lines of force magnetic field

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.

but)	b)	in)

Rice. 1.2. Lines of force of the direct current magnetic field (a),

circular current (b), solenoid (c)

Magnetic lines of force just like electric ones, they 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 but 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 in 1820 conducted a study of magnetic fields created by currents flowing through 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 separate 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 .

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 into 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 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.

Characteristic elements terrestrial magnetism change very slowly over time secular changes. However, from time to time there are magnetic storms, 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. With powerful solar flares the magnetosphere is deformed, and these particles can pass into the upper atmosphere, where they collide with gas molecules, auroras are formed.

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.

Thus, the magnetic field induction on the axis of a circular coil with current decreases in inverse proportion to the third power of the distance from the center of the coil to a point on the axis. The vector of magnetic induction on the axis of the coil is parallel to the axis. Its direction can be determined using the right screw: if you direct the right screw parallel to the axis of the coil and rotate it in the direction of the current in the coil, then the direction of the translational movement of the screw will show the direction of the magnetic induction vector.

3.5 Magnetic field lines

The magnetic field, like the electrostatic one, is conveniently represented in graphical form - using magnetic field lines.

The line of force of a magnetic field is a line, the tangent to which at each point coincides with the direction of the magnetic induction vector.

The lines of force of the magnetic field are drawn in such a way that their density is proportional to the magnitude of the magnetic induction: the greater the magnetic induction at a certain point, the greater the density of the lines of force.

Thus, magnetic field lines are similar to electrostatic field lines.

However, they also have some peculiarities.

Consider a magnetic field created by a straight conductor with current I.

Let this conductor be perpendicular to the plane of the figure.

At different points located at the same distance from the conductor, the induction is the same in magnitude.

vector direction IN at different points shown in the figure.

The line, the tangent to which at all points coincides with the direction of the magnetic induction vector, is a circle.

Therefore, the magnetic field lines in this case are circles enclosing the conductor. The centers of all lines of force are located on the conductor.

Thus, the lines of force of the magnetic field are closed (the lines of force of an electrostatic field cannot be closed, they begin and end on charges).

Therefore the magnetic field is eddy(the so-called fields whose lines of force are closed).

The closedness of the lines of force means another, very important feature of the magnetic field - in nature there are no (at least not yet discovered) magnetic charges that would be the source of a magnetic field of a certain polarity.

Therefore, there is no separately existing north or south magnetic pole of a magnet.

Even if you saw a permanent magnet in half, you get two magnets, each of which has both poles.

3.6. Lorentz force

It has been experimentally established that a force acts on a charge moving in a magnetic field. This force is called the Lorentz force:

.

Lorentz force modulus

,

where a is the angle between the vectors v And B .

The direction of the Lorentz force depends on the direction of the vector . It can be determined using the right screw rule or the left hand rule. But the direction of the Lorentz force does not necessarily coincide with the direction of the vector !

The point is that the Lorentz force is equal to the result of the product of the vector [ v , IN ] to a scalar q. If the charge is positive, then F l is parallel to the vector [ v , IN ]. If q< 0, то сила Лоренца противоположна направлению вектора [v , IN ] (see figure).

If a charged particle moves parallel to the magnetic field lines, then the angle a between the velocity and magnetic induction vectors zero. Therefore, the Lorentz force does not act on such a charge (sin 0 = 0, F l = 0).

If the charge moves perpendicular to the magnetic field lines, then the angle a between the velocity and magnetic induction vectors is 90 0 . In this case, the Lorentz force has the maximum possible value: F l = q v B.

The Lorentz force is always perpendicular to the velocity of the charge. This means that the Lorentz force cannot change the magnitude of the speed of movement, but changes its direction.

Therefore, in a uniform magnetic field, a charge that has flown into a magnetic field perpendicular to its lines of force will move in a circle.

If only the Lorentz force acts on the charge, then the movement of the charge obeys the following equation, compiled on the basis of Newton's second law: ma = F l.

Since the Lorentz force is perpendicular to the velocity, the acceleration of a charged particle is centripetal (normal): (here R is the radius of curvature of the charged particle trajectory).

Without a doubt, the magnetic field lines are now known to everyone. At least, even at school, their manifestation is demonstrated in physics lessons. Remember how the teacher placed a permanent magnet (or even two, combining the orientation of their poles) under a sheet of paper, and on top of it he poured metal filings taken in the labor training room? It is quite clear that the metal had to be held on the sheet, but something strange was observed - lines were clearly traced along which sawdust lined up. Notice - not evenly, but in stripes. These are the magnetic field lines. Or rather, their manifestation. What happened then and how can it be explained?

Let's start from afar. Together with us in the visible physical world coexists a special kind of matter - a magnetic field. It provides interaction between moving elementary particles or larger bodies possessing an electric charge or a natural electric charge and are not only interconnected with each other, but often generate themselves. For example, a wire carrying electricity creates a magnetic field around itself. The reverse is also true: the action of alternating magnetic fields on a closed conducting circuit creates a movement of charge carriers in it. The latter property is used in generators that supply electrical energy to all consumers. A striking example of electromagnetic fields is light.

The lines of force of the magnetic field around the conductor rotate or, which is also true, are characterized by a directed vector of magnetic induction. The direction of rotation is determined by the gimlet rule. The indicated lines are a convention, since the field spreads evenly in all directions. The thing is that it can be represented as an infinite number of lines, some of which have a more pronounced tension. That is why some “lines” are clearly traced in and sawdust. Interestingly, the lines of force of the magnetic field are never interrupted, so it is impossible to say unequivocally where the beginning is and where the end is.

In the case of a permanent magnet (or an electromagnet similar to it), there are always two poles, conventionally named North and South. The lines mentioned in this case are rings and ovals connecting both poles. Sometimes this is described in terms of interacting monopoles, but then a contradiction arises, according to which the monopoles cannot be separated. That is, any attempt to divide the magnet will result in several bipolar parts.

Of great interest are the properties of lines of force. We have already talked about continuity, but the ability to create an electric current in a conductor is of practical interest. The meaning of this is as follows: if the conducting circuit is crossed by lines (or the conductor itself is moving in a magnetic field), then additional energy is imparted to the electrons in the outer orbits of the atoms of the material, allowing them to begin independent directed movement. It can be said that the magnetic field seems to “knock out” charged particles from the crystal lattice. This phenomenon has been named electromagnetic induction and is currently the main way to obtain primary electrical energy. It was discovered experimentally in 1831 by the English physicist Michael Faraday.

The study of magnetic fields began as early as 1269, when P. Peregrine discovered the interaction of a spherical magnet with steel needles. Almost 300 years later, W. G. Colchester suggested that he himself was a huge magnet with two poles. Further, magnetic phenomena were studied by such famous scientists as Lorentz, Maxwell, Ampère, Einstein, etc.

Magnetic field, what is it? - a special kind of matter;
Where does it exist? - around moving electric charges(including around a conductor with current)
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? - via 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.

Powerful magnets used in many modern goods, can affect the performance of 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. swapping 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 on it, moving his fingers naturally. 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 were carried out. square root. 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 long time could not figure it out, and the "learned elephant" was a huge success.