What are magnetic field lines. Magnetic field: permanent and variable magnets
When connected to two parallel conductors of electric current, they will attract or repel, depending on the direction (polarity) of the connected current. This is explained by the appearance of a special kind of matter around these conductors. This matter is called the magnetic field (MF). Magnetic force is the force with which conductors act on each other.
The theory of magnetism arose in antiquity, in the ancient civilization of Asia. In Magnesia, in the mountains, they found a special rock, pieces of which could be attracted to each other. By the name of the place, this breed was called "magnets". A bar magnet contains two poles. Its magnetic properties are especially pronounced at the poles.
A magnet hanging on a thread will show the sides of the horizon with its poles. Its poles will be turned north and south. The compass works on this principle. Opposite poles of two magnets attract and like poles repel.
Scientists have found that a magnetized needle, located near the conductor, deviates when an electric current passes through it. This suggests that an MF is formed around it.
The magnetic field affects:
Moving electric charges.
Substances called ferromagnets: iron, cast iron, their alloys.
Permanent magnets are bodies that have a common magnetic moment of charged particles (electrons).
1 - South pole of the magnet
2 - North pole of the magnet
3 - MP on the example of metal filings
4 - Direction of the magnetic field
Field lines appear when approaching permanent magnet to a paper sheet on which a layer of iron filings is poured. The figure clearly shows the places of the poles with oriented lines of force.
Magnetic field sources
- Electric field that changes with time.
- mobile charges.
- permanent magnets.
We have known permanent magnets since childhood. They were used as toys that attracted various metal parts. They were attached to the refrigerator, they were built into various toys.
Electric charges that are in motion most often have more magnetic energy than permanent magnets.
Properties
- chief hallmark and the property of the magnetic field is relativity. If a charged body is left motionless in a certain frame of reference, and a magnetic needle is placed nearby, then it will point to the north, and at the same time it will not “feel” an extraneous field, except for the earth's field. And if the charged body begins to move near the arrow, then magnetic field will appear around the body. As a result, it becomes clear that the MF is formed only when a certain charge moves.
- The magnetic field is capable of influencing and influencing electricity. It can be detected by monitoring the movement of charged electrons. In a magnetic field, particles with a charge will deviate, conductors with a flowing current will move. The current-powered frame will rotate, and the magnetized materials will move a certain distance. The compass needle is most often painted in Blue colour. It is a strip of magnetized steel. The compass is always oriented to the north, since the Earth has a magnetic field. The whole planet is like a big magnet with its poles.
The magnetic field is not perceived by human organs, and can only be detected by special devices and sensors. It is variable and permanent. An alternating field is usually created by special inductors that operate on alternating current. The constant field is formed unchanged electric field.
Rules
Consider the basic rules for the image of a magnetic field for various conductors.
gimlet rule
The line of force is depicted in a plane, which is located at an angle of 90 0 to the current path so that at each point the force is directed tangentially to the line.
To determine the direction of magnetic forces, you need to remember the rule of a gimlet with a right-hand thread.
The gimlet must be positioned along the same axis as the current vector, the handle must be rotated so that the gimlet moves in the direction of its direction. In this case, the orientation of the lines is determined by turning the handle of the gimlet.
Ring Gimlet Rule
The translational movement of the gimlet in the conductor, made in the form of a ring, shows how the induction is oriented, the rotation coincides with the current flow.
The lines of force have their continuation inside the magnet and cannot be open.
A magnetic field different sources summed up with each other. In doing so, they create a common field.
Magnets with the same pole repel each other, while those with different poles attract. The value of the strength of interaction depends on the distance between them. As the poles approach, the force increases.
Magnetic field parameters
- Stream chaining ( Ψ ).
- Magnetic induction vector ( IN).
- magnetic flux (F).
The intensity of the magnetic field is calculated by the size of the magnetic induction vector, which depends on the force F, and is formed by the current I through a conductor having a length l: V \u003d F / (I * l).
Magnetic induction is measured in Tesla (Tl), in honor of the scientist who studied the phenomena of magnetism and dealt with their calculation methods. 1 T is equal to the induction of the magnetic flux by the force 1 N on length 1m straight conductor at an angle 90 0 to the direction of the field, with a flowing current of one ampere:
1 T = 1 x H / (A x m).
left hand rule
The rule finds the direction of the magnetic induction vector.
If the palm of the left hand is placed in the field so that the magnetic field lines enter the palm from the north pole at 90 0, and 4 fingers are placed along the current, thumb shows the direction of the magnetic force.
If the conductor is at a different angle, then the force will directly depend on the current and the projection of the conductor onto a plane at a right angle.
