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) | in) |
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 in a given place.
On fig. 1.2 a the lines of force 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 in.
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 on 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
French physicists J. Biot and F. Savard conducted in 1820 a study of magnetic fields created by currents flowing through thin wires of 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 the 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 the magnetic induction of the field created by a current element with a 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 .
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. This force is 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- a physical quantity equal to the product of magnetic induction by 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.
Magnetic field, what is it? - a special kind of matter;
Where does it exist? - around moving electric charges (including around a current-carrying conductor)
How to discover? - using a magnetic needle (or iron filings) or by its action on a current-carrying conductor.
Oersted's experience:
The magnetic needle turns if electricity begins to flow through the conductor. current, because A magnetic field is formed around a current-carrying conductor.
Interaction of two conductors with current:
Each current-carrying conductor has its own magnetic field around it, which acts with some force on the adjacent conductor.
Depending on the direction of currents, conductors can attract or repel each other.
Think back to last school year:
MAGNETIC LINES (or otherwise lines of magnetic induction)
How to depict a magnetic field? - with the help of magnetic lines;
Magnetic lines, what is it?
These are imaginary lines along which magnetic needles are placed in a magnetic field. Magnetic lines can be drawn through any point of the magnetic field, they have a direction and are always closed.
Think back to last school year:
INHOMOGENEOUS MAGNETIC FIELD
Characteristics of an inhomogeneous magnetic field: the magnetic lines are curved; the density of the magnetic lines is different; the force with which the magnetic field acts on the magnetic needle is different at different points of this field in magnitude and direction.
Where does an inhomogeneous magnetic field exist?
Around a straight current-carrying conductor;
Around the bar magnet;
Around the solenoid (coils with current).
HOMOGENEOUS MAGNETIC FIELD
Characteristics of a homogeneous magnetic field: magnetic lines are parallel straight lines; the density of magnetic lines is the same everywhere; the force with which the magnetic field acts on the magnetic needle is the same at all points of this field in magnitude direction.
Where does a uniform magnetic field exist?
- inside the bar magnet and inside the solenoid, if its length is much greater than the diameter.
INTERESTING
The ability of iron and its alloys to be highly magnetized disappears when heated to a high temperature. Pure iron loses this ability when heated to 767 ° C.
The powerful magnets used in many modern products can interfere with pacemakers and implanted heart devices in cardiac patients. Ordinary iron or ferrite magnets, which are easily distinguished by their dull gray coloration, have little strength and are of little concern.
However, very strong magnets have recently appeared - brilliant silver in color and representing an alloy of neodymium, iron and boron. The magnetic field they create is very strong, which is why they are widely used in computer disks, headphones and speakers, as well as in toys, jewelry and even clothing.
Once on the roads of the main city of Mallorca, the French military ship "La Rolain" appeared. His condition was so miserable that the ship barely reached the berth on its own. When French scientists, including twenty-two-year-old Arago, boarded the ship, it turned out that the ship was destroyed by lightning. While the commission was inspecting the ship, shaking their heads at the sight of the burnt masts and superstructures, Arago hurried to the compasses and saw what he expected: the compass needles pointed in different directions ...
A year later, digging through the remains of a Genoese ship that had crashed near Algiers, Arago discovered that the compass needles had been demagnetized. . The ship was heading south towards the rocks, deceived by a lightning-struck magnetic compass.
V. Kartsev. Magnet for three millennia.
The magnetic compass was invented in China.
As early as 4,000 years ago, caravaners took an earthen pot with them and "took care of it on the way more than all their expensive cargoes." In it, on the surface of the liquid on a wooden float, lay a stone that loves iron. He could turn and, all the time, pointed to the travelers in the direction of the south, which, in the absence of the Sun, helped them go to the wells.
At the beginning of our era, the Chinese learned how to make artificial magnets by magnetizing an iron needle.
And only a thousand years later, Europeans began to use a magnetized compass needle.
EARTH'S MAGNETIC FIELD
The earth is a large permanent magnet.
The South Magnetic Pole, although located, by earthly standards, near the North Geographic Pole, they are nevertheless separated by about 2000 km.
There are territories on the surface of the Earth where its own magnetic field is strongly distorted by the magnetic field of iron ores occurring at a shallow depth. One of these territories is the Kursk magnetic anomaly located in the Kursk region.
The magnetic induction of the Earth's magnetic field is only about 0.0004 Tesla.
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The Earth's magnetic field is affected by increased solar activity. Approximately once every 11.5 years, it increases so much that radio communication is disrupted, the well-being of people and animals worsens, and the compass needles begin to “dance” unpredictably from side to side. In this case, they say that a magnetic storm is coming. It usually lasts from several hours to several days.
