Magnetic induction

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We know that a conductor with current placed in amagnetic field, is exposed to force. Its direction depends on the direction of the field lines and the direction of the current: if the latter are known, the direction of the force can be determined using the rule of the left hand or the right screw.

Let us now consider the extent to which this force depends. Let us turn to experience.

Suspend the lever arm to the left armlinear conductor AB and place it between the poles N and S of the electromagnet so that it is perpendicular to the lines of force of the magnetic field. In series with this conductor, we turn on the ammeter, and also the rheostat, with which it is possible to measure the current in our conductor. We balance the balance and close the circuit. Let the current in the conductor AB be directed from B to A. The equilibrium of the scales is violated; to restore it, the right cup will have to put additional weights, the weight of which will be equal to the force that acts on the conductor vertically down. We now change the current in our conductor; we notice that as the current increases, the force that acts on the conductor also increases. Changes will show us that the force with which a magnetic field affects the conductor is directly proportional to the current flowing through it.

Does this force depend on the length of the conductor AB? To solve this problem, we will take conductors of different lengths with the same current. Measurements will show us that the force with which a magnetic field acts on a conductor with a current will be directly proportional to the length of the part of the conductor located in the magnetic field.

Let F be the force that acts on a conductor with current placed in a magnetic field, l is the length of this conductor and I is the current in it.

With a change in the length of the conductor l and the current in it, as we have seen, the force F

The ratio of the force F to the length of the conductor I and the current in it is a constant value, independent of the current in it; consequently, the magnitude of this ratio can characterize the magnetic field.

This value is called the magnetic induction or induction of the magnetic field.

We denote the magnetic induction by B. By definition, we can write:

B = F / (I · l).

In the SI system, the unit of magnetic inductionis the induction of a field in which a conductor with a current of 1 A and a length of 1 m is exposed to a force of 1 N. The name of this unit is 1 newton / (ampere meter) (abbreviated to 1 N / (A˖m)).

Let us show that 1 N / (A˖m) = 1 (V˖sec) / m²:

1 N / (А˖м) = 1 (Н˖м) / (А˖м²) = 1 j / (А˖м²) = 1 (В˖А˖се) / (А˖м²) = 1 (В˖ sec) / m².

A unit of 1 volt-second is called a Weber (Vb). Therefore, 1 in / m² or 1 Tesla (T) is a unit of magnetic induction. Whereas in the system of measuring the SGSM the unit of measurement of magnetic induction is gauss (Gs):

1 T = 10⁴ Gs.

Magnetic induction is a vector quantity. The direction of the induction vector at a given point coincides with the direction of the magnetic force line passing through this point.

In the SI system, magnetic induction is the force characteristic of a magnetic field, similar to the way the electric field strength expresses the force characteristic of an electric field.

Knowing the induction of the magnetic field, we can calculate its force acting on the conductor with current, according to the formula:

F = BI l.

In a conductor with a current, charges move not onlychaotically in different directions, but also in a certain direction. Each of the charges is affected by a magnetic force, which is transmitted to the conductor. The sum of all forces from the chaotic motion is zero, and the sum of the forces of directed motion is called the Ampere force.

In the general case, the magnitude of the force that acts on a conductor with a current placed in a magnetic field is determined by the Ampere law:

F = BI l sin α, where α is the angle between the current direction (I) and the magnetic field vector (B).

The induction of the magnetic field is numerically equal to the force,with which the magnetic field acts on a unit current element perpendicular to the induction vector. Magnetic induction depends on the properties of the medium.

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