The direction of the magnetic lines of a current-carrying conductor. Magnetic field of a straight conductor carrying current

If a magnetic needle is brought close to a straight conductor carrying current, it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the needle (Fig. 67). This indicates that the arrow is being acted upon

When an electric current passes through the conductor, a magnetic field appears around the conductor. A magnetic field can be considered as a special state of space surrounding current-carrying conductors.

If you pass a thick conductor through cardboard and pass an electric current through it, then the steel filings poured onto the cardboard will be located around the conductor in concentric circles, which in this case represent the so-called magnetic lines (Fig. 68). We can move the cardboard up or down the conductor, but the location of the steel filings will not change. Consequently, a magnetic field arises around the conductor along its entire length.

If you place 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 (Fig. 69). This shows that the direction magnetic lines changes with a change in the direction of current in the conductor.

The magnetic field around a current-carrying conductor has the following features: the magnetic lines of a straight conductor have the shape of concentric circles; the closer to the conductor, the denser the magnetic lines are located, the greater the magnetic induction; magnetic induction (field intensity) depends on the magnitude of the current in the conductor; The direction of the magnetic lines depends on the direction of the current in the conductor.

To show the direction of current in a conductor shown in section, it is accepted symbol, which we will use later. If you mentally place an arrow in a conductor in the direction of the current (Fig. 70), then in a 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).

The direction of magnetic lines around a current-carrying conductor can be determined using the “gimlet rule.” 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 lines around the conductor (Fig. 71).

A magnetic needle introduced into the field of a current-carrying conductor is located along the magnetic lines. Therefore, to determine its location, you can also use the “gimlet rule” (Fig. 72).

The magnetic field is one of the most important manifestations of electric current and cannot be obtained independently and separately from the current.

In permanent magnets, the magnetic field is also caused by the movement of electrons that make up the atoms and molecules of the magnet.

Intensity magnetic field at each of its points is determined by the magnitude of magnetic induction, which is usually denoted by the letter B. Magnetic induction is a vector quantity, that is, it is characterized not only by a certain value, but also by a certain direction at each point of the magnetic field. The direction of the magnetic induction vector coincides with the tangent to the magnetic line at a given point in the field (Fig. 73).

As a result of generalizing experimental data, French scientists Biot and Savard established that magnetic induction B (magnetic field intensity) at a distance r from an infinitely long straight conductor with current is determined by the expression

where r is the radius of the circle drawn through the field point under consideration; the center of the circle is on the axis of the conductor (2πr is the circumference);

I is the amount of current flowing through the conductor.

The value μa characterizing magnetic properties medium is called the absolute magnetic permeability of the medium.

For emptiness, the absolute magnetic permeability has a minimum value and is usually denoted by __ and called the absolute magnetic permeability of emptiness.

The ratio showing how many times the absolute magnetic permeability of a given medium is greater than the absolute magnetic permeability of emptiness is called relative magnetic permeability and is denoted by the letter μ.

The International System of Units (SI) uses the units of measurement of magnetic induction B - tesla or weber per square meter (tl, wb/m2).

In engineering practice, magnetic induction is usually measured in gauss (gs): 1 t = 10 4 gs.

If at all points of the magnetic field the magnetic induction vectors are equal in magnitude and parallel to each other, then such a field is called uniform.

The product of magnetic induction B and the area S perpendicular to the direction of the field (magnetic induction vector) is called the flux of the magnetic induction vector, or simply

magnetic flux, and is designated by the letter F (Fig. 74):

The International System uses the weber (wb) as the unit of measurement for magnetic flux.

In engineering calculations, magnetic flux is measured in maxwells (μ):

1vb=10 8 μs.

When calculating magnetic fields, a quantity called magnetic field strength (denoted H) is also used. Magnetic induction B and magnetic field strength H are related by the relation

The unit of measurement for magnetic field strength is N - ampere per meter (A/m).

The magnetic field strength in a homogeneous medium, as well as magnetic induction, depends on the magnitude of the current, the number and shape of the conductors through which the current passes. But unlike magnetic induction, magnetic field strength does not take into account the influence of the magnetic properties of the medium.

Magnets are bodies that have the property of attracting iron objects. The attractive property exhibited by magnets is called magnetism. Magnets can be natural or artificial. Mined iron ores Having the property of attraction are called natural magnets, and magnetized pieces of metal are called artificial magnets, which are often called permanent magnets.

The properties of a magnet to attract iron objects to the greatest extent appear at its ends, which are called magnetic poles and, or simply poles. Each magnet has two poles: north (N - north) and south (S - south). The line passing through the middle of the magnet is called the neutral line, or neutral, since no magnetic properties are detected along this line.

Permanent magnets form a magnetic field in which they act magnetic forces in certain directions called lines of force. The power lines leave the north pole and enter the south pole.

