the "Discovery Tables" eng. philosopher F. Bacon ...

    Dictionary of logic

  • - tasks related to the study of the movement of electrically conductive liquids and gases in the presence of a magnetic field. ...

    Mathematical Encyclopedia

  • - unusable units. magnetic induction in CGS and SGSM systems. Designation - Gs. The connection between Gs and tesla - unit. magnetic induction in SI: 1 Gs = 10-4T...

    Big encyclopedic polytechnic dictionary

  • - Herman is Swiss. philosopher, prof. University of Basel and Bern University, a student of G. Schmalenbach. He studied the works of Plato and systematized the entire post-Platonic philosophy...

    Philosophical Encyclopedia

  • - "... - flux linkage of one element electrical circuit caused by electric current in another element of the circuit..." Source: "ELECTRICAL TECHNIQUE. TERMS AND DEFINITIONS OF BASIC CONCEPTS ...

    Official terminology

  • famous German mathematician. Genus. April 28, 1777 in Braunschweig and from early age discovered outstanding mathematical abilities...

    Encyclopedic Dictionary of Brockhaus and Euphron

  • - I Gauss Karl Friedrich, a German mathematician who also made a fundamental contribution to astronomy and geodesy...
  • - Tesla, a unit of magnetic induction of the International System of Units, equal to magnetic induction, at which the magnetic flux through a cross section of 1 m2 is equal to 1 weber. Named after N. Tesla...

    Great Soviet Encyclopedia

  • - Zharg. they say Shuttle. Bypass. Maksimov, 246...

    Big Dictionary Russian sayings

"Gauss (unit of magnetic induction)" in books

GAUSS, LOBACHEVSKY AND JANOS BOLJAI

From the book Lobachevsky author

GAUSS, LOBACHEVSKY AND JANOSZ BOLJAI In Göttingen, hiding from people in an astronomical tower, lives indifferent to everything except his formulas, the "king of mathematicians" Gauss. This "king" does not care about "subjects". He does not lecture, does not bear any administrative

Gauss, Lobachevsky and Riemann

From the book Lobachevsky author Kolesnikov Mikhail Sergeevich

GAUSS, LOBACHEVSKY AND RIEMANN Gauss thought about Lobachevsky before last day: The Princeps Mathematicorum believed in its genius and knew that after his death all his personal correspondence would be published. That's how it has been for centuries. He appreciated irony and anticipated

Search for the magnetic component of DNA

From the book Passing the milestone. Keys to Understanding the Energy of the New Millennium by Carroll Lee

Search for the magnetic component of DNA DNA (deoxyribonucleic acid) is a molecule of two helix chains chemical compounds called nucleotides. The chains are organized in a twisted double helix ladder. Chromosomes are almost entirely made up of

12. The Traditional Problem of Induction and the Failure of All Principles or Rules of Induction

From book Objective knowledge. evolutionary approach author Popper Karl Raimund

12. The Traditional Problem of Induction and the Failure of All Principles or Rules of Induction I will now return to what I call the traditional philosophical problem induction. By this name, I mean the point of view of a person who sees the challenge posed by Hume

GAUSS CARL FRIEDRICH (1777 - 1855)

From the book of 100 famous scientists author Sklyarenko Valentina Markovna

GAUSS CARL FRIEDRICH (1777 - 1855) Carl Friedrich Gauss was born on April 30, 1777 in German city Brunswick, in a very poor family. His father worked as a locksmith, later he mastered another profession and became a gardener. In addition, he worked as an accountant in a trading office. Mother

6.1. View, its criteria and structure. A population is a structural unit of a species and an elementary unit of evolution. Speciation methods. microevolution

From the book Biology [ Complete reference to prepare for the exam] author Lerner Georgy Isaakovich

6.1. View, its criteria and structure. Population - structural unit kind and elementary unit evolution. Speciation methods. Microevolution A species is a set of individuals that actually exists in nature, occupying a certain area, having common origin,

3rd comment - Cook and Wheatstone, Gauss and Weber, Steingel

From the book Popular History - From Electricity to Television the author Kuchin Vladimir

3rd comment - Cook and Wheatstone, Gauss and Weber, Steingel Let us briefly highlight the work of Schilling's colleagues from European countries: The Englishman William Cook was familiar with the work of Schilling, he attracted Wheatstone, and at the end of 1837 this couple received the privilege to invented the telegraph with 5 -Yu

Surprises of "magnetic" water

From the book of Miracles: A popular encyclopedia. Volume 2 author Mezentsev Vladimir Andreevich

