EntranceA magnetic field. Properties of magnetic field
If you bring the magnetic needle close, it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the needle. This indicates that special forces act on the arrow, which are called magnetic forces. In addition to the effect on the magnetic needle, the magnetic field affects moving charged particles and current-carrying conductors located in the magnetic field. In conductors moving in a magnetic field, or in stationary conductors located in an alternating magnetic field, inductive (emf) occurs.
A magnetic field
In accordance with the above, we can give the following definition of a magnetic field.
A magnetic field is one of the two sides of the electromagnetic field, excited by the electric charges of moving particles and changes in the electric field and characterized by a force effect on moving infected particles, and therefore on electric currents.
If you pass a thick conductor through the cardboard and pass it along it, then the steel filings poured onto the cardboard will be located around the conductor in concentric circles, which in this case are the so-called magnetic induction lines (Figure 1). We can move the cardboard up or down the conductor, but the location of the sawdust will not change. Consequently, a magnetic field arises around the conductor along its entire length.
If you put small magnetic arrows on the cardboard, then by changing the direction of the current in the conductor, you can see that the magnetic arrows will rotate (Figure 2). This shows that the direction of magnetic induction lines changes with the direction of current in the conductor.
Magnetic induction lines around a current-carrying conductor have the following properties: 1) magnetic induction lines of a straight conductor have the shape of concentric circles; 2) the closer to the conductor, the denser the magnetic induction lines are located; 3) magnetic induction (field intensity) depends on the magnitude of the current in the conductor; 4) the direction of magnetic induction lines depends on the direction of the current in the conductor.
To show the direction of the current in the conductor shown in section, a symbol has been adopted, which we will use in the future. If you mentally place an arrow in the conductor in the direction of the current (Figure 3), then in the conductor in which the current is directed away from us, we will see the tail of the arrow’s feathers (a cross); if the current is directed towards us, we will see the tip of an arrow (point).
Figure 3. Symbol for the direction of current in conductors
The gimlet rule allows you to determine the direction of magnetic induction lines around a current-carrying conductor. If a gimlet (corkscrew) with a right-hand thread moves forward in the direction of the current, then the direction of rotation of the handle will coincide with the direction of the magnetic induction lines around the conductor (Figure 4).
A magnetic needle introduced into the magnetic field of a current-carrying conductor is located along the magnetic induction lines. Therefore, to determine its location, you can also use the “gimlet rule” (Figure 5). The magnetic field is one of the most important manifestations of electric current and cannot be obtained independently and separately from the current.
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| Figure 4. Determining the direction of magnetic induction lines around a current-carrying conductor using the “gimlet rule” | Figure 5. Determining the direction of deviation of a magnetic needle brought to a conductor with current, according to the “gimlet rule” |
A magnetic field is characterized by a magnetic induction vector, which therefore has a certain magnitude and a certain direction in space.
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| Figure 6. To Biot and Savart's law |
A quantitative expression for magnetic induction as a result of generalization of experimental data was established by Biot and Savart (Figure 6). Measuring the magnetic fields of electric currents of various sizes and shapes by the deflection of the magnetic needle, both scientists came to the conclusion that every current element creates a magnetic field at some distance from itself, the magnetic induction of which is Δ B is directly proportional to the length Δ l this element, the magnitude of the flowing current I, the sine of the angle α between the direction of the current and the radius vector connecting the field point of interest to us with a given current element, and is inversely proportional to the square of the length of this radius vector r:
Where K– coefficient depending on the magnetic properties of the medium and on the chosen system of units.
In the absolute practical rationalized system of units of ICSA
where µ 0 – magnetic permeability of vacuum or magnetic constant in the MCSA system:
µ 0 = 4 × π × 10 -7 (henry/meter);
Henry (gn) – unit of inductance; 1 gn = 1 ohm × sec.
µ – relative magnetic permeability– a dimensionless coefficient showing how many times the magnetic permeability of a given material is greater than the magnetic permeability of vacuum.
The dimension of magnetic induction can be found using the formula
Volt-second is also called Weber (wb):
In practice, there is a smaller unit of magnetic induction - gauss (gs):
Biot-Savart's law allows us to calculate the magnetic induction of an infinitely long straight conductor:
Where A– the distance from the conductor to the point where the magnetic induction is determined.
Magnetic field strength
The ratio of magnetic induction to the product of magnetic permeabilities µ × µ 0 is called magnetic field strength and is designated by the letter H:
B = H × µ × µ 0 .
The last equation connects two magnetic quantities: induction and magnetic field strength.