Electric current passing through a conductor also creates a magnetic field around the conductor. It has been established that magnetic phenomena are inextricably linked with electric current.

Magnetic lines of force are located around a conductor with current in a circle, the center of which is the conductor itself, while closer to the conductor they are located more densely, and further from the conductor - less often. The location of magnetic field lines around a current-carrying conductor depends on the shape of its cross-section.

To determine the direction of the field lines, use the gimlet rule, which is formulated as follows: if you screw the gimlet in the direction of the current in the conductor, then the rotation of the gimlet handle will show the direction of magnetic field lines.

The magnetic field of a straight conductor is a series of concentric circles (Fig. 157, A). To enhance the magnetic field in a conductor, the latter is made in the form of a coil (Fig. 157, b).

if the direction of rotation of the gimlet handle coincides with the direction of the electric current in the turns of the coil, then forward movement The gimlet is directed towards the North Pole.

The magnetic field of a current-carrying coil is similar to the field of a permanent magnet, so the current-carrying coil (solenoid) has all the properties of a magnet.

Here too, the direction of the magnetic field lines around each turn of the coil is determined by the gimlet rule. The field lines of adjacent turns add up, enhancing the overall magnetic field of the coil. As follows from Fig. 158, the magnetic field lines of the coil exit from one end and enter the other, closing inside the coil. The coil, like permanent magnets, has a polarity (south and north poles), which is also determined by the gimlet rule, if stated as follows: if the direction of rotation of the gimlet handle coincides with the direction of the electric current in the turns of the coil, then the forward movement of the gimlet is directed towards the north pole.

To characterize the magnetic field from the quantitative side, the concept of magnetic induction was introduced.

Magnetic induction is the number of magnetic lines of force per 1 cm 2 (or 1 m 2) of surface perpendicular to the direction of the lines of force. In the SI system, magnetic induction is measured in teslas (abbreviated as T) and is denoted by the letter IN(tesla = weber/m2 = volt second/m2

Weber is a unit of measurement of magnetic flux.

The magnetic field can be strengthened by inserting an iron rod (core) into the coil. The presence of an iron core enhances the field, since, being in the magnetic field of the coil, the iron core is magnetized, creates its own field, which adds up to the original one and intensifies. Such a device is called an electromagnet.

Total number lines of force passing through the cross section of the core is called magnetic flux. The magnitude of the magnetic flux of an electromagnet depends on the current passing through the coil (winding), the number of turns and the resistance of the magnetic circuit.

A magnetic circuit, or magnetic circuit, is the path along which magnetic lines of force are closed. The magnetic resistance of the magnetic core depends on the magnetic permeability of the medium through which the power lines pass, the length of these lines and the cross-section of the core.

The product of the current passing through the winding and the number of its turns is called magnetomotive force (mf s). Magnetic flux is equal to magnetomotive force divided by the magnetic reluctance of the circuit- this is how Ohm’s law is formulated for a magnetic circuit. Since the number of turns and magnetic resistance for a given electromagnet are constant values, the magnetic flux of an electromagnet can be changed by adjusting the current in its winding.

Electromagnets find the widest application in various machines and devices (electric machines, electric bells, telephones, measuring instruments etc.).

If there is a straight conductor carrying current, then you can detect the presence of a magnetic field around this conductor using iron filings...

Or magnetic needles.

Under the influence of the magnetic field of the current, magnetic needles or iron filings are located in concentric circles.

Magnetic lines

The magnetic field can be represented graphically using magnetic lines.
The magnetic lines of the magnetic field of the current are the lines along which the axes of small magnetic arrows are located in the magnetic field.
Magnetic lines of a current's magnetic field are closed curves that enclose a conductor.
A straight conductor carrying current has concentric expanding circles.
The direction of the magnetic line is taken to be the direction indicated by the north pole of the magnetic needle at each point in the field.

Graphic representation magnetic field of a straight conductor carrying current.

The direction of the magnetic lines of the magnetic field of the current is related to the direction of the current in the conductor

It is interesting to see how iron filings, attracted to the pole of a magnet, form brushes that repel each other. But they are simply located along the magnetic field lines!
___

Can you draw a picture of the magnetic field lines of a current-carrying conductor folded into a figure eight?
Is this drawing similar to the one you imagined?

IS IT POSSIBLE TO SEE A MAGNETIC FIELD

You need to turn on the color TV to some still frame and bring a magnet to it. The colors of the image on the screen near the magnet will change!
The picture will shine with rainbow stains. The colored stripes thicken near the contour of the magnet, as if visualizing the magnetic field. In England, it was used in crushed form as a laxative. It is interesting to rotate the magnet, move it, or bring it closer and further away from the screen.
The picture of the magnetic field will be much more interesting than in experiments with sawdust!

