Two parallel conductors are repelled by current. Two parallel conductors

The laws of Biot - Savart - Laplace and Ampère are used to determine the force of interaction of two parallel conductors with current. Consider two infinite rectilinear conductors with currents I1 and I2, the distance between which is equal to a. On fig. 1.10 conductors are located perpendicular to the drawing. The currents in them are directed in the same way (because of the drawing on us) and are indicated by dots. Each of the conductors creates a magnetic field that acts on the other conductor. The current I1 creates a magnetic field around itself, the lines of magnetic induction of which are concentric circles. Direction is determined by the rule of the right screw, and its module according to the Biot-Savart-Laplace law. According to the above calculations, the module is equal to
Then, according to Ampère's law, dF1=I2B1dl or
and likewise
. H
power direction , with which the field acts on the section dℓ of the second conductor with current I 2 (Fig. 1.10), is determined by the left hand rule (see Section 1.2). As can be seen from Fig. 1.10 and calculations, the forces
identical in modulus and opposite in direction. In our case, they are directed towards each other and the conductors are attracted. If the currents flow in opposite directions, then the forces arising between them repel the conductors from each other. So, parallel currents (of the same direction) attract, and anti-parallel (opposite directions) repel. To determine the force F acting on a conductor of finite length ℓ, it is necessary to integrate the resulting equality over ℓ from 0 to ℓ:
With magnetic interaction, the law of action and reaction is fulfilled, i.e. Newton's third law:

.

1.5. The action of a magnetic field on a moving charged particle [email protected]

As already noted, the most important feature magnetic field is that it acts only on moving electric charges. As a result of the experiments, it was found that any charged particle moving in a magnetic field experiences the action of a force F, which is proportional to the magnitude of the magnetic field at this point. The direction of this force is always perpendicular to the velocity of the particle and depends on the angle between the directions
. This force is called Lorentz force. The modulus of this force is equal to
where q is the charge value; v is the speed of its movement; is the field magnetic induction vector; α is the angle between vectors and . In vector form, the expression for the Lorentz force is
.

For the case when the charge velocity is perpendicular to the magnetic induction vector, the direction of this force is determined using the left hand rule: if the palm of the left hand is positioned so that the vector entered the palm, and point the fingers along (for q>0), then the thumb bent at a right angle will indicate the direction of the Lorentz force for q>0 (Fig. 1.11, a). For q< 0 сила Лоренца имеет противоположное направление (рис.1.11,б).

Since this force is always perpendicular to the speed of the particle, it only changes the direction of the speed, not its modulus, and therefore the Lorentz force does no work. That is, the magnetic field does not do work on a charged particle moving in it and its kinetic energy does not change during this movement.

The deflection of a particle caused by the Lorentz force depends on the sign of q. This is the basis for determining the sign of the charge of particles moving in magnetic fields. The magnetic field does not act on a charged particle (
) in two cases: if the particle is stationary (
) or if the particle moves along the magnetic field line. In this case the vectors
are parallel and sinα=0. If the velocity vector perpendicular , then the Lorentz force creates a centripetal acceleration and the particle will move in a circle. If the velocity is directed at an angle to , then the charged particle moves in a spiral, the axis of which is parallel to the magnetic field.

This phenomenon is the basis for the work of all charged particle accelerators - devices in which beams of high-energy particles are created and accelerated under the action of electric and magnetic fields.

The action of the Earth's magnetic field near the earth's surface changes the trajectory of particles emitted by the Sun and stars. This explains the so-called latitudinal effect, which consists in the fact that the intensity of cosmic rays reaching the Earth is less near the equator than at higher latitudes. The action of the Earth's magnetic field explains the fact that the aurora is observed only at the highest latitudes, in the Far North. It is in that direction that the Earth's magnetic field deflects charged cosmic particles, which cause an atmospheric glow called the aurora.

In addition to the magnetic force, the electric force already familiar to us can also act on the charge.
, and the resulting electromagnetic force acting on the charge has the form

E
that formula is called Lorentz formula. For example, electrons in cathode-ray tubes of televisions, radars, electron oscilloscopes, and electron microscopes are exposed to the action of such a force.

Let's apply Ampère's law to calculate the force of interaction of two long straight conductors with currents I 1 and I 2 at a distance d from each other (Fig. 6.26).

