Themes USE codifier : interaction of magnets, magnetic field of a conductor with current.

The magnetic properties of matter have been known to people for a long time. Magnets got their name from the ancient city of Magnesia: a mineral (later called magnetic iron ore or magnetite) was widespread in its vicinity, pieces of which attracted iron objects.

Interaction of magnets

On two sides of each magnet are located North Pole and South Pole. Two magnets are attracted to each other by opposite poles and repel by like poles. Magnets can act on each other even through a vacuum! All this is reminiscent of the interaction of electric charges, however the interaction of magnets is not electrical. This is evidenced by the following experimental facts.

The magnetic force weakens when the magnet is heated. The strength of the interaction of point charges does not depend on their temperature.

The magnetic force is weakened by shaking the magnet. Nothing similar happens with electrically charged bodies.

Positive electric charges can be separated from negative ones (for example, when bodies are electrified). But it is impossible to separate the poles of the magnet: if you cut the magnet into two parts, then poles also appear at the place of the cut, and the magnet breaks up into two magnets with opposite poles at the ends (oriented in exactly the same way as the poles of the original magnet).

So the magnets always bipolar, they exist only in the form dipoles. Isolated magnetic poles (so-called magnetic monopoles- analogues of electric charge) in nature do not exist (in any case, they have not yet been experimentally detected). This is perhaps the most impressive asymmetry between electricity and magnetism.

Like electrically charged bodies, magnets act on electrical charges. However, the magnet only acts on moving charge; If the charge is at rest relative to the magnet, then no magnetic force acts on the charge. On the contrary, an electrified body acts on any charge, regardless of whether it is at rest or in motion.

According to modern concepts of the theory of short-range action, the interaction of magnets is carried out through magnetic field . Namely, a magnet creates a magnetic field in the surrounding space, which acts on another magnet and causes a visible attraction or repulsion of these magnets.

An example of a magnet is magnetic needle compass. With the help of a magnetic needle, one can judge the presence of a magnetic field in a given region of space, as well as the direction of the field.

Our planet Earth is a giant magnet. Not far from the geographic north pole of the Earth is the south magnetic pole. Therefore, the north end of the compass needle, turning to the south magnetic pole of the Earth, points to the geographical north. Hence, in fact, the name "north pole" of the magnet arose.

Magnetic field lines

The electric field, we recall, is investigated with the help of small test charges, by the action on which one can judge the magnitude and direction of the field. An analogue of a test charge in the case of a magnetic field is a small magnetic needle.

For example, you can get some geometric idea of ​​the magnetic field if you place in different points spaces are very small compass needles. Experience shows that the arrows will line up along certain lines - the so-called magnetic field lines. Let us define this concept in the form next three points.

1. Lines of a magnetic field, or magnetic lines of force, are directed lines in space that have the following property: a small compass needle placed at each point of such a line is oriented tangentially to this line.

2. The direction of the magnetic field line is the direction of the northern ends of the compass needles located at the points of this line.

3. The thicker the lines go, the stronger the magnetic field in a given region of space..

The role of compass needles can be successfully performed by iron filings: in a magnetic field, small filings are magnetized and behave exactly like magnetic needles.

So, pouring iron filings around permanent magnet, we will see approximately the following pattern of magnetic field lines (Fig. 1).

Rice. 1. Permanent magnet field

The north pole of the magnet is indicated in blue and the letter ; the south pole - in red and the letter . Note that the field lines exit the north pole of the magnet and enter the south pole, because it is to the south pole of the magnet that the north end of the compass needle will point.

Oersted's experience

Although electrical and magnetic phenomena were known to people since antiquity, no relationship between them long time was not observed. For several centuries, research on electricity and magnetism proceeded in parallel and independently of each other.

The remarkable fact that electrical and magnetic phenomena are actually related to each other was first discovered in 1820 in the famous experiment of Oersted.

The scheme of Oersted's experiment is shown in fig. 2 (image from rt.mipt.ru). Above the magnetic needle (and - the north and south poles of the arrow) is a metal conductor connected to a current source. If you close the circuit, then the arrow turns perpendicular to the conductor!
This simple experiment pointed directly to the relationship between electricity and magnetism. The experiments that followed Oersted's experience firmly established the following pattern: the magnetic field is generated by electric currents and acts on currents.

Rice. 2. Oersted's experiment

The picture of the lines of the magnetic field generated by a conductor with current depends on the shape of the conductor.

Magnetic field of a straight wire with current

The magnetic field lines of a straight wire carrying current are concentric circles. The centers of these circles lie on the wire, and their planes are perpendicular to the wire (Fig. 3).

