Magnetic lines of a conductor with current. Magnetic field of a straight conductor with current

Consider a straight conductor (Fig. 3.2), which is part of a closed electrical circuit. According to the Biot-Savart-Laplace law, the magnetic induction vector
field created at a point BUT element conductor with current I, has the meaning
, where - angle between vectors and . For all plots this conductor vectors and lie in the plane of the drawing, so at the point BUT all vectors
generated by each section , directed perpendicular to the plane of the drawing (to us). Vector is determined by the principle of superposition of fields:

,

its modulus is:

.

Denote the distance from the point BUT to conductor . Consider a section of the conductor
. From a point BUT draw an arc WithD radius ,
is small, so
and
. It can be seen from the drawing that
;
, but
(CD=
) Therefore, we have:

.

For we get:

where and - angle values ​​for the extreme points of the conductor MN.

If the conductor is infinitely long, then
,
. Then

the induction at each point of the magnetic field of an infinitely long rectilinear current-carrying conductor is inversely proportional to the shortest distance from this point to the conductor.

3.4. Circular current magnetic field

Consider a circular loop of radius R through which current flows I (Fig. 3.3) . According to the Biot-Savart-Laplace law, induction
field created at a point O element coil with current is equal to:

,

and
, That's why
, and
. With that said, we get:

.

All vectors
directed perpendicular to the plane of the drawing towards us, so induction

tension
.

Let be S- the area covered by the circular coil,
. Then the magnetic induction at an arbitrary point on the axis of a circular coil with current:

,

where is the distance from the point to the coil surface. It is known that
is the magnetic moment of the coil. Its direction coincides with the vector at any point on the axis of the coil, so
, and
.

Expression for similar in appearance to the expression for the electric displacement at the points of the field lying on the axis of the electric dipole far enough from it:

.

Therefore, the magnetic field of the ring current is often considered as the magnetic field of some conditional “magnetic dipole”, the positive (north) pole is considered to be the side of the coil plane from which the magnetic lines of force exit, and the negative (south) is the one into which they enter.

For a current loop having an arbitrary shape:

,

where - the unit vector of the outer normal to the element surfaces S, limited contour. In the case of a flat contour, the surface S – flat and all vectors match.

3.5. Solenoid magnetic field

A solenoid is a cylindrical coil with a large number of turns of wire. The coils of the solenoid form a helix. If the turns are closely spaced, then the solenoid can be considered as a system of series-connected circular currents. These turns (currents) have the same radius and a common axis (Fig. 3.4).

Consider the section of the solenoid along its axis. Circles with a dot will denote the currents coming from behind the plane of the drawing to us, and a circle with a cross - the currents going beyond the plane of the drawing, from us. L is the length of the solenoid, n – the number of turns per unit length of the solenoid; - R- turn radius. Consider a point BUT lying on the axis
solenoid. It is clear that the magnetic induction at this point is directed along the axis
and is equal to the algebraic sum of the inductions of the magnetic fields created at this point by all turns.

Draw from a point BUT radius - vector to any thread. This radius vector forms with the axis
injection α . The current flowing through this coil creates at the point BUT magnetic field with induction

.

Consider a small area
solenoid, it has
turns. These turns are created at the point BUT magnetic field whose induction

.

It is clear that the distance along the axis from the point BUT to the site
equals
; then
.Obviously,
, then

Magnetic induction of fields created by all turns at a point BUT is equal to

Magnetic field strength at a point BUT
.

From Fig.3. 4 we find:
;
.

Thus, the magnetic induction depends on the position of the point BUT on the axis of the solenoid. She is

maximum in the middle of the solenoid:

.

If a L>> R, then the solenoid can be considered infinitely long, in this case
,
,
,
; then

;
.

At one end of a long solenoid
,
or
;
,
,
.

If a magnetic needle is brought to a straight conductor with electric current, then it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the arrow. This indicates that special forces are acting on the needle, which are called magnetic forces. In addition to acting on a magnetic needle, a magnetic field affects moving charged particles and current-carrying conductors that are in a magnetic field. In conductors moving in a magnetic field, or in stationary conductors in an alternating magnetic field, an inductive e. d.s.

