The direction of the magnetic lines of a current-carrying conductor. Ampere's hypothesis

Let us calculate the field created by a current flowing through a thin straight wire of infinite length.

Magnetic field induction at an arbitrary point A(Fig. 6.12) created by the conductor element d l , will be equal

Rice. 6.12. Magnetic field of a straight conductor

Fields from different elements have the same direction (tangential to a circle with radius R, lying in a plane orthogonal to the conductor). This means we can add (integrate) absolute values

Let's express r and sin through the integration variable l

Then (6.7) can be rewritten as

Thus,

The picture of the magnetic field lines of an infinitely long straight conductor carrying current is shown in Fig. 6.13.

Rice. 6.13. Magnetic field lines of a straight conductor carrying current:
1 - side view; 2, 3 - section of the conductor by a plane perpendicular to the conductor

Rice. 6.14. Designations for the direction of current in a conductor

To indicate the direction of current in a conductor perpendicular to the plane of the figure, we will use the following notation (Fig. 6.14):

Let us recall the expression for the electric field strength of a thin thread charged with a linear charge density

The similarity of expressions is obvious: we have the same dependence on the distance to the thread (current), the linear charge density has been replaced by current strength. But the directions of the fields are different. For a thread, the electric field is directed along the radii. The magnetic field lines of an infinite rectilinear conductor carrying current form a system of concentric circles surrounding the conductor. The directions of the power lines form a right-handed system with the direction of the current.

In Fig. Figure 6.15 presents an experiment in studying the distribution of magnetic field lines around a straight conductor carrying current. A thick copper conductor is passed through holes in a transparent plate on which iron filings are poured. After turning on a direct current of 25 A and tapping on the plate, the sawdust forms chains that repeat the shape of the magnetic field lines.

Around a straight wire perpendicular to the plate, ring lines of force are observed, located most densely near the wire. As you move away from it, the field decreases.

Rice. 6.15. Visualization of magnetic field lines around a straight conductor

In Fig. Figure 6.16 presents experiments to study the distribution of magnetic field lines around wires crossing a cardboard plate. Iron filings poured onto the plate are aligned along the magnetic field lines.

Rice. 6.16. Distribution of magnetic field lines
near the intersection of one, two or several wires with a plate

You can show how to use Ampere's law by determining the magnetic field near a wire. Let's ask the question: what is the field outside a long straight wire of cylindrical cross-section? We will make one assumption, perhaps not so obvious, but nevertheless correct: the field lines B go around the wire in a circle. If we make this assumption, then Ampere's law [equation (13.16)] tells us what the magnitude of the field is. Due to the symmetry of the problem, field B has the same value at all points of the circle concentric with the wire (Fig. 13.7). Then we can easily take the line integral of B·ds. It is simply equal to the value of B multiplied by the circumference. If the radius of the circle is r, That

The total current through the loop is simply the current / in the wire, so

The magnetic field strength decreases in inverse proportion to r, distance from the wire axis. If desired, equation (13.17) can be written in vector form. Recalling that B is directed perpendicular to both I and r, we have

We highlighted the factor 1/4πε 0 with 2 because it appears frequently. It is worth remembering that it is exactly 10 - 7 (in SI units), because an equation of the form (13.17) is used to definitions units of current, ampere. At a distance of 1 m a current of 1 A creates a magnetic field equal to 2·10 - 7 weber/m2.

Since the current creates a magnetic field, it will act with some force on the adjacent wire through which the current also passes. In ch. 1 we described a simple experiment showing the forces between two wires through which current flows. If the wires are parallel, then each of them is perpendicular to the B field of the other wire; then the wires will repel or attract each other. When currents flow in one direction, the wires attract; when currents flow in opposite directions, they repel.

Let's take another example, which can also be analyzed using Ampere's law, if we also add some information about the nature of the field. Let there be a long wire coiled into a tight spiral, the cross-section of which is shown in Fig. 13.8. This spiral is called solenoid. We observe experimentally that when the length of the solenoid is very large compared to the diameter, the field outside it is very small compared to the field inside. Using only this fact and Ampere's law, one can find the magnitude of the field inside.