Surprises of "magnetic" water The history of this extraordinary water (probably, it is more correct to call it magnetic) is very curious. 30s of the XX century. Soviet physicists R. Berlaga and F. Gorsky discover an interesting phenomenon: precipitation of crystals from a saturated salt solution

CARL GAUSS

From the book of 100 great scientists author Samin Dmitry

Carl Friedrich Gauss

From the book Aphorisms author Ermishin Oleg

Carl Friedrich Gauss (1777-1855) mathematician ... We must honestly and frankly admit that in essence we have not gone two thousand years further than Euclid. Such a frank and unambiguous confession seems to us more in keeping with the dignity of science than

From the book Big Soviet Encyclopedia(TE) author TSB

GAUSS

From the book Secret Protocols, or Who Forged the Molotov-Ribbentrop Pact author Kungurov Alexey Anatolievich

GAUSS The first, and for many decades the only artifact "proving" the existence of " secret protocols"- cloudy photocopies that Hess' lawyer Alfred Seidl unsuccessfully tried to attach to the case file on Nuremberg Trials in March 1946 the first, and on

General information

In a surprising way, the ideas of one person can influence the subsequent development. human society generally. Such a person was Michael Faraday, not too versed in the intricacies of contemporary mathematics, but perfectly understanding physical meaning known by that time information about the nature of electricity and magnetism due to the concept of field interactions put forward by him.

existence modern society based on the use of electricity, magnetism and electrodynamics, we owe a whole galaxy of remarkable scientists. Among them, Ampère, Oersted, Henry, Gauss, Weber, Lorentz and, of course, Maxwell should be noted. Ultimately, they brought the science of electricity and magnetism into a single picture, which served as the basis for a whole cohort of inventors who created the prerequisites for the emergence of the modern information society with their creations.

We live surrounded by electric motors and generators: they are our first assistants in production, transport and at home. Any self-respecting person cannot imagine existence without a refrigerator, vacuum cleaner and washing machine. A priority is also a microwave oven, a hair dryer, a coffee grinder, a mixer, a blender and - the ultimate dream - an electric meat grinder and a bread machine. Of course, air conditioning is also a terribly useful thing, but if there are no funds to purchase it, then a simple fan will do.

For some men, the requests are somewhat more modest: the ultimate dream of the most inept man is an electric drill. Some of us, unsuccessfully trying to start the car in forty degrees of frost and hopelessly tormenting the starter (also an electric motor), secretly dream of purchasing a Tesla Motors car with electric motors and batteries in order to forget forever about the problems of gasoline and diesel engines.

Electric motors are everywhere: they lift us up in elevators, they transport us in subways, commuter trains, trams, trolleybuses and high-speed trains. They bring us water to the floors of skyscrapers, operate fountains, pump water from mines and wells, roll steel, lift weights, working in various cranes. And they do a lot of other useful things, setting in motion machine tools, tools and mechanisms.

Even exoskeletons for people with handicapped and for the military are made using electric motors, not to mention a whole army of industrial and research robots.

Today, electric motors work in space - just remember rover Curiosity. They work on the ground, underground, on water, under water and even in the air - if not today, then tomorrow (article written in November 2015) the Solar Impulse 2 aircraft will finally finish its trip around the world, and unmanned aircraft on electric motors, there are simply no numbers. No wonder quite serious corporations are now working on delivery services postal items using unmanned aerial vehicles.

History reference

Built in 1800 by the Italian physicist Alessandro Volta, the chemical battery, later named after the inventor “Voltaic column”, truly turned out to be a “horn of plenty” for scientists. It made it possible to set in motion electric charges in conductors, that is, to create electricity. New discoveries using the voltaic column continuously followed one after another in various areas physics and chemistry.

For example, the English scientist Sir Humphrey Davy in 1807, studying the electrolysis of melts of sodium and potassium hydroxides, obtained metallic sodium and potassium. Earlier, in 1801, he also discovered the electric arc, although the Russians consider it to be the discoverer of Vasily Vladimirovich Petrov. Petrov in 1802 described not only the arc itself, but also its possibilities practical application for the purposes of smelting, welding of metals and their recovery from ores, as well as lighting.

But the most important discovery was made by the Danish physicist Hans Christian Oersted: on April 21, 1820, during a demonstration of experiments at a lecture, he noticed the deviation of the arrow magnetic compass when turning on and off an electric current flowing through a conductor in the form of a wire. Thus, for the first time, the relationship between electricity and magnetism was confirmed.