Rice. 3. Field of a direct wire with current

There are two alternative rules for determining the direction of direct current magnetic field lines.

hour hand rule. The field lines go counterclockwise when viewed so that the current flows towards us..

screw rule(or gimlet rule, or corkscrew rule- it's closer to someone ;-)). The field lines go where the screw (with conventional right-hand thread) must be turned to move along the thread in the direction of the current.

Use whichever rule suits you best. It's better to get used to the clockwise rule - you yourself will later see that it is more universal and easier to use (and then remember it with gratitude in your first year when you study analytic geometry).

On fig. 3, something new has also appeared: this is a vector, which is called magnetic field induction, or magnetic induction. The magnetic induction vector is an analog of the intensity vector electric field: he serves power characteristic magnetic field, determining the force with which the magnetic field acts on moving charges.

We will talk about forces in a magnetic field later, but for now we will only note that the magnitude and direction of the magnetic field is determined by the magnetic induction vector. At each point in space, the vector is directed in the same direction as the north end of the compass needle placed at this point, namely, tangent to the field line in the direction of this line. The magnetic induction is measured in teslach(Tl).

As in the case of an electric field, for the induction of a magnetic field, superposition principle. It lies in the fact that induction of magnetic fields created at a given point by various currents are added vectorially and give the resulting vector of magnetic induction:.

The magnetic field of a coil with current

Let us consider a circular coil along which circulates D.C.. We do not show the source that creates the current in the figure.

The picture of the lines of the field of our turn will have approximately the following form (Fig. 4).

Rice. 4. Field of the coil with current

It will be important for us to be able to determine in which half-space (relative to the plane of the coil) the magnetic field is directed. Again we have two alternative rules.

hour hand rule. The field lines go there, looking from where the current seems to be circulating counterclockwise.

screw rule. The field lines go where the screw (with conventional right hand threads) would move if rotated in the direction of the current.

As you can see, the roles of the current and the field are reversed - in comparison with the formulations of these rules for the case of direct current.

The magnetic field of a coil with current

Coil it will turn out, if tightly, coil to coil, wind the wire into a sufficiently long spiral (Fig. 5 - image from the site en.wikipedia.org). The coil may have several tens, hundreds or even thousands of turns. The coil is also called solenoid.

Rice. 5. Coil (solenoid)

The magnetic field of one turn, as we know, does not look very simple. Fields? individual turns of the coil are superimposed on each other, and, it would seem, the result should be a very confusing picture. However, this is not the case: the field of a long coil has an unexpectedly simple structure (Fig. 6).

Rice. 6. coil field with current

In this figure, the current in the coil goes counterclockwise when viewed from the left (this will happen if, in Fig. 5, the right end of the coil is connected to the “plus” of the current source, and the left end to the “minus”). We see that the magnetic field of the coil has two characteristic properties.

1. Inside the coil, away from its edges, the magnetic field is homogeneous: at each point, the magnetic induction vector is the same in magnitude and direction. The field lines are parallel straight lines; they bend only near the edges of the coil when they go out.

2. Outside the coil, the field is close to zero. The more turns in the coil, the weaker the field outside it.

Note that an infinitely long coil does not emit a field at all: there is no magnetic field outside the coil. Inside such a coil, the field is uniform everywhere.

Doesn't it remind you of anything? A coil is the "magnetic" counterpart of a capacitor. You remember that a capacitor creates a homogeneous electric field, whose lines are bent only near the edges of the plates, and outside the capacitor, the field is close to zero; a capacitor with infinite plates does not release the field at all, and the field is uniform everywhere inside it.

And now - the main observation. Compare, please, the picture of the magnetic field lines outside the coil (Fig. 6) with the field lines of the magnet in Fig. one . It's the same thing, isn't it? And now we come to a question that you probably had a long time ago: if a magnetic field is generated by currents and acts on currents, then what is the reason for the appearance of a magnetic field near a permanent magnet? After all, this magnet does not seem to be a conductor with current!

Ampère's hypothesis. Elementary currents

At first, it was thought that the interaction of magnets was due to special magnetic charges concentrated at the poles. But, unlike electricity, no one could isolate the magnetic charge; after all, as we have already said, it was not possible to obtain separately the north and south poles of the magnet - the poles are always present in the magnet in pairs.

Doubts about magnetic charges were aggravated by the experience of Oersted, when it turned out that the magnetic field is generated by an electric current. Moreover, it turned out that for any magnet it is possible to choose a conductor with a current of the appropriate configuration, such that the field of this conductor coincides with the field of the magnet.

Ampere put forward a bold hypothesis. There are no magnetic charges. The action of a magnet is explained by closed electric currents inside it..

What are these currents? These elementary currents circulate within atoms and molecules; they are associated with the movement of electrons in atomic orbits. The magnetic field of any body is made up of the magnetic fields of these elementary currents.

Elementary currents can be randomly located relative to each other. Then their fields cancel each other, and the body does not show magnetic properties.

But if elementary currents are coordinated, then their fields, adding up, reinforce each other. The body becomes a magnet (Fig. 7; the magnetic field will be directed towards us; the north pole of the magnet will also be directed towards us).

Rice. 7. Elementary magnet currents

Ampere's hypothesis about elementary currents clarified the properties of magnets. Heating and shaking a magnet destroys the arrangement of its elementary currents, and the magnetic properties weaken. The inseparability of the magnet poles became obvious: at the place where the magnet was cut, we get the same elementary currents at the ends. The ability of a body to be magnetized in a magnetic field is explained by the coordinated alignment of elementary currents that “turn” properly (read about the rotation of a circular current in a magnetic field in the next sheet).

Ampère's hypothesis turned out to be correct - it showed further development physics. The concept of elementary currents has become an integral part of the theory of the atom, developed already in the twentieth century - almost a hundred years after Ampère's brilliant conjecture.

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 – special kind 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. 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- scalar characteristic of the 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 what it is. electricity, generating a 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 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.

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 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 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 .

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 the 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 captures 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 removed without surgery with a magnetic probe.

> Magnetic field lines

How to determine magnetic field lines: a diagram of the strength and direction of magnetic field lines, using a compass to determine the magnetic poles, drawing.

Magnetic field lines useful for visually displaying the strength and direction of a magnetic field.

Learning task

• Correlate the strength of the magnetic field with the density of the lines of the magnetic field.

Key Points

• The direction of the magnetic field displays the compass needles touching the magnetic field lines at any specified point.
• The strength of the B-field is inversely proportional to the distance between the lines. It is also exactly proportional to the number of lines per unit area. One line never crosses another.
• The magnetic field is unique at every point in space.
• The lines are not interrupted and create closed loops.
• The lines stretch from the north to the south pole.

Terms

• Magnetic field lines are a graphic representation of the magnitude and direction of a magnetic field.
• B-field is a synonym for magnetic field.

Magnetic field lines

As a child, Albert Einstein is said to have loved looking at the compass, thinking about how the needle felt force without direct physical contact. Deep thinking and serious interest, led to the fact that the child grew up and created his revolutionary theory of relativity.

Since magnetic forces affect distances, we calculate magnetic fields to represent these forces. Line graphics are useful for visualizing the strength and direction of a magnetic field. The elongation of the lines indicates the north orientation of the compass needle. The magnetic is called the B-field.

(a) - If a small compass is used to compare the magnetic field around a bar magnet, it will show right direction from the north pole to the south. (b) - Adding arrows creates continuous lines magnetic field. Strength is proportional to the proximity of the lines. (c) - If you can examine the inside of the magnet, then the lines will be displayed in the form of closed loops

There is nothing difficult in matching the magnetic field of an object. First, calculate the strength and direction of the magnetic field at several locations. Mark these points with vectors pointing in the direction of the local magnetic field with a magnitude proportional to its strength. You can combine arrows and form magnetic field lines. The direction at any point will be parallel to the direction of the nearest field lines, and the local density can be proportional to the strength.

The lines of force of the magnetic field resemble contour lines on topographic maps, because they show something continuous. Many of the laws of magnetism can be formulated in simple terms, such as the number of field lines through a surface.

Direction of magnetic field lines, represented by the alignment of iron filings on paper placed above a bar magnet

Various phenomena affect the display of lines. For example, iron filings on a magnetic field line create lines that correspond to magnetic ones. They are also visually displayed in auroras.

A small compass sent into the field aligns parallel to the field line, with the north pole pointing to B.

Miniature compasses can be used to show fields. (a) - The magnetic field of the circular current circuit resembles a magnetic one. (b) - A long and straight wire forms a field with magnetic field lines creating circular loops. (c) - When the wire is in the plane of the paper, the field appears perpendicular to the paper. Note which symbols are used for the box pointing in and out

A detailed study of magnetic fields helped to derive a number of important rules:

• The direction of the magnetic field touches the field line at any point in space.
• The strength of the field is proportional to the proximity of the line. It is also exactly proportional to the number of lines per unit area.
• The lines of the magnetic field never collide, which means that at any point in space the magnetic field will be unique.
• The lines remain continuous and follow from the north to the south pole.

The last rule is based on the fact that the poles cannot be separated. And this is different from electric field lines, in which the end and the beginning are marked by positive and negative charges.