In accordance with the above, we can give the following definition of the magnetic field.

A magnetic field is one of the two sides of the electromagnetic field, excited by the electric charges of moving particles and a change in the electric field and characterized by a force effect on moving charged particles, and therefore on electric currents.

If a thick conductor is passed through the cardboard and an electric current is passed through it, then the steel filings sprinkled on the cardboard will be located around the conductor in concentric circles, which in this case are the so-called magnetic induction lines (Fig. 78). We can move the cardboard up or down the conductor, but the location of the steel filings will not change. Therefore, a magnetic field arises around the conductor along its entire length.

If you put small magnetic arrows on cardboard, then by changing the direction of the current in the conductor, you can see that the magnetic arrows will turn (Fig. 79). This shows that the direction of the magnetic induction lines changes with the direction of the current in the conductor.

Magnetic induction lines around a conductor with current have the following properties: 1) magnetic induction lines of a rectilinear conductor are in the form of concentric circles; 2) the closer to the conductor, the denser the magnetic induction lines are; 3) magnetic induction (field intensity) depends on the magnitude of the current in the conductor; 4) the direction of the magnetic induction lines depends on the direction of the current in the conductor.

The direction of magnetic induction lines around a conductor with current can be determined by the "rule of the gimlet:". If a gimlet (corkscrew) with a right-hand thread moves forward in the direction of the current, then the direction of rotation of the handle will coincide with the direction of the magnetic induction lines around the conductor (Fig. 81),

A magnetic needle introduced into the field of a current-carrying conductor is located along the magnetic induction lines. Therefore, to determine its location, you can also use the "rule of the gimlet" (Fig. 82). The magnetic field is one of the most important manifestations of electric current and cannot be

Obtained independently and separately from the current. The magnetic field is characterized by the magnetic induction vector, which, therefore, has a certain magnitude and a certain direction in space.

A quantitative expression for magnetic induction as a result of generalization of experimental data was established by Biot and Savart (Fig. 83). By measuring the magnetic fields of electric currents of various sizes and shapes by the deviation of the magnetic needle, both scientists came to the conclusion that each current element creates a magnetic field at some distance from itself, the magnetic induction of which AB is directly proportional to the length A1 of this element, the magnitude of the flowing current I, the sine the angle a between the direction of the current and the radius vector connecting the field point of interest to us with a given current element, and is inversely proportional to the square of the length of this radius vector r:

henry (h) - unit of inductance; 1 h= 1 ohm sec.

- relative magnetic permeability - a dimensionless coefficient showing how many times the magnetic permeability of a given material is greater than the magnetic permeability of the void. The dimension of magnetic induction can be found by the formula

volt-second is otherwise called weber (vb):

In practice, there is a smaller unit of magnetic induction, gauss (gs):

Biot and Savart's law allows you to calculate the magnetic induction of an infinitely long straight conductor:

where is the distance from the conductor to the point where

Magnetic induction. The ratio of magnetic induction to the product of magnetic permeabilities is called the magnetic field strength and is denoted by the letter H:

The last equation relates two magnetic quantities: induction and magnetic field strength. Let's find the dimension H:

Sometimes they use another unit of tension - an oersted (er):

1 er = 79.6 a/m = 0.796 a/cm.

The magnetic field strength H, like the magnetic induction B, is a vector quantity.

A line tangent to each point of which coincides with the direction of the magnetic induction vector is called a magnetic induction line or a magnetic induction line.

The product of magnetic induction by the size of the area 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 denoted by the letter F:

Magnetic flux dimension:

i.e. magnetic flux is measured in volt-seconds or webers. A smaller unit of magnetic flux is the maxwell (µs):

1 wb = 108 µs. 1 µs = 1 gs cm2.

If a magnetic needle is brought to a straight conductor with current, then it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the arrow (Fig. 67). This indicates that special forces act on the needle, which are called magnetic. In other words, if an electric current flows through a conductor, then a magnetic field arises around the conductor. The magnetic field can be considered as a special state of space surrounding conductors with current.