Since the field remains inside (and has zero divergence), its lines should run parallel to the axis, as shown in Fig. 13.8. If this is the case, then we can use Ampere's law for the rectangular "curve" G in the figure. This curve travels a distance L inside the solenoid, where the field is, say, equal to B o, then goes at right angles to the field and returns back along the outer region, where the field can be neglected. The line integral of B along this curve is exactly At 0 L, and this must equal 1/ε 0 c 2 times the total current inside G, i.e. NI(where N is the number of solenoid turns along the length L). We have

Or by entering n- number of turns per unit length solenoid (so n= N/L), we get

What happens to the B lines when they reach the end of the solenoid? Apparently, they somehow diverge and return to the solenoid from the other end (Fig. 13.9). Exactly the same field is observed outside a magnetic rod. well and what is it magnet? Our equations say that field B arises from the presence of currents. And we know that ordinary iron bars (not batteries or generators) also create magnetic fields. You might expect that there would be other terms on the right-hand side of (13.12) or (16.13) representing the "density of magnetized iron" or some similar quantity. But there is no such member. Our theory says that the magnetic effects of iron arise from some internal currents already taken into account by the j term.

Matter is very complex when viewed from a deep point of view; We were already convinced of this when we tried to understand dielectrics. In order not to interrupt our presentation, we will postpone a detailed discussion of the internal mechanism of magnetic materials such as iron. For now we will have to accept that any magnetism arises due to currents and that there are constant internal currents in a permanent magnet. In the case of iron, these currents are created by electrons rotating around their own axes. Each electron has a spin that corresponds to a tiny circulating current. One electron, of course, does not produce a large magnetic field, but an ordinary piece of matter contains billions and billions of electrons. Usually they rotate in any way so that the overall effect disappears. The surprising thing is that in a few substances like iron, most of the electrons rotate around axes directed in one direction - in iron, two electrons from each atom take part in this joint movement. A magnet contains a large number of electrons spinning in the same direction, and, as we will see, their combined effect is equivalent to the current circulating across the surface of the magnet. (This is very similar to what we find in dielectrics—a uniformly polarized dielectric is equivalent to a distribution of charges on its surface.) It is therefore no coincidence that a bar magnet is equivalent to a solenoid.

If you bring a magnetic needle to a straight conductor carrying an electric 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. This indicates that the needle is subject to special forces called magnetic forces. In addition to the effect on the magnetic needle, the magnetic field affects moving charged particles and current-carrying conductors located in the magnetic field. In conductors moving in a magnetic field, or in stationary conductors located in an alternating magnetic field, an inductive emission occurs. d.s.

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

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

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 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. 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. 79). This shows that the direction of magnetic induction lines changes with the direction of current in the conductor.

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

The direction of magnetic induction lines around a current-carrying conductor can be determined by the “gimlet rule:”. If a gimlet (corkscrew) with a right-hand thread moves translationally 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 “gimlet rule” (Fig. 82). The magnetic field is one of the most important manifestations of electric current and cannot be

Obtained independently and separately from current. A magnetic field is characterized by a 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 a generalization of experimental data, was established by Biot and Savart (Fig. 83). Measuring the magnetic fields of electric currents of various sizes and shapes by the deflection of the magnetic needle, both scientists came to the conclusion that every current element creates a magnetic field at some distance from itself, the magnetic induction AB of which is directly proportional to the length A1 of this element, the magnitude of the flowing current I, sine 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 gn = 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 using 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 us to calculate the magnetic induction of an infinitely long straight conductor:

where is the distance from the conductor to the point where it is determined

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

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

Sometimes they use another unit of tension - the 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 magnetic induction line.

The product of magnetic induction and the magnitude 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 gf cm2.