The Earth's magnetic field changes its orientation from time to time, making both secular fluctuations (lasting 5–10 thousand years) and completely reorienting, i.e. reversing magnetic poles (2–3 times per million years). This is indicated by the magnetic field of distant epochs "frozen" in sedimentary and volcanic rocks. The behavior of the geomagnetic field cannot be called chaotic, it obeys a kind of "schedule".
The direction and magnitude of the geomagnetic field are determined by the processes taking place in the Earth's core. The characteristic polarity reversal time determined by the inner solid core is from 3 to 5 thousand years, and determined by the outer liquid core is about 500 years. These times can explain the observed dynamics of the geomagnetic field. Computer modeling, taking into account various intraterrestrial processes, has shown the possibility of a polarity reversal of the magnetic field in about 5 thousand years.
FOCUSES WITH MAGNETS
The "temple of charms, or the mechanical, optical and physical cabinet of Mr. Gamuletsky de Coll" by the famous Russian illusionist Gamuletsky, which existed until 1842, became famous, among other things, for the fact that visitors climbing the stairs decorated with candelabra and carpeted with carpets could still notice from afar at the top of the stairs, a gilded figure of an angel, made in natural human growth, which hovered in a horizontal position above the office door without being suspended or supported. Everyone could make sure that the figure did not have any supports. When visitors entered the platform, the angel raised his hand, brought the horn to his mouth and played it, moving his fingers in the most natural way. For ten years, Gamuletsky said, I have been laboring to find the point and weight of the magnet and iron in order to keep the angel in the air. In addition to labor, I used a lot of money for this miracle.
In the Middle Ages, the so-called "obedient fish", made of wood, were a very common illusion number. They swam in the pool and obeyed the slightest wave of the magician's hand, which made them move in all sorts of directions. The secret of the trick was extremely simple: a magnet was hidden in the sleeve of the magician, and pieces of iron were inserted into the heads of the fish.
Closer to us in time were the manipulations of the Englishman Jonas. His signature number: Jonas invited some viewers to put the clock on the table, after which he, without touching the clock, arbitrarily changed the position of the hands.
The modern embodiment of such an idea is electromagnetic clutches, well known to electricians, with the help of which it is possible to rotate devices separated from the engine by some kind of obstacle, for example, a wall.
In the mid-80s of the 19th century, a rumor swept about the scientist elephant, who could not only add and subtract, but even multiply, divide and extract roots. This was done in the following way. The trainer, for example, asked the elephant: "What is seven eight?" There was a board with numbers in front of the elephant. After the question, the elephant took the pointer and confidently showed the number 56. In the same way, division and extraction of the square root were carried out. The trick was simple enough: there was a small electromagnet hidden under each number on the board. When the elephant was asked a question, a current was applied to the winding of a magnet located meaning the correct answer. The iron pointer in the elephant's trunk was itself attracted to the correct number. The answer came automatically. Despite the simplicity of this training, the secret of the trick could not be unraveled for a long time, and the "learned elephant" enjoyed tremendous success.
Already in the VI century. BC. in China, it was known that some ores had the ability to attract each other and attract iron objects. Pieces of such ores were found near the city of Magnesia in Asia Minor, so they got the name magnets.
What is the interaction between a magnet and iron objects? Recall why electrified bodies are attracted? Because a peculiar form of matter is formed near an electric charge - an electric field. Around the magnet there is a similar form of matter, but it has a different nature of origin (after all, the ore is electrically neutral), it is called magnetic field.
To study the magnetic field, straight or horseshoe-shaped magnets are used. Certain places of the magnet have the greatest attractive effect, they are called poles(North and South). Opposite magnetic poles attract, and like poles repel.
For the power characteristic of the magnetic field, use magnetic field induction vector B. The magnetic field is graphically depicted using lines of force ( lines of magnetic induction). Lines are closed, have neither beginning nor end. The place from which the magnetic lines come out is the North Pole (North), the magnetic lines enter the South Pole (South).
The magnetic field can be made "visible" with iron filings.
The magnetic field of a current-carrying conductor
And now what we found Hans Christian Oersted and André Marie Ampère in 1820. It turns out that a magnetic field exists not only around a magnet, but also around any conductor with current. Any wire, for example, the cord from a lamp, through which an electric current flows, is a magnet! A wire with current interacts with a magnet (try to bring a compass to it), two wires with current interact with each other.
The lines of force of the direct current magnetic field are circles around the conductor.
