Lecture 5

Topic: "Electromagnetic induction"

Questions of the lecture:

1. The phenomenon of electromagnetic induction. Faraday's Law. Lenz rule.

2. Explanation of the phenomenon of electromagnetic induction by the Lorentz force.

3. The emergence of vortex electric field by changing the magnetic field. Explanation of the phenomenon of electromagnetic induction on that basis.

4. Vortex currents. Their useful and harmful role in engineering.

5. Amount of electricity that is transferred by the induction current. Ballistic Stoletov method of measuring the magnetic field.

1. The phenomenon of electromagnetic induction. Faraday's Law. Lenz rule.

Рис. 5.1

In 1831 Faraday discovered that in a closed circuit by changing the flux of magnetic induction through the surface, bounded by this circuit, there appears an electric current. This phenomenon is called electromagnetic induction, and the current that arises - induction. The phenomenon of electromagnetic induction can be demonstrated by experiments with a magnet, approaching or distancing it from the circuit (рис. 5.1), or changing the current and the magnetic field in the coil (Fig. 5.2).

Рис. 5.2

The phenomenon of electromagnetic induction shows that, that by changing the magnetic flux in the circuit there occurs an electromotive force ε_і – the so called ЕРС iduction.

The magnitude ε_і does not depend on how the magnetic flux changes Ф, and is determined only by the speed of this change ( ). The sign ЕРС of the induction ε_і is determined by the change in the flow direction, i.e. the ascending or descending order. This can be written in a formula as follows:

The proportionality factor k depends on the choice of units of measurement. In the international system (SI) . The sign " " takes into account the direction of ЕРС Thus, in the system SI it can be written as:

This is Faraday's law of electromagnetic induction.

We examined the occurrence of emf induction in the simplest circuit of one turn. If the path consists of N turns connected in series, then the EMF is equal to the EMF of each induction coil (Fig. 5.Z):

Let:

Fig. 5.3

Then:

The magnitude , is referred to as full magnetic flux.

Fig. 5.4

Let us consider in more detail what direction should the induction current have.

Рис. 5.5

Russian scientist Lenz formulated the following rule (Lenz rule): induction current is proportionally directed so as to oppose the reason that it causes. Let in circuit 1 the current І₁ flows and creates a magnetic field ₁, whose field lines penetrate the circuits 1 and 2 (fig. 5.4). If the current І₁ increases ( ), then the flux of magnetic induction Ф₂ through the circuit 2 also increases, and it arises emf induction and the current , a direction to counteract the reason that it has caused, that is, to counter increasing flux of magnetic induction. This means that the current in the circuit 2 flows in the opposite direction relative to the current I₁ and creates a stream of F_2 ', directed against the flow of F1. Now consider the case of reducing the current I₁ (Fig. 5.5). The current Ф₁, while also decreases ( ) and circuit 2 according to Lenz's rule, there is an induction current of such a direction so the created current opposed to reducing the flow Ф₂, i.e. to complement it. In this case, should have the same direction as the current І₁.