Magnetic induction

Magnetic induction is a vector quantity characterizing the strength and direction of the magnetic field at a point in space. You probably saw it in the pictures on the lessons of physics: turbulence in the form of planetary meridians converging to the poles of a red and blue horseshoe. The first images of the magnetic field were tried to be built in the 17th century. Apparently, using metal filings. The magnitude of the magnetic induction is determined by the parameters of the medium.

Magnetic field lines

Magnetic field and magnetism

Magnetic induction describes a field much more accurately than other methods. Entangled terms interfere with understanding. Induction is confused with tension. Both terms are vector, describe a field. Tension does not depend on the characteristics of the environment, differing in this. Magnetism has been known since ancient times. Scientists are powerless to pinpoint the date when the field of the Earth began to be used for navigation by sailors, historians have revealed the following curious facts:

  1. Olmec( an ancient Indian tribe) used magnetized needles in 1500 BC.There is no accurate evidence regarding the purpose of the structure. It is believed, using magnetism, the ancient people determined the direction.
  2. In China, the first written records refer to the II century BC.Magnetic needles were used for predictions on the nature of the terrain of the earth’s surface, for the purpose of arranging dwellings according to Feng Shui techniques.

Historical facts are called the first modern civilization, which began to practice navigation with orientation by the magnetic field of the Earth, China. X - XI century AD.The design is carefully ignored by written sources. We take the risk to assume that the compass repeated the achievements of the soothsayers:

  • The end of a metal needle is magnetized with iron.
  • The product is hung on a silk thread, wax acts as a fixer for the attachment point.

Devices made in this way look to the south, then to the north. Depending on the conditions of magnetization of the needle. Europe learned the compass a few centuries later. The first source describing the design of such devices, along with astrolabe, is a simple letter( 1269 AD), sketched by Petrus "Peregrinus"( Pilgrim) to a certain landowner in the days of the siege of the Italian Lucera. Apparently, the author's nickname indicates that the author is well acquainted with the topic. The astrolabe helped to determine the local time, in combination with the compass it became possible to calculate the geographical coordinates. Both devices simplified navigation( of course, priority is given to sea travel).

The Earth’s magnetic field has long been used by travelers to target the surface of the planet. Along with exotic devices: crystals, splitting sunlight and thus allowing to determine the location of the main star in the sky. The astrolabe added a stereographic projection( of a sphere onto a plane) of all bodies. Allowing to make calculations in the dark. It is enough to measure with alidade( arrow of the reverse side of the astrolabe) the elevation of the star above the horizon.

There was a minus: for each latitude it was necessary to make a map on the tympanum( rotating tab of the astrolabe case).A sailor, using the necessary disk, solved the problem at any latitude. Of course, I have to take care in advance to acquire the necessary tympanic cards. Otherwise, the measurements became inaccurate, incorrect. You see how many hardships the travelers had to endure, let us return to the magnetic field of the Earth. The phenomenon describes induction. It was rumored: Tesla used the knowledge of the magnitude of the magnetic field of the Earth, choosing the parameters of electrical devices. However, it smacks of fantasies, aliens from the stars, World War II.

Induction at the magnetic field of the Earth is present, everyone will find an electronic card, if there is a need. Magnetic poles do not coincide with the true. A magnetic induction map will have meridians that differ from spatial ones. At mid-latitudes, it does not prevent the navigators from navigating, using a compass.

The emergence of the concept of magnetic induction

At the dawn of the era of the development of electricity, people began to explore related phenomena. So, Hans Oersted discovered in 1819: a conductor with a current creates a circular magnetic field around, André-Marie Amper showed that if the direction of motion of the charges coincides, the adjacent conductors attract each other. An end to the controversy put the creation of the law of Bio-Savar( domestic sources add Laplace), describing the magnitude, direction of magnetic induction at a point in space. Sources admit of a clause regarding the research being conducted by direct current.

Interconnection of induction and magnetic field strength

Integration( see figure) follows a circuit with a current. In the formula, r implies the elementary midpoint of the current segment, r0 is the place of the space for which the magnetic induction is calculated. Note that in the denominator of the fraction for the integral two vectors are multiplied. The result is a value whose direction is determined by the rule of a gimlet( left or right hand).The integration is carried out over the contour element dr, r - the midpoint of the small cut of the full length. Identical differences in the numerator and denominator we reduce, remains at the top of the unit vector, which sets the direction of the result.