Direction of the magnetic induction vector
The direction of the magnetic field at a given point can be defined as the direction that indicates the north pole of a compass needle placed at that point.
The direction of the lines of magnetic induction depends on the direction of the current in the conductor.
The direction of the induction vector is determined by the rule gimlet or rule right hand.
Magnetic induction vector
This is a vector quantity that characterizes the force action of the field.
Induction of the magnetic field of an infinite rectilinear conductor with current at a distance r from it:
Magnetic field induction at the center of a thin circular coil of radius r:
Magnetic field induction solenoid(a coil whose turns are energized in series in one direction):
Superposition principle
If the magnetic field at a given point in space is created by several sources of the field, then the magnetic induction is the vector sum of the inductions of each of the fields separately
The Earth is not only a large negative charge and a source of an electric field, but at the same time, the magnetic field of our planet is similar to the field of a giant direct magnet.
Geographic south is close to magnetic north, and geographic north is close to magnetic south. If the compass is placed in the Earth's magnetic field, then its north arrow is oriented along the lines of magnetic induction in the direction of the south magnetic pole, that is, it will tell us where the geographic north is located.
The characteristic elements of terrestrial magnetism change very slowly over time - secular changes. However, magnetic storms occur from time to time, when the Earth's magnetic field is strongly distorted for several hours, and then gradually returns to its previous values. Such a drastic change affects people's well-being.
The Earth's magnetic field is a "shield" covering our planet from particles penetrating from outer space ("solar wind"). Near the magnetic poles, particle flows come much closer to the Earth's surface. During powerful solar flares, the magnetosphere is deformed, and these particles can pass into the upper layers of the atmosphere, where they collide with gas molecules, forming auroras.
Particles of iron dioxide on a magnetic film are well magnetized during the recording process.
The maglev trains glide over the surface with absolutely no friction. The train is capable of speeds up to 650 km/h.
The work of the brain, the pulsation of the heart is accompanied by electrical impulses. In this case, a weak magnetic field arises in the organs.
A magnetic field - power field , acting on moving electric charges and on bodies with magnetic moment, regardless of the state of their movement;magnetic component of the electromagnetic fields .
The magnetic field lines are imaginary lines, the tangents to which at each point of the field coincide in direction with the magnetic induction vector.
For a magnetic field, the principle of superposition is valid: at each point in space, the vector of magnetic induction B∑ → B∑→created at this point by all sources of magnetic fields is equal to the vector sum of the magnetic induction vectors bk→ Bk→created at this point by all sources of magnetic fields:
28. Law of Biot-Savart-Laplace. Full current law.
The formulation of Biot Savart Laplace's law is as follows: When a direct current passes through a closed circuit in vacuum, for a point at a distance r0 from the circuit, the magnetic induction will have the form.
where I current in the circuit
gamma contour along which the integration is carried out
r0 arbitrary point
Full current law this is the law relating the circulation of the magnetic field strength vector and the current.
The circulation of the magnetic field strength vector along the circuit is equal to the algebraic sum of the currents covered by this circuit.
29. Magnetic field of a conductor with current. Magnetic moment of circular current.
30. The action of a magnetic field on a conductor with current. Ampere's law. Interaction of currents .
F = B I l sinα ,
where α - the angle between the vectors of magnetic induction and current,B - magnetic field induction,I - current in the conductor,l - conductor length.
Interaction of currents. If two wires are included in the DC circuit, then: Closely spaced parallel conductors connected in series repel each other. Conductors connected in parallel attract each other.
31. Action of electric and magnetic fields on a moving charge. Lorentz force.
Lorentz force - strength, with which electromagnetic field according to the classical (non-quantum) electrodynamics acts on point charged particle. Sometimes the Lorentz force is called the force acting on a moving with a speed charge only from the side magnetic field, often the full force - from the electromagnetic field in general , in other words, from the side electric and magnetic fields.
32. The action of a magnetic field on matter. Dia-, para- and ferromagnets. Magnetic hysteresis.
B= B 0 + B 1
where B⃗ B → - magnetic field induction in matter; B⃗ 0 B→0 - magnetic field induction in vacuum, B⃗ 1 B→1 - magnetic induction of the field that arose due to the magnetization of the substance.
Substances for which the magnetic permeability is slightly less than unity (μ< 1), называются diamagnets, slightly greater than one (μ > 1) - paramagnets.
ferromagnet - the substance or material in which the phenomenon is observed ferromagnetism, i.e., the appearance of spontaneous magnetization at a temperature below the Curie temperature.
Magnetic hysteresis - phenomenon dependencies vector magnetization and vector magnetic fields in substance not only from attached external fields, but and from background this sample
