What do we know about the lines of force of a magnetic field, besides the fact that in the local space near permanent magnets or conductors with current, there is a magnetic field that manifests itself in the form of lines of force, or in a more familiar combination - in the form of magnetic lines of force?

There is a very convenient way get a clear picture of the magnetic field lines using iron filings. To do this, you need to pour a little iron filings on a sheet of paper or cardboard and bring one of the poles of the magnet from below. The sawdust is magnetized and arranged along the magnetic field lines in the form of chains of micro magnets. In classical physics, magnetic lines of force are defined as lines of a magnetic field, the tangents to which at each point indicate the direction of the field at that point.

Using the example of several drawings with different arrangements of magnetic lines of force, let us consider the nature of the magnetic field around current-carrying conductors and permanent magnets.

Figure 1 shows a view of the magnetic force lines of a circular coil with current, and Figure 2 shows a picture of magnetic force lines around a straight wire with current. In Fig. 2, small magnetic needles are used instead of sawdust. This figure shows how when the direction of the current changes, the direction of the magnetic field lines also changes. The relationship between the direction of the current and the direction of the magnetic field lines is usually determined using the "rule of the gimlet", the rotation of the handle of which will show the direction of the magnetic field lines if the gimlet is screwed in in the direction of the current.

Figure 3 shows a picture of the magnetic force lines of a bar magnet, and Figure 4 shows a picture of the magnetic force lines of a long solenoid with current. Attention is drawn to the similarity of the external location of the magnetic field lines in both figures (Fig. 3 and Fig. 4). The lines of force from one end of the current-carrying solenoid extend to the other in the same way as a bar magnet. The very shape of the magnetic field lines outside the solenoid with current is identical to the shape of the lines of a bar magnet. A current carrying solenoid also has north and south poles and a neutral zone. Two current-carrying solenoids or a solenoid and a magnet interact like two magnets.

What can you see when looking at pictures of the magnetic fields of permanent magnets, straight conductors with current, or coils with current using iron filings? main feature magnetic field lines, as the pictures of the location of the sawdust show, this is their isolation. Another feature of magnetic field lines is their directionality. A small magnetic needle, placed at any point in the magnetic field, with its north pole will indicate the direction of the magnetic lines of force. For definiteness, we agreed to assume that the magnetic field lines emanate from the north magnetic pole of a bar magnet and enter its south pole. The local magnetic space near magnets or conductors with current is a continuous elastic medium. The elasticity of this medium is confirmed by numerous experiments, for example, when the same-name poles of permanent magnets are repelled.

Even earlier, I hypothesized that the magnetic field around magnets or current-carrying conductors is a continuous elastic medium with magnetic properties, in which interference waves are formed. Some of these waves are closed. It is in this continuous elastic medium that an interference pattern of magnetic field lines is formed, which manifests itself with the use of iron filings. A continuous medium is created by the radiation of sources in the microstructure of matter.

Recall the experiments on wave interference from a physics textbook, in which an oscillating plate with two tips hits the water. In this experiment, it can be seen that the mutual intersection under different angles two waves has no effect on their further movement. In other words, the waves pass through each other without further affecting the propagation of each one. For light (electromagnetic) waves, the same regularity is true.

What happens in those areas of space in which two waves intersect (Fig. 5) - they are superimposed on one another? Each particle of the medium that is in the path of two waves simultaneously participates in the oscillations of these waves, i.e. its movement is the sum of the oscillations of two waves. These fluctuations are a pattern of interference waves with their maxima and minima as a result of the superposition of two or more waves, i.e. addition of their oscillations at each point of the medium through which these waves pass. Experiments have established that the phenomenon of interference is observed both for waves propagating in media and for electromagnetic waves, that is, interference is exclusively a property of waves and does not depend either on the properties of the medium or on its presence. It should be remembered that wave interference occurs under the condition that the oscillations are coherent (matched), i.e. oscillations must have a constant phase difference and the same frequency.

In our case with iron filings magnetic field lines are lines with the largest number sawdust located at the maxima of the interference waves, and lines with a smaller amount of sawdust are located between the maxima (at the minima) of the interference waves.

Based on the above hypothesis, the following conclusions can be drawn.

1. A magnetic field is a medium that is formed near a permanent magnet or current-carrying conductor as a result of radiation from sources in the microstructure of a magnet or conductor of individual micromagnetic waves.

2. These micromagnetic waves interact at each point of the magnetic field, forming an interference pattern in the form of magnetic force lines.

3. Micromagnetic waves are closed micro energy vortices with micro poles capable of being attracted to each other, forming elastic closed lines.

4. Micro sources in the microstructure of a substance that emit micromagnetic waves, which form an interference pattern of a magnetic field, have the same oscillation frequency, and their radiation has a phase difference that is constant in time.

How does the process of magnetization of bodies take place, which leads to the formation of a magnetic field around them, i.e. what processes occur in the microstructure of magnets and current-carrying conductors? To answer this and other questions, it is necessary to recall some features of the structure of the atom.

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 in 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).

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.

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, 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 but the field lines of the direct current field are shown, which are concentric circles, the center of which is located on the current axis, and the direction is determined by the rule of the right screw (the current in the conductor is directed to the reader).

Lines of magnetic induction can be "showed" using iron filings that are magnetized in the field under study and behave like small magnetic needles. On fig. 1.2 b shows the lines of force of the magnetic field of the circular current. The magnetic field of the solenoid is shown in fig. 1.2 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 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 .

> 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 it's different from the lines electric field, in which the end and the beginning are marked by positive and negative charges.

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 electrifying bodies). 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 cut point, 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 by placing very small compass needles at different points in space. 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, having poured iron filings around a permanent magnet, we will see approximately the following picture 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: magnetic field is generated 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 analogue of the electric field strength vector: it 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 exacerbated 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 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 guess.