The next step was taken French physicist André Marie Ampère a few months after experiencing Oersted's experience. Curious is the course of reasoning of this scientist, set out in the messages sent to him one after another in French Academy Sciences. At first, observing the turn of the compass needle at a current-carrying conductor, Ampere suggested that the Earth's magnetism is also caused by currents flowing around the Earth in the direction from west to east. From this they concluded that magnetic properties bodies can be explained by the circulation of a current within it. Further, Ampère rather boldly concluded that the magnetic properties of any body are determined by closed electric currents inside it, and magnetic interaction not due to special magnetic charges, but just a movement electric charges, i.e. current.

Amper immediately took over pilot study of this interaction and found that conductors with current flowing in one direction are attracted, and in the opposite direction they are repelled. Mutually perpendicular conductors do not interact with each other.

It's hard to resist not to lead open by ampere law in its own formulation:

"The force of interaction of moving charges is proportional to the product of these charges, inversely proportional to the square of the distance between them, as in Coulomb's law, but, moreover, it also depends on the speeds of these charges and the direction of their movement."

So in physics were discovered fundamental forces depending on speeds.

But the real breakthrough in the science of electricity and magnetism was the discovery by Michael Faraday of the phenomenon electromagnetic induction- the occurrence of an electric current in a closed circuit when changing magnetic flux passing through it. Regardless of Faraday, the phenomenon of electromagnetic induction was also discovered by Joseph Henry in 1832, who discovered the phenomenon of self-induction along the way.

A public demonstration by Faraday on August 29, 1831 was performed on a device he invented, consisting of a volt pole, a switch, iron ring, on which two identical coils of copper wire were wound on opposite sides. One of the coils was connected to a battery through a switch, and a galvanometer was connected to the ends of the other. When the current was turned on and off, the galvanometer recorded the appearance of a current different directions in the second coil.

In Faraday's experiments, an electric current, called the induction current, also appeared when a magnet was inserted into the coil or pulled out of the coil loaded on the measuring circuit. Similarly, the current also appeared when a smaller coil with current was inserted/pulled in/out. big coil from previous experience. And the direction induction current changed to the opposite when a magnet or a small coil with current was inserted / extended in accordance with the rule formulated by the Russian scientist Emil Khristianovich Lenz. in 1833.

Based on the experiments performed, Faraday derived a law for electromotive force later named after him.

The ideas and results of Faraday's experiments were rethought and generalized by another great compatriot - the brilliant English physicist and mathematician James Clerk Maxwell in his four differential equations electrodynamics, later called Maxwell's equations.

It should be noted that in three of the four Maxwell equations, magnetic induction appears in the form of a magnetic field vector.

Magnetic induction. Definition

Magnetic induction is a vector physical quantity, which is the power characteristic of the magnetic field (its action on charged particles) at a given point in space. It determines how strong F magnetic field acts on a charge q, moving at a speed v. Denoted Latin letter AT(pronounced vector B) and the force is calculated using the formula:

F = q [vB]

where F is the Lorentz force acting from the side of the magnetic field on the charge q; v- charge movement speed; B- magnetic field induction; [ v × B] - vector product vectors v and B.

Algebraically, the expression can be written as:

F = qvB sinα

where α - angle between velocity and magnetic induction vectors. vector direction F perpendicular to both of them and directed according to the rule of the left hand.

Magnetic induction is the main fundamental characteristic of a magnetic field, similar to the electric field strength vector.

AT international system SI units, the magnetic induction of the field is measured in teslas (T), in the CGS system - in gauss (Gs)

1 T = 10⁴ Gs

Other quantities of magnetic induction measurement used in various applications, and their conversion from one quantity to another, can be found in the converter of physical quantities.

Measuring instruments for measuring the magnitude of magnetic induction are called teslameters or gaussmeters.

Magnetic field induction. Physics of phenomena

Depending on the reaction to an external magnetic field, all substances are divided into three groups:

  • Diamagnets
  • Paramagnets
  • ferromagnets

The terms diamagnetism and paramagnetism were introduced by Faraday in 1845. For quantification these reactions introduced the concept of magnetic permeability. In the SI system introduced absolute magnetic permeability, measured in H/m, and relative dimensionless magnetic permeability, equal to the ratio the permeability of a given medium to the permeability of vacuum. For diamagnets, the relative magnetic permeability is somewhat less than one, for paramagnets - a little more than unity. In ferromagnets, the magnetic permeability is much greater than unity and is non-linear.

Phenomenon diamagnetism It consists in the ability of a substance to counteract the influence of an external magnetic field due to magnetization against its direction. That is, diamagnets are repelled by a magnetic field. In this case, the atoms, molecules or ions of the diamagnet acquire magnetic moment, directed against the external field.

