Lines of force of the magnetic field of a current-carrying conductor. Magnetic field of a straight conductor with current

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 the arrow is affected

An electric current passes through the 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 cardboard and pass an electric current 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 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 the 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).

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).

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 μa, 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 __ and call it 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 a void is called the 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 F (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 (mc):

1vb=10 8 ms.

When calculating magnetic fields, a quantity called the magnetic field strength (denoted H) is also used. The magnetic induction B and the strength of the magnetic field 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.

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 FROMD 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 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
corner 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
;
,
,
.

Magnetic field of electric current

A magnetic field is created not only by natural or artificial ones, but also by a conductor if an electric current passes through it. Therefore, there is a connection between magnetic and electrical phenomena.

It is not difficult to make sure that a magnetic field is formed around the conductor through which the current passes. Above the movable magnetic needle, place a straight conductor parallel to it and pass an electric current through it. The arrow will take a position perpendicular to the conductor.

What forces could make the magnetic needle turn? Obviously, the strength of the magnetic field that has arisen around the conductor. Turn off the current, and the magnetic needle will return to its normal position. This suggests that with the current turned off, the magnetic field of the conductor also disappeared.

Thus, the electric current passing through the conductor creates a magnetic field. To find out in which direction the magnetic needle will deviate, apply the right hand rule. If the right hand is placed over the conductor with the palm down so that the direction of the current coincides with the direction of the fingers, then the bent thumb will show the direction of deviation of the north pole of the magnetic needle placed under the conductor. Using this rule and knowing the polarity of the arrow, you can also determine the direction of the current in the conductor.

Magnetic field of a straight conductor has the form of concentric circles. If you place your right hand over the conductor with your palm down so that the current seems to come out of your fingers, then the bent thumb will point to the north pole of the magnetic needle.Such a field is called a circular magnetic field.

The direction of the lines of force of a circular field depends on in the conductor and is determined by the so-called "Gimlet" rule. If the gimlet is mentally screwed in the direction of the current, then the direction of rotation of its handle will coincide with the direction of the magnetic field lines of force. Applying this rule, you can find out the direction of the current in the conductor, if you know the direction of the field lines of the field created by this current.

Returning to the experiment with the magnetic needle, we can make sure that it is always located with its northern end in the direction of the magnetic field lines.

So, A straight conductor carrying an electric current creates a magnetic field around it. It has the form of concentric circles and is called a circular magnetic field.

Pickles e. Solenoid magnetic field

A magnetic field arises around any conductor, regardless of its shape, provided that an electric current passes through the conductor.

In electrical engineering, we are dealing with, consisting of a number of turns. To study the magnetic field of the coil of interest to us, we first consider what shape the magnetic field of one turn has.

Imagine a coil of thick wire penetrating a sheet of cardboard and connected to a current source. When an electric current passes through a coil, a circular magnetic field is formed around each individual part of the coil. According to the “gimlet” rule, it is easy to determine that the magnetic lines of force inside the coil have the same direction (toward or away from us, depending on the direction of the current in the coil), and they exit from one side of the coil and enter the other side. A series of such coils, having the shape of a spiral, is the so-called solenoid (coil).

Around the solenoid, when a current passes through it, a magnetic field is formed. It is obtained by adding the magnetic fields of each coil and resembles the magnetic field of a rectilinear magnet in shape. The lines of force of the magnetic field of the solenoid, as well as in a rectilinear magnet, exit from one end of the solenoid and return to the other. Inside the solenoid, they have the same direction. Thus, the ends of the solenoid have polarity. The end from which the lines of force come out is north pole solenoid, and the end into which the lines of force enter is its south pole.

Solenoid poles can be determined by right hand rule, but for this you need to know the direction of the current in its turns. If you put your right hand on the solenoid with your palm down, so that the current would seem to come out of your fingers, then the bent thumb will point to the north pole of the solenoid. From this rule it follows that the polarity of the solenoid depends on the direction of the current in it. It is easy to verify this in practice by bringing a magnetic needle to one of the poles of the solenoid and then changing the direction of the current in the solenoid. The arrow will instantly turn 180°, i.e., it will indicate that the poles of the solenoid have changed.

The solenoid has the property of drawing light iron objects into itself. If a steel bar is placed inside the solenoid, then after a while, under the influence of the magnetic field of the solenoid, the bar will become magnetized. This method is used in the manufacture.

electromagnets

It is a coil (solenoid) with an iron core placed inside it. The shapes and sizes of electromagnets are varied, but the general arrangement of all of them is the same.

The coil of an electromagnet is a frame, most often made of pressboard or fiber, and has various shapes depending on the purpose of the electromagnet. A copper insulated wire is wound on the frame in several layers - the winding of an electromagnet. It has a different number of turns and is made of wire of different diameters, depending on the purpose of the electromagnet.

To protect the winding insulation from mechanical damage, the winding is covered with one or more layers of paper or some other insulating material. The beginning and end of the winding is brought out and connected to the output terminals mounted on the frame, or to flexible conductors with lugs at the ends.

The electromagnet coil is mounted on a core made of soft, annealed iron or iron alloys with silicon, nickel, etc. Such iron has the least residual. Cores are most often made composite of thin sheets isolated from each other. The shape of the cores can be different, depending on the purpose of the electromagnet.