Let's find the dimension H:
Sometimes another unit of measurement of magnetic field strength is used - Oersted (er):
1 er = 79,6 A/m ≈ 80 A/m ≈ 0,8 A/cm .
Magnetic field strength H, like magnetic induction B, is a vector quantity.
A line tangent to each point of which coincides with the direction of the magnetic induction vector is called magnetic induction line or magnetic induction line.
Magnetic flux
The product of magnetic induction by the area perpendicular to the direction of the field (magnetic induction vector) is called flux of the magnetic induction vector or simply magnetic flux and is designated by the letter F:
F = B × S .
Magnetic flux dimension:
that is, magnetic flux is measured in volt-seconds or webers.
The smaller unit of magnetic flux is Maxwell (mks):
1 wb = 108 mks.
1mks = 1 gs× 1 cm 2.
Video 1. Ampere's hypothesis
Video 2. Magnetism and electromagnetism
Magnetic field, what is it? - a special type of matter;
Where does it exist? - around moving electric charges (including around a conductor carrying current)
How to detect? - 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 conductor carrying current.
Interaction of two conductors with current:
Each current-carrying conductor has its own magnetic field around itself, which acts with some force on the neighboring conductor.
Depending on the direction of currents, conductors can attract or repel each other.
Remember last school year:
MAGNETIC LINES (or otherwise magnetic induction lines)
How to depict a magnetic field? - using magnetic lines;
Magnetic lines, what are they?
These are imaginary lines along which magnetic needles placed in a magnetic field are located. Magnetic lines can be drawn through any point in the magnetic field, they have a direction and are always closed.
Remember last school year:
INHOMOGENEOUS MAGNETIC FIELD
Characteristics of a non-uniform magnetic field: magnetic lines are curved; the density of 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 a non-uniform magnetic field exist?
Around a straight conductor carrying current;
Around the strip magnet;
Around the solenoid (coil with current).
HOMOGENEOUS MAGNETIC FIELD
Characteristics of a uniform 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 and direction.
Where does a uniform magnetic field exist?
- inside a strip magnet and inside a solenoid, if its length is much greater than its diameter.
INTERESTING
The ability of iron and its alloys to be strongly magnetized disappears when heated to high temperatures. Pure iron loses this ability when heated to 767 °C.
The powerful magnets used in many modern products can interfere with the performance of pacemakers and implanted cardiac devices in cardiac patients. Regular iron or ferrite magnets, easily identified by their dull gray color, are low in strength and cause little to no trouble.
However, very strong magnets have recently appeared - shiny silver in color and an alloy of neodymium, iron and boron. The magnetic field they create is very strong, making them widely used in computer disks, headphones and speakers, as well as toys, jewelry and even clothing.
One day, in the roadstead of the main city of Mallorca, the French warship La Rolaine appeared. Its condition was so pitiful that the ship barely reached the pier under its own power. 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 examined 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 arrows were pointing in different directions...
A year later, while digging through the remains of a Genoese ship that crashed near Algeria, Arago discovered that the compass needles were demagnetized. In the pitch darkness of a foggy night, the captain, having directed the ship north on the compass, away from dangerous places, was in fact uncontrollably heading towards what he was trying so hard to avoid . The ship sailed south toward the rocks, deceived by the lightning-struck magnetic compass.
V. Kartsev. Magnet for three millennia.
The magnetic compass was invented in China.
Already 4,000 years ago, caravan riders took a clay pot with them and “took care of it on the road more than all their expensive cargo.” 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 travelers towards the south, which, in the absence of the Sun, helped them go to the wells.
At the beginning of our era, the Chinese learned 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, close to the North Geographic Pole, is nevertheless separated by about 2000 km.
There are areas on the Earth's surface where its own magnetic field is strongly distorted by the magnetic field of iron ores located at shallow depths. One of such 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. About once every 11.5 years it increases so much that radio communications are disrupted, the well-being of people and animals worsens, and compass needles begin to “dance” unpredictably from side to side. In this case, they say that a magnetic storm is occurring. It usually lasts from several hours to several days.
The Earth's magnetic field changes its orientation from time to time, performing secular oscillations (lasting 5–10 thousand years), and completely reorienting, i.e. swapping magnetic poles (2–3 times per million years). This is indicated by the magnetic field of distant eras “frozen” into 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 processes occurring in the Earth's core. The characteristic time of polarity reversal, determined by the inner solid core, is from 3 to 5 thousand years, and determined by the outer liquid core - about 500 years. These times may explain the observed dynamics of the geomagnetic field. Computer modeling, taking into account various intraterrestrial processes, showed the possibility of reversing the polarity of the magnetic field in about 5 thousand years.