Phenomenon paramagnetism is the ability of a substance to become magnetized when exposed to an external magnetic field. Unlike diamagnets, paramagnets are pulled in by a magnetic field. In this case, the atoms, molecules or ions of the paramagnet acquire a magnetic moment in the direction coinciding with the direction of the external magnetic field. When the field is removed, paramagnets do not retain magnetization.

Phenomenon ferromagnetism is the ability of a substance to spontaneously magnetize in the absence of an external magnetic field or to be magnetized under the influence of an external magnetic field and retain magnetization when the field is removed. In this case, most of the magnetic moments of atoms, molecules or ions are parallel to each other. This order is maintained down to temperatures below a certain critical temperature, called the Curie point. At temperatures above the Curie point for given substance, ferromagnets become paramagnets.

The magnetic permeability of superconductors is zero.

The absolute magnetic permeability of air is approximately equal to the magnetic permeability of vacuum and in technical calculations is taken equal to 4π 10 ⁻⁷ H/m

Peculiarities of the Behavior of the Magnetic Field in Diamagnets

As mentioned above, diamagnetic materials create an induced magnetic field directed against an external magnetic field. Diamagnetism is a quantum mechanical effect inherent in all substances. In paramagnets and ferromagnets, it is leveled due to other, stronger effects.

Diamagnets include, for example, substances such as inert gases, nitrogen, hydrogen, silicon, phosphorus and pyrolytic carbon; some metals - bismuth, zinc, copper, gold, silver. Many other inorganic and organic compounds are also diamagnetic, including water.

In an inhomogeneous magnetic field, diamagnets are shifted to a region more weak field. Magnetic lines of force as if pushed out of the body by diamagnetic materials. The phenomenon of diamagnetic levitation is based on this property. In a sufficiently strong magnetic field created by modern magnets, it is possible to levitate not only various diamagnets, but also small living creatures, consisting mainly of water.

Scientists from the University of Niemingen, the Netherlands, succeeded in hanging a frog in the air in a field with a magnetic induction of about 16 T, and researchers from a NASA laboratory using a superconductor magnet - levitation of a mouse, which, as a biological object, is much closer to a person than a frog .

All conductors exhibit diamagnetism when exposed to an alternating magnetic field.

The essence of the phenomenon is that under the influence of an alternating magnetic field, eddy currents - Foucault currents - directed against the action of an external magnetic field are induced in the conductors.

Features of the behavior of a magnetic field in paramagnets

The interaction of a magnetic field with paramagnets is completely different. Because the atoms, molecules, or ions of paramagnetic materials have their own magnetic moment, they align in the direction of the external magnetic field. This creates a resulting magnetic field that is greater than the original field.

Paramagnets include aluminum, platinum, alkaline and alkaline earth metals lithium, cesium, sodium, magnesium, tungsten, as well as alloys of these metals. Paramagnets are also oxygen, nitric oxide, manganese oxide, ferric chloride and many other chemical compounds.

Paramagnets are weakly magnetic substances, their magnetic permeability is slightly more than unity. In an inhomogeneous magnetic field, paramagnets are drawn into a region more strong field. In the absence of a magnetic field, paramagnets do not retain magnetization, because due to thermal motion own magnetic moments of their atoms, molecules or ions are directed randomly.

Features of the behavior of a magnetic field in ferromagnets

Due to their inherent property to spontaneously magnetize, ferromagnets form natural magnets, which known to mankind With ancient times. Magnets were attributed magical properties, they were used in various religious rituals and even in the construction of buildings. The first prototype of the compass, invented by the Chinese in the second or first centuries BC, was used by inquisitive ancestors to build houses according to the rules of Feng Shui. The use of the compass as a means of navigation began as early as the 11th century to travel across the deserts along the Great Silk Road. Later, the use of the compass in maritime affairs played a significant role in the development of navigation, the discovery of new lands and the development of new sea trade routes.

Ferromagnetism is a manifestation of the quantum mechanical properties of electrons that have spin, i.e. own dipole magnetic moment. Simply put, electrons behave like tiny magnets. For each completed electron shell an atom can only have a pair of electrons with opposite spins, i.e. the magnetic field of such electrons is directed in opposite sides. Because of this, atoms that have a pair number of electrons have a total magnetic moment zero Therefore, only atoms with an unfilled outer shell and an unpaired number of electrons are ferromagnets.

Ferromagnetic materials include transition group metals (iron, copper, nickel) and rare earth metals (gadolinium, terbium, dysprosium, holmium, and erbium), as well as alloys of these metals. Alloys of the above elements with non-ferromagnetic materials are also ferromagnets; alloys and compounds of chromium and manganese with non-ferromagnetic elements, as well as some of the metals of the actinide group.