Formula shows how to find a field for contours of any shape, conducting integration by points. Modern numerical methods underlie the action of computer applications( like Maxwell 3D) to solve the corresponding problem. The equation is consistent with the laws of Gauss( magnetic induction) and Ampere( circulation of the magnetic field).Georg Ohm used knowledge of the compass, inferring a known dependency. The shape of the field lines will be obtained with the help of magnetic arrows and the force of leaving the direction unchanged( see the note about Ohm's law for the chain section).This will be a picture of magnetic induction in space, experimentally confirming the law of Bio-Savart-Laplace.

Allowed by Ampère in 1825 to show: electric current in some cases is an analogue of a permanent magnet. There was a new model that was more consistent with reality than the Poisson dipole scheme. Such an abstraction explained the absence of isolated magnetic poles in nature. According to modern concepts, a piece of steel is magnetized, because dipoles of elementary particles and molecules acquire orderliness. The demagnetization circuits of transformer cores are based on this, which, before turning off the power, cause damped current oscillations. As a result, the effect of order is blurred, the pronounced properties disappear.

Electron Spin

The presence of a magnetic moment is explained by the existence of spins( the concept introduced in the 1920s) - the angular momentum of the particles of the microworld. Real, not abstract things, existence is confirmed experimentally( Stern-Gerlach).Spin is a vector quantity that is the same for all particles of the same type( for example, electrons) and is described by a special quantum number. In SI, the unit of measurement is j s, as for the other angular momentum( Planck constant).Sometimes a simplified dimensionless recording is used. Constant Planck is lowered. The spin number is simply indicated( s, ms).

Due to the presence of a spin, an elementary particle acquires a magnetic moment calculated by the formula: in the numerator, the product of the spin angular momentum of the particle charge and the g-factor( constants given in various directories for certain elementary particles);in the denominator - double the mass of the elementary particle. As you can see, it can be counted, the maximum magnetization of the material under given conditions can be calculated in advance. The real triumph of quantum electrodynamics was the prediction of g-factors for some elementary particles.

The discovery by Michael Faraday in 1831 of the generation of a circular electric field by a circular electric field showed that two phenomena are closely related, which was a prerequisite for the creation of( four) Maxwell equations, a special case of which are the majority of formulas in this field, considering those mentioned above. Research went on as usual, but in slightly different ways. The integration was made by Lord Kelvin, known as William Thompson, who showed the presence of H( intensity) and B magnetic induction, the first characterizes the Poisson model, the second - Ampere.

B and H magnetic induction

Magnetic induction B is measured by Tesla( SI), T is equivalent to N s / Cl m. N is newton, unit of measurement of force;s is the second of time;CL - pendant, electric charge;m - meter distance. GHS for the same purpose applies gauss( G = √ g / s √ cm), g - gram of mass;s is the second of time;cm - centimeter distance. H magnetic induction is measured by amperes per meter( SI) or Oersteds( GHS).Russian-language literature refers to H field strength.

The Tesla unit was introduced in 1960 by the International Conference on Weights and Measures in Honor of the Deceased Nikola Tesla. In fact, since the beginning of the SI.How did scientists live before that? By 1948, the idea of ​​introducing the SI was born, the GHS already existed. The origins of the latter were laid in 1832 by Karl Friedrich Gauss, who was looking for a single basis for the branches of physics, so that it was easier to relate heterogeneous laws. The scientist asked three basic units: millimeter, milligram, second.

Gauss died shortly after introducing the concept of magnetic induction and dividing magnitude into B and H; however, in 1874, James Maxwell, Lord Kelvin supplemented the list with new quantities. Magnetic induction was named after the founder, at the same time the system was called the GHS( previously called Gaussian).As for SI, tesla can be represented in different ways through basic or derived units. Weber, per square meter.

. Repulsion of coils with current.

. In vacuum, two types of induction( H and B) are connected via constant currents. To distinguish one from the other, H is called the magnetic field intensity vector. It is clear that the meaning is not very different from B. In the formula:

  1. μ is the magnetic permeability of the medium.
  2. μ0 is the magnetic constant( vacuum permeability).In the system, the GHS is equal to 1, in vacuum, B and H are the same. The SI is 1.257 micronewton per square ampere.

Constants are specifically introduced to relate H and B - magnetic field characteristics. By the way, there are many versions why Lord Kelvin called vectors in this way( letters H and B).Those interested are encouraged to familiarize themselves with the following concepts: relative magnetic permeability( ratio of absolute μ to constant μ0), magnetic susceptibility( relative magnetic permeability increased by 1).It will help to better understand the formulas of literary sources, where the relationship between B and H is of another kind given in the review.

You can find many laws, formulas concerning magnetic induction, showing how important a parameter is in theory. It is not known to the authors whether Nikola Tesla used similar quantities when developing a multi-phase asynchronous motor, but it was not without reason that they gave the name to the great scientist!

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