If you pass a thick conductor through the card and pass an electric current through it, then steel filings sprinkled on cardboard will be located around the conductor in concentric circles, which in this case are 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. Therefore, a magnetic field arises around the conductor along its entire length.

If you put small magnetic arrows on cardboard, then by changing the direction of the current in the conductor, you can see that the magnetic arrows will turn (Fig. 69). This shows that the direction of the magnetic lines changes with the direction of the current in the conductor.

The magnetic field around a conductor with current has the following features: the magnetic lines of a rectilinear conductor are in the form of concentric circles; the closer to the conductor, the denser the magnetic lines are, 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 the current in the conductor shown in the section, a symbol is adopted, which we will use in the future. If we mentally place an arrow in the conductor in the direction of the current (Fig. 70), then in the conductor, the current in which is directed away from us, we will see the tail of the arrow plumage (cross); if the current is directed towards us, we will see the tip of the arrow (point).

The direction of magnetic lines around a conductor with current can be determined by the "rule of the gimlet". 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).

Rice. 71. Determining the direction of magnetic lines around a conductor with current according to the "rule of the gimlet"

A magnetic needle inserted 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).

Rice. 72. Determining the direction of deviation of a magnetic needle brought to a conductor with current, according to the "rule of a gimlet"

The magnetic field is one of the most important manifestations of the 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.

The intensity of the magnetic field at each of its points is determined by the magnitude of the 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 the generalization of experimental data, the French scientists Biot and Savard found that the magnetic induction B (magnetic field intensity) at a distance r from an infinitely long rectilinear current-carrying conductor is determined by the expression

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

I is the amount of current flowing through the conductor.

The value of μ a, which characterizes the magnetic properties of the medium, is called the absolute magnetic permeability of the medium.

For emptiness, the absolute magnetic permeability has a minimum value and it is customary to designate it μ 0 and call it the absolute magnetic permeability of emptiness.

1 h = 1 ohm⋅sec.

The ratio μ a / μ 0 , showing how many times the absolute magnetic permeability of a given medium is greater than the absolute magnetic permeability of the void, is called relative magnetic permeability and is denoted by the letter μ.

In the International System of Units (SI), units of measurement of magnetic induction B are accepted - tesla or weber per square meter (t, wb / m 2).

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

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 homogeneous.

The product of magnetic induction B and the size of 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 denoted by the letter Φ (Fig. 74):

In the International System, the unit of measure for magnetic flux is weber (wb).

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

1 wb \u003d 10 8 μs.

When calculating magnetic fields, a quantity called the 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 the magnetic field strength H is ampere per meter (a/m).

The strength of the magnetic field 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, the magnetic field strength does not take into account the influence of the magnetic properties of the medium.

Topics of the 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 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 of the following three paragraphs.

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

Despite the fact that electrical and magnetic phenomena have been known to people since antiquity, no relationship between them has been observed for a long time. 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 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

Consider a circular coil through which a direct current circulates. 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 that 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 the capacitor creates a uniform electric field inside itself, the lines of which are curved 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).

Ampere's hypothesis turned out to be correct - this was shown by the further development of 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.

Electric current in a conductor creates 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 generated 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 rectilinear conductor are in the form of concentric circles located in a plane perpendicular to the conductor. The direction of the 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: if 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 handle of the gimlet 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 of force inside the coil (Fig. 4.4).

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

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

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

F = I L B sin

I - current strength in the conductor; B is the modulus of the magnetic field induction vector; L is the length of the conductor in the magnetic field;  - 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 Ampère force.

The maximum force of Ampere is:

F = I L B

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

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

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

The resulting force is equal to one of these forces. If these two conductors act on the third, then their magnetic fields must 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 Ampère forces acting on the sides of the frame will create a torque, the magnitude of which is proportional to the magnetic induction, the current strength in the frame, its area S and depends on the angle a between the vector and the normal to the area:

The direction of the normal is chosen so that the right screw moves in the direction of the normal 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 induction of a magnetic field:

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 a direct current flows is subject to a torque M, which rotates it so that the magnetic moment vector is parallel to the magnetic field induction vector.