Several steel needles were hung loosely from a small brass disk.

If you slowly bring a magnet from below to the needles (for example, with the south pole), then first the needles will move apart, and then, when the magnet gets very close, they will return to the vertical position again.
Why?

EXPERIMENTS WITH IRON SAWDS

Take a magnet of any shape, cover it with a piece of thin cardboard, sprinkle iron filings on top and smooth them out.
It's so interesting to observe magnetic fields!
After all, each “sawdust”, like a magnetic needle, is located along magnetic lines.
This makes the magnetic field lines of your magnet “visible”.
When the cardboard moves over the magnet (or vice versa, the magnet under the cardboard), the sawdust begins to move, changing the patterns of the magnetic field.

Topics of the Unified State Examination 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: in its vicinity there was a widespread mineral (later called magnetic iron ore or magnetite), pieces of which attracted iron objects.

Magnet interaction

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

Magnetic force weakens as the magnet heats up. The strength of the interaction of point charges does not depend on their temperature.

The magnetic force weakens if the magnet is shaken. Nothing like this happens with electrically charged bodies.

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

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

Like electrically charged bodies, magnets act on electric charges. However, the magnet only acts on moving charge; if the charge is at rest relative to the magnet, then the effect of magnetic force on the charge is not observed. On the contrary, an electrified body acts on any charge, regardless of whether it is at rest or in motion.

By modern ideas short-range theory, 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. Using a magnetic needle, you 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 north geographic pole of the Earth is the south magnetic pole. Therefore, the northern end of the compass needle, turning to the southern magnetic pole Earth, points to geographic north. This is where the name “north pole” of a magnet came from.

Magnetic field lines

The electric field, we recall, is studied using small test charges, by the effect on which one can judge the magnitude and direction of the field. The analogue of a test charge in the case of a magnetic field is a small magnetic needle.

For example, you can get some geometric understanding of the magnetic field if you place it in different points space very small compass arrows. 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 of the following three points.

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

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

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

Iron filings can successfully serve as compass needles: in a magnetic field, small filings are magnetized and behave exactly like magnetic needles.

So, by pouring 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 a magnet is indicated by the color blue and the letter ; the south pole - in red and the letter . Please note that the field lines leave the north pole of the magnet and enter the south pole: after all, it is towards the south pole of the magnet that the north end of the compass needle will be directed.

Oersted's experience

Despite the fact that electrical and magnetic phenomena have been known to people since antiquity, there is no relationship between them for a long time was not observed. For several centuries, research into 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 diagram of Oersted's experiment is shown in Fig. 2 (image from the site rt.mipt.ru). Above the magnetic needle (and are the north and south poles of the needle) there is a metal conductor connected to a current source. If you close the circuit, the arrow turns perpendicular to the conductor!
This simple experiment directly indicated the relationship between electricity and magnetism. The experiments that followed Oersted's experiment firmly established the following pattern: magnetic field is generated electric currents and acts on currents.

Rice. 2. Oersted's experiment

The pattern of magnetic field lines generated by a current-carrying conductor depends on the shape of the conductor.

Magnetic field of a straight wire carrying 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 straight wire with current

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

Clockwise rule. The field lines go counterclockwise if you look so that the current flows towards us.

Screw rule(or gimlet rule, or corkscrew rule- this is something closer to someone ;-)). The field lines go where you need to rotate the screw (with a regular right-hand thread) so that it moves along the thread in the direction of the current.

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

In Fig. 3 something new has appeared: this is a vector called magnetic field induction, or magnetic induction. The magnetic induction vector is analogous to 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 northern end of the compass needle placed in this point, namely tangent to the field line in the direction of this line. Magnetic induction is measured in Tesla(Tl).

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

Magnetic field of a coil with current

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 field lines of our orbit will look approximately as follows (Fig. 4).

Rice. 4. Field of a coil with current

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

Clockwise rule. The field lines go there, looking from where the current appears to circulate counterclockwise.

Screw rule. The field lines go where the screw (with a normal right-hand thread) will move if rotated in the direction of the current.

As you can see, the current and the field change roles - compared to the formulation of these rules for the case of direct current.

Magnetic field of a current coil

Coil It will work if you wind the wire tightly, turn to turn, into a sufficiently long spiral (Fig. 5 - image from 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 that the result should be a very confusing picture. However, this is not so: the field of a long coil has unexpectedly simple structure(Fig. 6).

Rice. 6. current coil field

In this figure, the current in the coil flows 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, far from its edges, the magnetic field is homogeneous: at each point the magnetic induction vector is the same in magnitude and direction. Field lines are parallel straight lines; they bend only near the edges of the coil when they come 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 release the field outward at all: there is no magnetic field outside the coil. Inside such a coil, the field is uniform everywhere.

Doesn't remind you of anything? A coil is the “magnetic” analogue of a capacitor. You remember that a capacitor creates a uniform electric field inside itself, the lines of which bend 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 to the outside at all, and the field is uniform everywhere inside it.

And now - the main observation. Please compare the picture of the magnetic field lines outside the coil (Fig. 6) with the magnet field lines in Fig. 1. It's the same thing, isn't it? And now we come to a question that has probably arisen in your mind for a long time: 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!

Ampere's hypothesis. Elementary currents

At first it was thought that the interaction of magnets was explained by 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 the north and south poles of a magnet separately - the poles are always present in a magnet in pairs.

Doubts about magnetic charges were aggravated by Oersted's experiment, when it turned out that the magnetic field is generated by electric current. Moreover, it turned out that for any magnet it is possible to select 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 inside atoms and molecules; they are associated with the movement of electrons along atomic orbits. The magnetic field of any body consists of the magnetic fields of these elementary currents.

Elementary currents can be randomly located relative to each other. Then their fields are mutually cancelled, and the body does not exhibit magnetic properties.

But if the elementary currents are arranged in a coordinated manner, 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 order of its elementary currents, and the magnetic properties weaken. The inseparability of the poles of the magnet has become obvious: at the point where the magnet is 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).

Ampere's hypothesis turned out to be true - this showed further development physics. Ideas about elementary currents became an integral part of the theory of the atom, developed already in the twentieth century - almost a hundred years after Ampere’s brilliant guess.

An electric current in a conductor produces a magnetic field around the conductor. Electric current and magnetic field are two inseparable parts of a single physical process. The magnetic field of permanent magnets is ultimately also generated by molecular electric currents formed by the movement of electrons in orbits and their rotation around their axes.

The magnetic field of a conductor and the direction of its lines of force can be determined using a magnetic needle. The magnetic lines of a straight conductor have the shape of concentric circles located in a plane perpendicular to the conductor. The direction of magnetic field lines depends on the direction of the current in the conductor. If the current in the conductor comes from the observer, then the lines of force are directed clockwise.

The dependence of the direction of the field on the direction of the current is determined by the gimlet rule: when the translational movement of the gimlet coincides with the direction of the current in the conductor, the direction of rotation of the handle coincides with the direction of the magnetic lines.

The gimlet rule can also be used to determine the direction of the magnetic field in the coil, but in the following formulation: if the direction of rotation of the gimlet handle is combined with the direction of the current in the turns of the coil, then the translational movement of the gimlet will show the direction of the field lines inside the coil (Fig. 4.4).

Inside the coil these lines come from south pole to the north, and outside it - from north to south.

The gimlet rule can also be used to determine the direction of current if the direction of the magnetic field lines is known.

A current-carrying conductor in a magnetic field experiences a force equal to

F = I·L·B·sin

I is the current strength in the conductor; B - module of the magnetic field induction vector; L is the length of the conductor located in the magnetic field;  is the angle between the magnetic field vector and the direction of the current in the conductor.

The force acting on a current-carrying conductor in a magnetic field is called the Ampere force.

The maximum ampere force is:

F = I L B

The direction of the Ampere force is determined by the left hand rule: if the left hand is positioned so that the perpendicular component of the magnetic induction vector B enters the palm, and the four extended fingers are directed in the direction of the current, then the bent one is 90 degrees thumb will show the direction of the force acting on a section of conductor carrying current, that is, the Ampere force.

If and lie in the same plane, then the angle between and is straight, therefore . Then the force acting on the current element is

(of course, from the side of the first conductor, exactly the same force acts on the second).

The resulting force is equal to one of these forces. If these two conductors influence the third, then their magnetic fields need to be added vectorially.

Circuit with current in a magnetic field

Rice. 4.13

Let a frame with current be placed in a uniform magnetic field (Fig. 4.13). Then the Ampere forces acting on sides frames will create a torque, the magnitude of which is proportional to the magnetic induction, current strength in the frame, its area S and depends on the angle a between the vector and the normal to the area:

The normal direction is chosen so that the right screw moves in the normal direction when rotating in the direction of the current in the frame.

The maximum value of the torque is when the frame is installed perpendicular to the magnetic lines of force:

This expression can also be used to determine the magnetic field induction:

A value equal to the product is called the magnetic moment of the circuit R t. The magnetic moment is a vector whose direction coincides with the direction of the normal to the contour. Then the torque can be written

At angle a = 0 the torque is zero. The value of the torque depends on the area of ​​the contour, but does not depend on its shape. Therefore, any closed circuit through which direct current flows is subject to a torque M, which rotates it so that the vector magnetic moment established parallel to the magnetic field induction vector.