If an electric current is passed through the winding of an electromagnet, then a magnetic field is formed around the winding, which magnetizes the core. Since the core is made of soft iron, it will be magnetized instantly. If the current is then turned off, the magnetic properties of the core will also quickly disappear, and it will cease to be a magnet. The poles of an electromagnet, like a solenoid, are determined by the right hand rule. If the electromagnet winding is changed, then the polarity of the electromagnet will change accordingly.

The action of an electromagnet is similar to that of a permanent magnet. However, there is a big difference between them. A permanent magnet always has magnetic properties, and an electromagnet only when an electric current passes through its winding.

In addition, the attractive force of a permanent magnet is unchanged, since the magnetic flux of a permanent magnet is unchanged. The force of attraction of an electromagnet is not a constant value. The same electromagnet can have different attractive forces. The force of attraction of any magnet depends on the magnitude of its magnetic flux.

The force of attraction, and hence its magnetic flux, depends on the magnitude of the current passing through the winding of this electromagnet. The greater the current, the greater the force of attraction of the electromagnet, and, conversely, the smaller the current in the winding of the electromagnet, the less force it attracts magnetic bodies to itself.

But for electromagnets of various design and size, the force of their attraction depends not only on the magnitude of the current in the winding. If, for example, we take two electromagnets of the same device and dimensions, but one with a small number of winding turns, and the other with a much larger number, then it is easy to see that with the same current the attractive force of the latter will be much greater. Indeed, the greater the number of turns of the winding, the greater at a given current a magnetic field is created around this winding, since it is composed of the magnetic fields of each turn. This means that the magnetic flux of the electromagnet, and hence the force of its attraction, will be the greater, the greater the number of turns the winding has.

There is another reason that affects the magnitude of the magnetic flux of an electromagnet. This is the quality of his magnetic circuit. A magnetic circuit is a path along which a magnetic flux closes. The magnetic circuit has a certain magnetic resistance. Magnetic resistance depends on the magnetic permeability of the medium through which the magnetic flux passes. The greater the magnetic permeability of this medium, the lower its magnetic resistance.

Since m the magnetic permeability of ferromagnetic bodies (iron, steel) is many times greater than the magnetic permeability of air, therefore it is more profitable to make electromagnets so that their magnetic circuit does not contain air sections. The product of the current and the number of turns in the winding of an electromagnet is called magnetomotive force. The magnetomotive force is measured by the number of ampere turns.

For example, the winding of an electromagnet having 1200 turns carries a current of 50 mA. Magnetic motive force such an electromagnet equals 0.05 x 1200 = 60 ampere turns.

The action of the magnetomotive force is similar to the action of the electromotive force in an electrical circuit. Just as EMF causes an electric current, the magnetomotive force creates a magnetic flux in an electromagnet. Just as in an electric circuit, with an increase in EMF, the current in the price increases, so in a magnetic circuit, with an increase in the magnetomotive force, the magnetic flux increases.

Action magnetic resistance similar to the action of the electrical resistance of the circuit. As the current decreases with an increase in the resistance of an electric circuit, so in a magnetic circuit an increase in magnetic resistance causes a decrease in magnetic flux.

The dependence of the magnetic flux of an electromagnet on the magnetomotive force and its magnetic resistance can be expressed by a formula similar to Ohm's law formula: magnetomotive force \u003d (magnetic flux / magnetic resistance)

The magnetic flux is equal to the magnetomotive force divided by the magnetic resistance.

The number of turns of the winding and the magnetic resistance for each electromagnet is a constant value. Therefore, the magnetic flux of a given electromagnet changes only with a change in the current passing through the winding. Since the force of attraction of an electromagnet is determined by its magnetic flux, in order to increase (or decrease) the force of attraction of an electromagnet, it is necessary to increase (or decrease) the current in its winding accordingly.

polarized electromagnet

A polarized electromagnet is a combination of a permanent magnet and an electromagnet. It is arranged in such a way. So-called soft iron pole extensions are attached to the poles of the permanent magnet. Each pole extension serves as the core of an electromagnet; a coil with a winding is mounted on it. Both windings are connected in series.

Since the pole extensions are directly attached to the poles of a permanent magnet, they have magnetic properties even in the absence of current in the windings; at the same time, their attraction force is unchanged and is determined by the magnetic flux of a permanent magnet.

The action of a polarized electromagnet lies in the fact that when current passes through its windings, the force of attraction of its poles increases or decreases depending on the magnitude and direction of the current in the windings. On this property of a polarized electromagnet, the action of other electrical devices.

The action of a magnetic field on a current-carrying conductor

If a conductor is placed in a magnetic field so that it is located perpendicular to the lines of force of the field, and an electric current is passed through this conductor, then the conductor will begin to move and will be pushed out of the magnetic field.

As a result of the interaction of the magnetic field with the electric current, the conductor sets in motion, i.e., the electrical energy is converted into mechanical energy.

The force with which the conductor is pushed out of the magnetic field depends on the magnitude of the magnetic flux of the magnet, the current strength in the conductor and the length of that part of the conductor that the field lines cross. The direction of this force, i.e. the direction of movement of the conductor, depends on the direction of the current in the conductor and is determined by left hand rule.

If you hold the palm of your left hand so that it includes the magnetic field lines of the field, and the outstretched four fingers are facing the direction of the current in the conductor, then the bent thumb will indicate the direction of movement of the conductor. When applying this rule, we must remember that the field lines come out of the north pole of the magnet.

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 the 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.