The force does not depend on the type of conductor material and its cross section. If there is no conductor, and the charges move in another medium, then the force will not change.
When the direction of the magnetic field vector in one direction of one magnitude, the field is called uniform. Different environments affect the size of the induction vector.
magnetic flux
Magnetic induction passing through a certain area S and limited by this area is a magnetic flux.
If the area has a slope at some angle α to the induction line, the magnetic flux is reduced by the size of the cosine of this angle. Its greatest value is formed when the area is at right angles to the magnetic induction:
F \u003d B * S.
Magnetic flux is measured in a unit such as "weber", which is equal to the flow of induction by the value 1 T by area in 1 m 2.
Flux linkage
This concept is used to create general meaning magnetic flux, which is created from a certain number of conductors located between the magnetic poles.
When the same current I flows through the winding with the number of turns n, the total magnetic flux formed by all the turns is the flux linkage.
Flux linkage Ψ measured in webers, and is equal to: Ψ = n * F.
Magnetic properties
Permeability determines how much the magnetic field in a particular medium is lower or higher than the field induction in a vacuum. A substance is said to be magnetized if it has its own magnetic field. When a substance is placed in a magnetic field, it becomes magnetized.
Scientists have determined the reason why bodies acquire magnetic properties. According to the hypothesis of scientists, there are electric currents of microscopic magnitude inside substances. An electron has its own magnetic moment, which has a quantum nature, moves along a certain orbit in atoms. It is these small currents that determine the magnetic properties.
If the currents move randomly, then the magnetic fields caused by them are self-compensating. The external field makes the currents ordered, so a magnetic field is formed. This is the magnetization of the substance.
Various substances can be divided according to the properties of interaction with magnetic fields.
They are divided into groups:
Paramagnets- substances that have magnetization properties in the direction external field having a low possibility of magnetism. They have a positive field strength. Such substances include ferric chloride, manganese, platinum, etc.
Ferrimagnets- substances with magnetic moments unbalanced in direction and value. They are characterized by the presence of uncompensated antiferromagnetism. Field strength and temperature affect their magnetic susceptibility (various oxides).
ferromagnets- substances with increased positive susceptibility, depending on the intensity and temperature (crystals of cobalt, nickel, etc.).
Diamagnets- have the property of magnetization in the opposite direction of the external field, that is, a negative value of magnetic susceptibility, independent of the intensity. In the absence of a field, this substance will not have magnetic properties. These substances include: silver, bismuth, nitrogen, zinc, hydrogen and other substances.
Antiferromagnets
- have a balanced magnetic moment, resulting in a low degree of magnetization of the substance. When heated, they undergo a phase transition of the substance, in which paramagnetic properties arise. When the temperature drops below a certain limit, such properties will not appear (chromium, manganese).
The considered magnets are also classified into two more categories:
Soft magnetic materials
. They have low coercive force. In weak magnetic fields, they can saturate. During the process of magnetization reversal, they have insignificant losses. As a result, such materials are used for the production of cores. electrical devices operating on alternating voltage ( , generator, ).
hard magnetic materials. They have an increased value of coercive force. To remagnetize them, a strong magnetic field is required. Such materials are used in the production of permanent magnets.
The magnetic properties of various substances find their use in technical designs and inventions.
Magnetic circuits
The combination of several magnetic substances is called a magnetic circuit. They are similarities and are determined by analogous laws of mathematics.
On the base magnetic circuits operate electrical devices, inductance, . In a functioning electromagnet, the flow flows through a magnetic circuit made of a ferromagnetic material and air, which is not a ferromagnet. The combination of these components is a magnetic circuit. Many electrical devices contain magnetic circuits in their design.
Let's understand together what a magnetic field is. After all, many people live in this field all their lives and do not even think about it. Time to fix it!
A magnetic field
A magnetic field is a special kind of matter. It manifests itself in the action on moving electric charges and bodies that have their own magnetic moment (permanent magnets).
Important: a magnetic field does not act on stationary charges! A magnetic field is also created by moving electric charges, or by a time-varying electric field, or by the magnetic moments of electrons in atoms. That is, any wire through which current flows also becomes a magnet!
A body that has its own magnetic field.
A magnet has poles called north and south. The designations "northern" and "southern" are given only for convenience (as "plus" and "minus" in electricity).
The magnetic field is represented by force magnetic lines. The lines of force are continuous and closed, and their direction always coincides with the direction of the field forces. If metal shavings are scattered around a permanent magnet, the metal particles will show a clear picture of the magnetic field lines emerging from the north and entering the south pole. Graphical characteristic of the magnetic field - lines of force.
Magnetic field characteristics
The main characteristics of the magnetic field are magnetic induction, magnetic flux And magnetic permeability. But let's talk about everything in order.
Immediately, we note that all units of measurement are given in the system SI.
Magnetic induction B - vector physical quantity, which is the main power characteristic of the magnetic field. Denoted by letter B . The unit of measurement of magnetic induction - Tesla (Tl).
Magnetic induction indicates how strong a field is by determining the force with which it acts on a charge. Given power called Lorentz force.
Here q - charge, v - its speed in a magnetic field, B - induction, F is the Lorentz force with which the field acts on the charge.
F- physical quantity, equal to the product magnetic induction on the area of the contour and the cosine between the induction vector and the normal to the plane of the contour through which the flow passes. Magnetic flux is a scalar characteristic of a magnetic field.
We can say that the magnetic flux characterizes the number of magnetic induction lines penetrating a unit area. The magnetic flux is measured in Weberach (WB).
Magnetic permeability is the coefficient that determines the magnetic properties of the medium. One of the parameters on which the magnetic induction of the field depends is the magnetic permeability.
Our planet has been a huge magnet for several billion years. The induction of the Earth's magnetic field varies depending on the coordinates. At the equator, it is about 3.1 times 10 to the minus fifth power of Tesla. In addition, there are magnetic anomalies, where the value and direction of the field differ significantly from neighboring areas. One of the largest magnetic anomalies on the planet - Kursk And Brazilian magnetic anomaly.
The origin of the Earth's magnetic field is still a mystery to scientists. It is assumed that the source of the field is the liquid metal core of the Earth. The core is moving, which means that the molten iron-nickel alloy is moving, and the movement of charged particles is the electric current that generates the magnetic field. The problem is that this theory geodynamo) does not explain how the field is kept stable.
The earth is a huge magnetic dipole. The magnetic poles do not coincide with the geographic ones, although they are in close proximity. Moreover, the Earth's magnetic poles are moving. Their displacement has been recorded since 1885. For example, over the past hundred years, the magnetic pole in the Southern Hemisphere has shifted by almost 900 kilometers and is now in the Southern Ocean. The pole of the Arctic hemisphere is moving across the Arctic Ocean towards the East Siberian magnetic anomaly, the speed of its movement (according to 2004 data) was about 60 kilometers per year. Now there is an acceleration of the movement of the poles - on average, the speed is growing by 3 kilometers per year.
What is the significance of the Earth's magnetic field for us? First of all, the Earth's magnetic field protects the planet from cosmic rays and the solar wind. Charged particles from deep space do not fall directly to the ground, but are deflected by a giant magnet and move along its lines of force. Thus, all living things are protected from harmful radiation.
During the history of the Earth, there have been several inversions(changes) of magnetic poles. Pole inversion is when they change places. The last time this phenomenon occurred about 800 thousand years ago, and there were more than 400 geomagnetic reversals in the history of the Earth. Some scientists believe that, given the observed acceleration of the movement of the magnetic poles, the next pole reversal should be expected in the next couple of thousand years.
Fortunately, no reversal of poles is expected in our century. So, you can think about the pleasant and enjoy life in the good old constant field of the Earth, having considered the main properties and characteristics of the magnetic field. And so that you can do this, there are our authors, who can be entrusted with some of the educational troubles with confidence in success! and other types of work you can order at the link.
1. The description of the properties of a magnetic field, as well as an electric field, is often greatly facilitated by introducing into consideration the so-called lines of force of this field. By definition, magnetic field lines are lines, the direction of the tangents to which at each point of the field coincides with the direction of the field strength at the same point. The differential equation of these lines will obviously have the form equation (10.3)]
Magnetic lines of force, like electric lines, are usually drawn in such a way that in any section of the field the number of lines crossing the area of \u200b\u200bthe unit surface perpendicular to them is, if possible, proportional to the field strength on this area; however, as we shall see below, this requirement is by no means always feasible.
2 Based on equation (3.6)
we came to the following conclusion in § 10: electric lines of force can begin or end only at those points in the field at which electric charges are located. Applying the Gauss theorem (17) to the magnetic vector flux, we obtain on the basis of equation (47.1)
Thus, in contrast to the flow of an electric vector, the flow of a magnetic vector through an arbitrary closed surface is always zero. This position is a mathematical expression of the fact that there are no magnetic charges similar to electric charges: the magnetic field is excited not by magnetic charges, but by the movement of electric charges (ie, currents). Based on this position and on comparing equation (53.2) with equation (3.6), it is easy to verify, by the reasoning given in § 10, that the magnetic lines of force at any point in the field can neither begin nor end
3. From this circumstance, it is usually concluded that magnetic lines of force, unlike electric lines, must be closed lines or go from infinity to infinity.