Rice. 6.26. Force interaction of rectilinear currents:
1 - parallel currents; 2 - antiparallel currents

Conductor with current I 1 creates an annular magnetic field, the value of which at the location of the second conductor is

This field is directed "away from us" orthogonally to the plane of the figure. The element of the second conductor experiences the action of the Ampère force from the side of this field

Substituting (6.23) into (6.24), we get

At parallel currents strength F 21 is directed to the first conductor (attraction), with antiparallel - in reverse side(repulsion).

Similarly, the element of conductor 1 is affected by a magnetic field created by a conductor with current I 2 at a point in space with an element with power F 12 . Arguing in the same way, we find that F 12 = –F 21 , that is, in this case Newton's third law is satisfied.

So, the force of interaction of two rectilinear infinitely long parallel conductors, calculated per element of the length of the conductor, is proportional to the product of the current forces I 1 and I 2 flowing in these conductors, and is inversely proportional to the distance between them. In electrostatics, two long charged filaments interact according to a similar law.

On fig. 6.27 presents an experiment demonstrating the attraction of parallel currents and the repulsion of antiparallel ones. For this, two aluminum strips are used, suspended vertically next to each other in a loosely stretched state. When parallel direct currents of about 10 A are passed through them, the tapes are attracted. and when the direction of one of the currents changes to the opposite, they repel each other.

Rice. 6.27. Force interaction of long straight conductors with current

Based on the formula (6.25), the unit of current strength is set - ampere, which is one of the base units in the SI.

Example. On two thin wires bent in the form of identical rings with a radius R\u003d 10 cm, the same currents flow I= 10 A each. The planes of the rings are parallel, and the centers lie on a straight line orthogonal to them. The distance between the centers is d= 1 mm. Find the interaction forces of the rings.

Solution. In this problem, it should not be embarrassing that we only know the law of interaction of long straight conductors. Since the distance between the rings is much less than their radius, the interacting elements of the rings "do not notice" their curvature. Therefore, the force of interaction is given by expression (6.25), where instead of it is necessary to substitute the circumference of the rings. We then get

If conductors with currents of the same direction are located close to one another, then the magnetic lines of these conductors, covering both conductors, having the property of longitudinal tension and tending to shorten, will force the conductors to attract (Fig. 90, a).

Magnetic lines two conductors with currents of different directions in the space between the conductors are directed in the same direction. Magnetic lines that have the same direction will repel each other. Therefore, conductors with currents of the opposite direction repel each other (Fig. 90, b).

Consider the interaction of two parallel conductors with currents located at a distance a from one another. Let the length of the conductors be l.

The magnetic induction created by the current I 1 on the location line of the second conductor is equal to

An electromagnetic force will act on the second conductor

The magnetic induction created by the current I 2 on the location line of the first conductor will be equal to

and an electromagnetic force acts on the first conductor

equal in magnitude to the force F2

The principle of operation of electrodynamic measuring instruments is based on the electromechanical interaction of conductors with current; used in direct and especially alternating current circuits.

Tasks for independent solution

1. Determine the strength of the magnetic field created by the current 100 a, passing along a long straight conductor at a point 10 cm.

2. Determine the strength of the magnetic field created by the current 20 a, passing through a ring conductor with a radius of 5 cm at a point at the center of the loop.

3. Determine magnetic flux passing through a piece of nickel placed in a uniform magnetic field of 500 a/m. The cross-sectional area of ​​a piece of nickel is 25 ohm 2 (relative magnetic permeability of nickel is 300).

4. straight conductor length 40 cm placed in a uniform magnetic field at an angle of 30°C to the direction of the magnetic field. Passes along the conductor § current 50 BUT. The field induction is 5000 ee. Determine the force with which the conductor is pushed out of the magnetic field.

5. Determine the force with which two rectilinear conductors located parallel in the air repel each other. Conductor length 2 m, distance between them 20 cm. Currents in conductors of 10 BUT.

test questions

1. What experience can be used to make sure that a magnetic field is formed around a current-carrying conductor?

2. What are the properties of magnetic lines?

3. How to determine the direction of magnetic lines?

4. What is called a solenoid and what is its magnetic field?

5. How to determine the poles of the solenoid?

6. What is called an electromagnet and how to determine its poles?

7. What is hysteresis?

8. What are the forms of electromagnets?

9. How do conductors interact with each other through which electric current flows?

10. What acts on a current-carrying conductor in a magnetic field?

11. How to determine the direction of the force acting on a current-carrying conductor in a magnetic field?

12. On what principle is the operation of electric motors based?

13. What bodies are called ferromagnetic?