Tricks with magnets
“The Temple of Enchantment, or the mechanical, optical and physical office of Mr. Gamuletsky de Colla” by the famous Russian illusionist Gamuletsky, which existed until 1842, became famous, among other things, for the fact that visitors ascending the staircase decorated with candelabra and carpeted with carpets could even notice from afar the At the top of the stairs, a gilded figure of an angel, made in natural human height, which hovered in a horizontal position above the office door without being suspended or supported. Anyone could verify that the figure had no 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,” said Gamuletsky, “I worked to find the point and weight of the magnet and iron in order to hold the angel in the air. In addition to work and a lot of money, I spent on this miracle.”
In the Middle Ages, a very common illusion act was the so-called “obedient fish” made of wood. They swam in the pool and obeyed the slightest wave of the magician's hand, who made them move in all sorts of directions. The secret of the trick was extremely simple: a magnet was hidden in the magician’s sleeve, 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 act: Jonas invited some spectators to put the watch on the table, after which he, without touching the watch, randomly changed the position of the hands.
The modern embodiment of this idea is electromagnetic couplings, well known to electricians, with which you can rotate devices separated from the engine by some obstacle, for example, a wall.
In the mid-80s of the 19th century, rumors spread about a learned elephant who could not only add and subtract, but even multiply, divide and extract roots. This was done as follows. 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. Dividing and extracting the square root were done in the same way. The trick was quite simple: a small electromagnet was hidden under each number on the board. When the elephant was asked a question, a current was supplied to the winding of the magnet located to indicate 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 enormous success.
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 electromagnetic fields .
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 magnetic induction vector 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. Biot-Savart-Laplace law. Law of total current.
The formulation of Biot-Savart-Laplace's law is as follows: When a direct current passes through a closed loop located in a vacuum, for a point located at a distance r0 from the loop, the magnetic induction will have the form.
where I is the current in the circuit
gamma contour along which integration takes place
r0 arbitrary point
Total current law This is the law connecting the circulation of the magnetic field strength vector and 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 current-carrying conductor. Magnetic moment of circular current.
30. The effect of a magnetic field on a current-carrying conductor. Ampere's law. Interaction of currents .
F = B I l sinα ,
Where α - the angle between the magnetic induction and current vectors,B - magnetic field induction,I - current strength in the conductor,l - length of the conductor.
Interaction of currents. If two wires are connected to a DC circuit, then: Parallel, closely spaced conductors connected in series repel each other. Conductors connected in parallel attract each other.
31. The effect of electric and magnetic fields on a moving charge. Lorentz force.
Lorentz force - force, with which electromagnetic field according to classical (non-quantum) electrodynamics acts on point charged particle. Sometimes the Lorentz force is called the force acting on a moving object with speed charge only from the outside magnetic field, often full strength - from the electromagnetic field in general , in other words, from the outside electrical And magnetic fields.
32. The effect 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 arising due to the magnetization of the substance.
Substances for which the magnetic permeability is slightly less than unity (μ< 1), называются diamagnetic materials, slightly greater than unity (μ > 1) - paramagnetic.
ferromagnet - substance or material in which a 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 strength fields V substance Not only from attached external fields, But And from background of this sample
Magnetic fields, just like electric ones, can be represented graphically using lines of force. A magnetic field line, or magnetic field induction line, is a line whose tangent at each point coincides with the direction of the magnetic field induction vector.
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| A) | b) | V) |
Rice. 1.2. Direct current magnetic field lines (a),
circular current (b), solenoid (c)
Magnetic lines of force, like electrical 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 location.
In Fig. 1.2, A The field lines of direct current are shown, which are concentric circles, the center of which is located on the current axis, and the direction is determined by the right-hand screw rule (the current in the conductor is directed towards the reader).
Magnetic induction lines can be “revealed” using iron filings, which become magnetized in the field under study and behave like small magnetic needles. In Fig. 1.2, b magnetic field lines of circular current are shown. The magnetic field of the solenoid is shown in Fig. 1.2, V.
The magnetic field lines are closed. Fields with closed lines of force are called vortex fields. It is obvious that the magnetic field is a vortex field. This is the significant 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
French physicists J. Biot and F. Savard conducted a study in 1820 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 magnetic field induction of any current can be calculated as a vector sum (superposition) of the magnetic field inductions created by individual elementary sections of the current. For the magnetic induction of the field created by a current element of 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); – radius vector drawn from the element to the point at which it is determined; – modulus of the radius vector.