Ferromagnets have a magnetic permeability value much greater than unity; the dependence of their magnetization under the action of an external magnetic field is non-linear and they are characterized by the manifestation of hysteresis - if the action of the magnetic field is removed, ferromagnets remain magnetized. To remove this remanent magnetization, it is necessary to apply a field in the opposite direction.

The plot of the dependence of the magnetic permeability μ on the strength of the magnetic field H in a ferromagnet, called the Stoletov curve, shows that at zero magnetic field strength H = 0, the magnetic permeability has small matterμ₀; then, as the intensity increases, the magnetic permeability rapidly increases to a maximum μ max , then slowly drops to zero.

The pioneer in the study of the properties of ferromagnets was the Russian physicist and chemist Alexander Stoletov. Now the curve of dependence of magnetic permeability on the strength of the magnetic field bears his name.

Modern ferromagnetic materials are finding wide application in science and technology: many technologies and devices are based on their use and on the use of the phenomenon of magnetic induction. For example, in computer science: the first generations of computers had memory on ferrite cores, information was stored on magnetic tapes, floppy disks and hard disks. However, the latter are still used in computers and are produced in hundreds of millions of pieces a year.

The use of magnetic induction in electrical engineering and electronics

AT modern world There are many examples of the use of magnetic field induction, primarily in power electrical engineering: in electricity generators, voltage transformers, in various electromagnetic drives of various devices, tools and mechanisms, in measuring technology and in science, in various physical installations for experiments, as well as in the means electrical protection and emergency shutdown.

Electric motors, generators and transformers

In 1824, the English physicist and mathematician Peter Barlow described the unipolar motor he invented, which became the prototype of modern electric motors. direct current. The invention is also valuable because it was made long before the discovery of the phenomenon of electromagnetic induction.

Nowadays, almost all electric motors use the Ampere force, which acts on a current-carrying circuit in a magnetic field, causing it to move.

Even Faraday, to demonstrate the phenomenon of magnetic induction in 1831, was created experimental setup, important part which was the device now known as the toroidal transformer. The principle of operation of the Faraday transformer is still used in all modern voltage and current transformers, regardless of power, design and scope.

In addition, Faraday scientifically substantiated and experimentally proved the possibility of converting mechanical movement into electricity using the unipolar DC generator he invented, which became the prototype of all DC generators.

First generator alternating current was created by the French inventor Hippolyte Pixie in 1832. Later, at the suggestion of Ampere, it was supplemented by a switching device, which made it possible to obtain a pulsating direct current.

Almost all electric power generators using the principle of magnetic induction are based on the occurrence of an electromotive force in a closed circuit, which is in a changing magnetic field. In this case, either the magnetic rotor rotates relative to the fixed stator coils in alternating current generators, or the rotor windings rotate relative to the fixed stator magnets (yoke) in DC generators.

The most powerful generator in the world, built in 2013 for the Taishan nuclear power plant by the Chinese company DongFang Electric, can generate a power of 1,750 MW.

In addition to conventional type generators and electric motors associated with the conversion mechanical energy in electrical energy and vice versa, there are so-called magnetohydrodynamic generators and engines operating on a different principle.

Relays and electromagnets

The electromagnet, invented by the American scientist J. Henry, became the first electric actuator and the forerunner of the familiar electric bell. Later, on its basis, Henry created an electromagnetic relay, which became the first automatic switching device with a binary state.

Shure dynamic microphone used in a video studio site

When transmitting a telegraph signal over long distances, relays were used as DC amplifiers, switching the connection of external batteries of intermediate stations for further signal transmission.

Dynamic heads and microphones

In modern audio technology, electromagnetic speakers are widely used, the sound in which appears due to the interaction of a moving coil attached to a diffuser through which current flows. audio frequency, with a magnetic field in the gap of a stationary permanent magnet. As a result, the coil together with the diffuser move and create sound waves.

Dynamic microphones use the same design as the dynamic head, but in a microphone, on the contrary, a moving coil with a mini-diffuser in the gap of a fixed permanent magnet oscillates under the influence of an acoustic signal and generates an electrical sound frequency signal.

Measuring instruments and sensors

Despite the abundance of modern digital measuring instruments, in measurement technology, devices of magnetoelectric, electromagnetic, electrodynamic, ferrodynamic and induction types are still used.

All systems of the above types use the principle of interaction of magnetic fields or a permanent magnet with the field of a coil with current, or a ferromagnetic core with fields of coils with current, or magnetic fields of coils with current.

Due to the relative inertia of such measurement systems, they are applicable for measuring the average values ​​of variables.