Indeed, both of these cases are possible. According to the results of solving problem 25 in § 42, the lines of force in the field of an infinite rectilinear current are circles perpendicular to the current and centered on the current axis. On the other hand (see Problem 26), the direction of the magnetic vector in the field of a circular current at all points lying on the axis of the current coincides with the direction of this axis. Thus, the axis of the circular current coincides with the line of force going from infinity to infinity; the drawing shown in fig. 53, is a section of the circular current by the meridional plane (i.e., the plane
perpendicular to the plane of the current and passing through its center), on which the dashed lines show the lines of force of this current
However, a third case is also possible, to which attention is not always drawn, namely: a line of force may have neither beginning nor end and at the same time not be closed and not go from infinity to infinity. This case takes place if the line of force fills a certain surface and, moreover, using a mathematical term, fills it densely everywhere. The easiest way to explain this is with a specific example.
4. Consider the field of two currents - a circular flat current and an infinite rectilinear current flowing along the current axis (Fig. 54). If there were only one current, then the field lines of the field of this current would lie in meridional planes and would have the form shown in the previous figure. Consider one of these lines shown in Fig. 54 dashed line. The set of all lines similar to it, which can be obtained by rotating the meridional plane around the axis, forms the surface of a certain ring or torus (Fig. 55).
The lines of force of the rectilinear current field are concentric circles. Therefore, at each point of the surface, both and are tangent to this surface; therefore, the intensity vector of the resulting field is also tangent to it. This means that each line of force of the field passing through any one point of the surface must lie on this surface with all its points. This line will obviously be a helix on
the surface of the torus The course of this helix will depend on the ratio of the strength of the currents and on the position and shape of the surface. It is obvious that only under certain specific selection of these conditions will this helix be closed; Generally speaking, when the line is continued, new turns of it will lie between the previous turns. When the line is continued indefinitely, it will come as close as it likes to any point it has passed, but it will never return to it a second time. And this means that, while remaining open, this line will densely fill the surface of the torus everywhere.
5. To strictly prove the possibility of the existence of non-closed lines of force, we introduce orthogonal curvilinear coordinates on the surface of the torus y (azimuth of the meridional plane) and (polar angle in the meridional plane with the vertex located at the intersection of this plane with the axis of the ring - Fig. 54).
The field strength on the surface of the torus is a function of only one angle, and the vector is directed in the direction of increase (or decrease) of this angle, and the vector is in the direction of increase (or decrease) of the angle. Let be the distance of a given point of the surface from central line torus, its distance from the vertical axis of the current As it is easy to see, the element of the length of the line lying on is expressed by the formula
Accordingly, the differential equation of the lines of forces [cf. equation (53.1)] on the surface takes the form
Taking into account that they are proportional to the strength of the currents and integrating, we obtain
where is some angle function independent of .
For the line to be closed, i.e., for it to return to the starting point, it is necessary that a certain integer number of revolutions of the line around the torus correspond to an integer number of its revolutions around the vertical axis. In other words, it is necessary that it be possible to find two such integers n, so that an increase in the angle by corresponds to an increase in the angle by
Let us now take into account what the integral of the periodic function of the angle with period is. As is known, the integral
of a periodic function in the general case is the sum of a periodic function and a linear function. Means,
where K is some constant, there is a function with a period Therefore,
Introducing this into the previous equation, we obtain the condition for the closure of the lines of force on the surface of the torus
Here K is a quantity independent of. It is obvious that two integers of heels satisfying this condition can be found only if the value - K is a rational number (integer or fractional); this will take place only for a certain ratio between the forces of the currents. Generally speaking, - K will be an irrational quantity and, therefore, the lines of force on the surface of the torus under consideration will be open. However, in this case, you can always choose an integer so that - arbitrarily little differs from some integer. This means that an open line of force, after a sufficient number of revolutions, will come as close as you like to any point of the field once passed. In a similar way, it can be shown that this line, after a sufficient number of revolutions, will come as close as desired to any forward given point surface, which means by definition that it densely fills this surface everywhere.
6. The existence of non-closed magnetic lines of force densely filling a certain surface everywhere obviously makes it impossible to accurately graphic image fields with these lines. In particular, it is far from always possible to satisfy the requirement that the number of lines crossing a unit area perpendicular to them be proportional to the field strength on this area. So, for example, in the case just considered, the same open line intersects an infinite number of times any finite area that intersects the surface of the ring
However, with due diligence, the use of the concept of lines of force is, although approximate, but still a convenient and illustrative way of describing a magnetic field.
7. According to equation (47.5), the circulation of the magnetic field vector along the curve that does not cover currents is equal to zero, while the circulation along the curve that covers currents is equal to the sum of the strengths of the covered currents (taken with proper signs). The circulation of the vector along the field line cannot be equal to zero (due to the parallelism of the length element of the field line and the vector, the value is essentially positive). Therefore, each closed magnetic field line must cover at least one of the current-carrying conductors. Moreover, open lines of force that densely fill some surface (unless they go from infinity to infinity) must also wind around currents. Indeed, the vector integral over an almost closed turn of such a line is essentially positive. Therefore, the circulation along the closed contour obtained from this coil by adding an arbitrarily small segment closing it is nonzero. Therefore, this circuit must be pierced by current.
Magnetic field lines
Magnetic fields, like electric fields, can be represented graphically using lines of force. A magnetic field line, or a magnetic field induction line, is a line, the tangent to which at each point coincides with the direction of the magnetic field induction vector.
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| A) | b) | V) |
Rice. 1.2. Lines of force of the direct current magnetic field (a),
circular current (b), solenoid (c)
Magnetic lines of force, like electric lines, do not intersect. They are drawn with such density that the number of lines crossing a unit surface perpendicular to them is equal to (or proportional to) the magnitude of the magnetic induction of the magnetic field at a given location.
On fig. 1.2 A the field lines of the direct current field are shown, which are concentric circles, the center of which is located on the current axis, and the direction is determined by the rule of the right screw (the current in the conductor is directed to the reader).
Lines of magnetic induction can be "showed" using iron filings that are magnetized in the field under study and behave like small magnetic needles. On fig. 1.2 b shows the lines of force of the magnetic field of the circular current. The magnetic field of the solenoid is shown in fig. 1.2 V.
The lines of force of the magnetic field are closed. Fields with closed lines of force are called vortex fields. Obviously, the magnetic field is a vortex field. This is the essential difference between a magnetic field and an electrostatic one.
In an electrostatic field, the lines of force are always open: they begin and end at electric charges. Magnetic lines of force have neither beginning nor end. This corresponds to the fact that there are no magnetic charges in nature.
1.4. Biot-Savart-Laplace law
The French physicists J. Biot and F. Savard conducted in 1820 a study of magnetic fields created by currents flowing along thin wires various shapes. Laplace analyzed the experimental data obtained by Biot and Savart and established a relationship that was called the Biot–Savart–Laplace law.
According to this law, the induction of a magnetic field of any current can be calculated as a vector sum (superposition) of the inductions of magnetic fields created by individual elementary sections of the current. For magnetic field induction, generated by the element current length , Laplace obtained the formula:
, (1.3)
where is a vector, modulo equal to the length of the conductor element and coinciding in direction with the current (Fig. 1.3); is the radius vector drawn from the element to the point where ; is the modulus of the radius vector .
Approximately two and a half thousand years ago, people discovered that some natural stones have the ability to attract iron. This property was explained by the presence of a living soul in these stones, and a certain “love” for iron.
Today we already know that these stones are natural magnets, and the magnetic field, and not at all a special location to iron, creates these effects. A magnetic field is a special kind of matter that differs from matter and exists around magnetized bodies.
permanent magnets
Natural magnets, or magnetites, are not very strong magnetic properties. But man has learned to create artificial magnets that have a much greater strength of the magnetic field. They are made of special alloys and magnetized by an external magnetic field. After that, you can use them on your own.
Magnetic field lines
Any magnet has two poles, they are called north and south poles. At the poles, the concentration of the magnetic field is maximum. But between the poles, the magnetic field is also located not arbitrarily, but in the form of stripes or lines. They are called magnetic field lines. Detecting them is quite simple - just place scattered iron filings in a magnetic field and shake them slightly. They will not be located arbitrarily, but form, as it were, a pattern of lines starting at one pole and ending at the other. These lines, as it were, come out of one pole and enter the other.
Iron filings in the field of the magnet themselves are magnetized and placed along the magnetic lines of force. This is how the compass works. Our planet is a big magnet. The compass needle picks up the Earth's magnetic field and, turning, is located along the lines of force, with one end pointing to the north magnetic pole, the other to the south. Earth's magnetic poles are a little off geographic, but when traveling away from the poles, this doesn't of great importance, and we can consider them to be identical.
Variable magnets
The scope of magnets in our time is extremely wide. They can be found inside electric motors, telephones, speakers, radios. Even in medicine, for example, when a person swallows a needle or other iron object, it can be taken out without operation by a magnetic probe.