If you bring the magnetic needle close, it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the needle. This indicates that special forces act on the arrow, which are called magnetic forces. In addition to the effect on the magnetic needle, the magnetic field affects moving charged particles and current-carrying conductors located in the magnetic field. In conductors moving in a magnetic field, or in stationary conductors located in an alternating magnetic field, an inductive electromotive force (emf) arises.

A magnetic field

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

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

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 are the so-called magnetic induction lines (Figure 1). 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 put 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 (Figure 2). This shows that the direction of magnetic induction lines changes with the direction of current in the conductor.

To show the direction of the current in the conductor shown in section, a symbol has been adopted, which we will use in the future. If you mentally place an arrow in the conductor in the direction of the current (Figure 3), then in the 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).

Figure 3. Symbol for the direction of current in conductors

The gimlet rule allows you to determine the direction of magnetic induction lines around a current-carrying conductor. 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 (Figure 4).

A magnetic needle introduced into the magnetic field of a current-carrying conductor is located along the magnetic induction lines. Therefore, to determine its location, you can also use the “gimlet rule” (Figure 5). The magnetic field is one of the most important manifestations of electric current and cannot be obtained independently and separately from the current.


Figure 4. Determining the direction of magnetic induction lines around a current-carrying conductor using the “gimlet rule”	Figure 5. Determining the direction of deviation of a magnetic needle brought to a conductor with current, according to the “gimlet rule”

Magnetic induction

A magnetic field is characterized by a 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 (Figure 6). Measuring the magnetic fields of electric currents of various sizes and shapes by the deflection of the magnetic needle, both scientists came to the conclusion that every current element creates a magnetic field at some distance from itself, the magnetic induction of which is Δ B is directly proportional to the length Δ l this element, the magnitude of the flowing current I, the sine of the angle α 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:

Where K– coefficient depending on the magnetic properties of the medium and on the chosen system of units.

In the absolute practical rationalized system of units of ICSA

where µ 0 – magnetic permeability of vacuum or magnetic constant in the MCSA system:

µ 0 = 4 × π × 10 -7 (henry/meter);

Henry (gn) – unit of inductance; 1 gn = 1 ohm × sec.

µ – relative magnetic permeability– a dimensionless coefficient showing how many times the magnetic permeability of a given material is greater than the magnetic permeability of vacuum.

The dimension of magnetic induction can be found using the formula

Volt-second is also called Weber (wb):

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

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

Where A– the distance from the conductor to the point where the magnetic induction is determined.

Magnetic field strength

The ratio of magnetic induction to the product of magnetic permeabilities µ × µ 0 is called magnetic field strength and is designated by the letter H:

B = H × µ × µ 0 .

The last equation connects two magnetic quantities: induction and magnetic field strength.

Let's find the dimension H:

Sometimes another unit of measurement of magnetic field strength is used - Oersted (er):

1 er = 79,6 A/m ≈ 80 A/m ≈ 0,8 A/cm .

Magnetic field strength H, like 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 magnetic induction line or magnetic induction line.

Magnetic flux

The product of magnetic induction by the area perpendicular to the direction of the field (magnetic induction vector) is called flux of the magnetic induction vector or simply magnetic flux and is designated by the letter F:

F = B × S .

Magnetic flux dimension:

that is, magnetic flux is measured in volt-seconds or webers.

The smaller unit of magnetic flux is Maxwell (mks):

1 wb = 108 mks.
1mks = 1 gs× 1 cm 2.

Video 1. Ampere's hypothesis

Video 2. Magnetism and electromagnetism

Electric current flowing through a conductor creates a magnetic field around this conductor (Fig. 7.1). The direction of the resulting magnetic field is determined by the direction of the current.
A method for indicating the direction of electric current in a conductor is shown in Fig. 7.2: point in Fig. 7.2(a) can be thought of as the tip of the arrow indicating the direction of the current towards the observer, and the cross as the tail of the arrow indicating the direction of the current away from the observer.
The magnetic field arising around a current-carrying conductor is shown in Fig. 7.3. The direction of this field is easily determined using the rule of the right screw (or the rule of the gimlet): if the tip of the gimlet is aligned with the direction of the current, then when it is screwed in, the direction of rotation of the handle will coincide with the direction of the magnetic field.

Rice. 7.1. Magnetic field around a conductor carrying current.

Rice. 7.2. Designation of the direction of current (a) towards the observer and (b) away from the observer.

Field created by two parallel conductors

1. The directions of currents in the conductors coincide. In Fig. Figure 7.4(a) shows two parallel conductors located at some distance from each other, and the magnetic field of each conductor is depicted separately. In the gap between the conductors, the magnetic fields they create are opposite in direction and cancel each other out. The resulting magnetic field is shown in Fig. 7.4(b). If the direction of both currents is reversed, then the direction of the resulting magnetic field will also be reversed (Fig. 7.4(b)).

Rice. 7.4. Two conductors with the same directions of currents (a) and their resulting magnetic field (6, c).

2. The directions of currents in conductors are opposite. In Fig. Figure 7.5(a) shows the magnetic fields for each conductor separately. In this case, in the gap between the conductors, their fields are summed up and here the resulting field (Fig. 7.5(b)) is maximum.

Rice. 7.5. Two conductors with opposite directions of currents (a) and their resulting magnetic field (b).

Rice. 7.6. Magnetic field of the solenoid.

A solenoid is a cylindrical coil consisting of a large number of turns of wire (Fig. 7.6). When current flows through the turns of the solenoid, the solenoid behaves like a bar magnet with north and south poles. The magnetic field it creates is no different from the field of a permanent magnet. The magnetic field inside the solenoid can be enhanced by winding a coil around a magnetic core of steel, iron, or other magnetic material. The strength (magnitude) of the magnetic field of the solenoid also depends on the strength of the transmitted electric current and the number of turns.

Electromagnet

The solenoid can be used as an electromagnet, with the core being made of a soft magnetic material such as ductile iron. The solenoid behaves like a magnet only when electric current flows through the coil. Electromagnets are used in electric bells and relays.

Conductor in a magnetic field

In Fig. Figure 7.7 shows a current-carrying conductor placed in a magnetic field. It can be seen that the magnetic field of this conductor is added to the magnetic field of a permanent magnet in the area above the conductor and subtracted in the area below the conductor. Thus, a stronger magnetic field is located above the conductor, and a weaker one is below (Fig. 7.8).
If you reverse the direction of the current in a conductor, the shape of the magnetic field will remain the same, but its magnitude will be greater under the conductor.

Magnetic field, current and motion

If a conductor with current is placed in a magnetic field, then a force will act on it, which tries to move the conductor from an area of a stronger field to an area of a weaker one, as shown in Fig. 7.8. The direction of this force depends on the direction of the current, as well as on the direction of the magnetic field.

Rice. 7.7. Conductor with current in a magnetic field.

Rice. 7.8. Result field

The magnitude of the force acting on a current-carrying conductor is determined by both the magnitude of the magnetic field and the force of the boom flowing through this conductor.
The movement of a conductor placed in a magnetic field when current is passed through it is called the motor principle. The operation of electric motors, magnetoelectric measuring instruments with a moving coil and other devices is based on this principle. If a conductor is moved in a magnetic field, a current is generated in it. This phenomenon is called the generator principle. The operation of direct and alternating current generators is based on this principle.

Until now, we have considered the magnetic field associated only with a direct electric current. In this case, the direction of the magnetic field is unchanged and is determined by the direction of the permanent dock. When alternating current flows, an alternating magnetic field is created. If a separate coil is placed in this alternating field, then an emf (voltage) will be induced (induced) in it. Or if two separate coils are placed in close proximity to each other, as shown in Fig. 7.9. and apply an alternating voltage to one winding (W1), then a new alternating voltage (induced EMF) will arise between the terminals of the second winding (W2). This is the working principle of a transformer.

Rice. 7.9. Induced emf.

This video explains the concepts of magnetism and electromagnetism: