Electrical and magnetic phenomena are closely related. And if current generates magnetism, then the opposite phenomenon must also exist - the appearance of electric current when the magnet moves. This is the reasoning of the English scientist Michael Faraday, who in 1822 made the following entry in his laboratory diary: “Convert magnetism into electricity.”
This event was preceded by the discovery of the phenomenon of electromagnetism by the Danish physicist Hans Christian Oersted, who discovered the emergence of a magnetic field around a current-carrying conductor. For many years, Faraday conducted various experiments, but his first experiments did not bring him success. The main reason was that the scientist did not know that only an alternating magnetic field can create an electric current. The real result was achieved only in 1831.
Faraday's experiments
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In an experiment carried out on August 29, 1931, the scientist wrapped coils of wire around opposite sides of the iron thin ring. He connected one wire to a galvanometer. At the moment the second wire was connected to the battery, the galvanometer needle sharply deviated and returned to its original position. The same picture was observed when the contact with the battery was opened. This meant that an electric current appeared in the circuit. It arose as a result of the fact that the magnetic field lines created by the turns of the first wire crossed the turns of the second wire and generated a current in them.
Faraday's experiment
A few weeks later, an experiment was carried out with a permanent magnet. Faraday connected a galvanometer to a coil of copper wire. Then, with a sharp movement, he pushed a cylindrical magnetic rod inside. At this moment, the galvanometer needle also swung sharply. When the rod was removed from the coil, the arrow also swung, but in the opposite direction. And this happened every time the magnet was pushed or pushed out of the coil. That is, current appeared in the circuit when the magnet moved in it. This is how Faraday managed to “transform magnetism into electricity.”
Faraday in the laboratory
Current in the coil also appears if, instead of a permanent magnet inside it, you move another coil connected to a current source.
In all these cases happened a change in the magnetic flux passing through the coil circuit, which led to the appearance of an electric current in a closed circuit. This is a phenomenon electromagnetic induction , and the current is induced current .
It is known that a current exists in a closed circuit if it is maintained by a potential difference using an electromotive force (EMF). Consequently, when the magnetic flux in the circuit changes, such an EMF arises in it. It is called induced emf .
Faraday's law
Michael Faraday
The magnitude of electromagnetic induction does not depend on the reason why the magnetic flux changes - whether the magnetic field itself changes or the circuit moves in it. It depends on the rate of change of the magnetic flux passing through the circuit.
Where ε – EMF acting along the contour;
F V – magnetic flux.
The magnitude of the EMF of a coil in an alternating magnetic field is affected by the number of turns in it and the magnitude of the magnetic flux. Faraday's law in this case looks like this:
Where N – number of turns;
F V – magnetic flux through one turn;
Ψ – flux linkage, or the total magnetic flux interlocking with all turns of the coil.
Ψ = N ·F i
F i – flow passing through one turn.
Even a weak magnet can create a large induction current if the speed of movement of this magnet is high.
Since an induced current appears in conductors when the magnetic flux passing through them changes, it will also appear in a conductor that moves in a stationary magnetic field. The direction of the induction current in this case depends on the direction of movement of the conductor and is determined by the right-hand rule: “ If you position the palm of your right hand in such a way that the magnetic field lines enter it, and the thumb bent by 90 0 would indicate the direction of movement of the conductor, then the extended 4 fingers will indicate the direction of the induced EMF and the direction of the current in the conductor».
Lenz's rule
Emily Khristianovich Lenz
The direction of the induction current is determined by a rule that applies in all cases when such a current occurs. This rule was formulated by a Russian physicist of Baltic origin Emily Khristianovich Lenz: “ The induced current arising in a closed circuit has such a direction that the magnetic flux it creates counteracts the change in the magnetic flux that this current caused.
It should be noted that this conclusion was made by the scientist based on the results of experiments. Lenz created a device consisting of a freely rotating aluminum plate, at one end of which a solid ring of aluminum was attached, and at the other - a ring with a notch.
If the magnet was brought closer to a solid ring, it was repelled and began to “run away.”
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As the magnet moved away, the ring tried to catch up with it.
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Nothing like this was observed with the cut ring.
Lenz explained this by saying that in the first case, the induced current creates a magnetic field, the induction lines of which are directed opposite to the induction lines of the external magnetic field. In the second case, the induction lines of the magnetic field created by the induced current coincide in direction with the induction lines of the permanent magnet field. In a cut ring, no induction current occurs, so it cannot interact with the magnet.
According to Lenz's rule, when the external magnetic flux increases, the induced current will have such a direction that the magnetic field created by it will prevent such an increase. If the external magnetic flux decreases, then the magnetic field of the induction current will support it and prevent it from decreasing.
Electric current generator
Alternator
Faraday's discovery of electromagnetic induction made it possible to use this phenomenon in practice.
What happens if you rotate the coil with bo more turns of metal wire in a stationary magnetic field? The magnetic flux passing through the coil circuit will constantly change. And an EMF of electromagnetic induction will arise in it. This means that such a design can generate electric current. The operation of alternating current generators is based on this principle.
The generator consists of 2 parts - the rotor and the stator. The rotor is the moving part. In low-power generators, a permanent magnet most often rotates. Powerful generators use an electromagnet instead of a permanent magnet. Rotating, the rotor creates a changing magnetic flux, which generates an electric induction current in the turns of the winding located in the grooves of the stationary part of the generator - the stator. The rotor is driven by a motor. This could be a steam engine, a water turbine, etc.
Transformer
This is perhaps the most common device in electrical engineering, designed to convert electrical current and voltage. Transformers are used in radio engineering and electronics. Without them, it is impossible to transmit electricity over long distances.
The simplest transformer consists of two coils having a common metal core. Alternating current supplied to one of the coils creates an alternating magnetic field in it, which is amplified by the core. The magnetic flux of this field, penetrating the turns of the second coil, creates an induction electric current in it. Since the magnitude of the induced emf depends on the number of turns, by changing their ratio in the coils, the magnitude of the current can also be changed. This is very important, for example, when transmitting electricity over long distances. After all, during transportation large losses occur due to the fact that the wires heat up. By reducing the current using a transformer, these losses are reduced. But at the same time the tension increases. At the final stage, using a step-down transformer, the voltage is reduced and the current is increased. Of course, such transformers are much more complex.
It must be said that Faraday was not the only one who tried to create an induced current. Similar experiments were also carried out by the famous American physicist Joseph Henry. And he managed to achieve success almost simultaneously with Faraday. But Faraday was ahead of him by publishing a message about his discovery before Henry.
Topics of the Unified State Examination codifier: phenomenon of electromagnetic induction, magnetic flux, Faraday’s law of electromagnetic induction, Lenz’s rule.
Oersted's experiment showed that electric current creates a magnetic field in the surrounding space. Michael Faraday came to the idea that the opposite effect could also exist: the magnetic field, in turn, generates an electric current.
In other words, let there be a closed conductor in a magnetic field; Will an electric current arise in this conductor under the influence of a magnetic field?
After ten years of searching and experimentation, Faraday finally managed to discover this effect. In 1831 he carried out the following experiments.
1. Two coils were wound on the same wooden base; the turns of the second coil were laid between the turns of the first and insulated. The terminals of the first coil were connected to a current source, the terminals of the second coil were connected to a galvanometer (a galvanometer is a sensitive device for measuring small currents). Thus, two circuits were obtained: “current source - first coil” and “second coil - galvanometer”.
There was no electrical contact between the circuits, only the magnetic field of the first coil penetrated the second coil.
When the circuit of the first coil was closed, the galvanometer registered a short and weak current pulse in the second coil.
When a constant current flowed through the first coil, no current was generated in the second coil.
When the circuit of the first coil was opened, a short and weak current pulse again arose in the second coil, but this time in the opposite direction compared to the current when the circuit was closed.
Conclusion.
The time-varying magnetic field of the first coil generates (or, as they say, induces) electric current in the second coil. This current is called induced current.
If the magnetic field of the first coil increases (at the moment the current increases when the circuit is closed), then the induced current in the second coil flows in one direction.
If the magnetic field of the first coil decreases (at the moment the current decreases when the circuit is opened), then the induced current in the second coil flows in a different direction.
If the magnetic field of the first coil does not change (direct current through it), then there is no induced current in the second coil.
Faraday called the discovered phenomenon electromagnetic induction(i.e. “induction of electricity by magnetism”).
2. To confirm the guess that the induction current is generated variables magnetic field, Faraday moved the coils relative to each other. The circuit of the first coil remained closed all the time, a direct current flowed through it, but due to movement (approach or distance), the second coil found itself in the alternating magnetic field of the first coil.
The galvanometer again recorded the current in the second coil. The induction current had one direction when the coils approached each other, and another direction when they moved away. In this case, the strength of the induction current was greater, the faster the coils moved..
3. The first coil was replaced by a permanent magnet. When a magnet was brought inside the second coil, an induction current arose. When the magnet was pulled out, the current appeared again, but in a different direction. And again, the faster the magnet moved, the greater the strength of the induction current.
These and subsequent experiments showed that an induced current in a conducting circuit occurs in all those cases when the “number of lines” of the magnetic field penetrating the circuit changes. The strength of the induction current turns out to be greater, the faster this number of lines changes. The direction of the current will be one when the number of lines through the circuit increases, and another when they decrease.
It is remarkable that for the magnitude of the current in a given circuit, only the rate of change in the number of lines is important. What exactly happens in this case does not matter - whether the field itself changes, penetrating the stationary contour, or whether the contour moves from an area with one density of lines to an area with another density.
This is the essence of the law of electromagnetic induction. But in order to write a formula and make calculations, you need to clearly formalize the vague concept of “the number of field lines through a contour.”
Magnetic flux
The concept of magnetic flux is precisely a characteristic of the number of magnetic field lines penetrating the circuit.
For simplicity, we restrict ourselves to the case of a uniform magnetic field. Let us consider a contour of an area located in a magnetic field with induction.
Let first the magnetic field be perpendicular to the plane of the circuit (Fig. 1).
Rice. 1.
In this case, the magnetic flux is determined very simply - as the product of the magnetic field induction and the area of the circuit:
(1)
Now consider the general case when the vector forms an angle with the normal to the contour plane (Fig. 2).
Rice. 2.
We see that now only the perpendicular component of the magnetic induction vector “flows” through the circuit (and the component that is parallel to the circuit does not “flow” through it). Therefore, according to formula (1), we have . But, therefore
(2)
This is the general definition of magnetic flux in the case of a uniform magnetic field. Note that if the vector is parallel to the plane of the loop (that is), then the magnetic flux becomes zero.
How to determine magnetic flux if the field is not uniform? Let's just point out the idea. The contour surface is divided into a very large number of very small areas, within which the field can be considered uniform. For each site, we calculate its own small magnetic flux using formula (2), and then we sum up all these magnetic fluxes.
The unit of measurement for magnetic flux is weber(Wb). As we see,
Wb = T · m = V · s. (3)
Why does magnetic flux characterize the “number of lines” of the magnetic field penetrating the circuit? Very simple. The “number of lines” is determined by their density (and therefore their size - after all, the greater the induction, the denser the lines) and the “effective” area penetrated by the field (and this is nothing more than ). But the multipliers form the magnetic flux!
Now we can give a clearer definition of the phenomenon of electromagnetic induction discovered by Faraday.
Electromagnetic induction- this is the phenomenon of the occurrence of electric current in a closed conducting circuit when the magnetic flux passing through the circuit changes.
induced emf
What is the mechanism by which induced current occurs? We will discuss this later. So far, one thing is clear: when the magnetic flux passing through the circuit changes, some forces act on the free charges in the circuit - outside forces, causing the movement of charges.
As we know, the work of external forces to move a single positive charge around a circuit is called electromotive force (EMF): . In our case, when the magnetic flux through the circuit changes, the corresponding emf is called induced emf and is designated .
So, Induction emf is the work of external forces that arise when the magnetic flux through a circuit changes, moving a single positive charge around the circuit.
We will soon find out the nature of the external forces arising in this case in the circuit.
Faraday's law of electromagnetic induction
The strength of the induction current in Faraday's experiments turned out to be greater, the faster the magnetic flux through the circuit changed.
If in a short time the change in magnetic flux is equal to , then speed changes in magnetic flux are a fraction (or, which is the same, the derivative of magnetic flux with respect to time).
Experiments have shown that the strength of the induction current is directly proportional to the magnitude of the rate of change of the magnetic flux:
The module is installed in order not to be associated with negative values for now (after all, when the magnetic flux decreases, it will be ). Subsequently we will remove this module.
From Ohm's law for a complete chain we at the same time have: . Therefore, the induced emf is directly proportional to the rate of change of the magnetic flux:
(4)
EMF is measured in volts. But the rate of change of magnetic flux is also measured in volts! Indeed, from (3) we see that Wb/s = V. Therefore, the units of measurement of both parts of proportionality (4) coincide, therefore the proportionality coefficient is a dimensionless quantity. In the SI system it is set equal to unity, and we get:
(5)
That's what it is law of electromagnetic induction or Faraday's law. Let's give it a verbal formulation.
Faraday's law of electromagnetic induction. When the magnetic flux penetrating a circuit changes, an induced emf appears in this circuit equal to the modulus of the rate of change of the magnetic flux.
Lenz's rule
We will call the magnetic flux, a change in which leads to the appearance of an induced current in the circuit external magnetic flux. And the magnetic field itself, which creates this magnetic flux, we will call external magnetic field.
Why do we need these terms? The fact is that the induction current arising in the circuit creates its own own a magnetic field that, according to the principle of superposition, is added to an external magnetic field.
Accordingly, along with the external magnetic flux, own magnetic flux created by the magnetic field of an induction current.
It turns out that these two magnetic fluxes - internal and external - are interconnected in a strictly defined way.
Lenz's rule. The induced current always has a direction such that its own magnetic flux prevents a change in the external magnetic flux.
Lenz's rule allows you to find the direction of the induced current in any situation.
Let's look at some examples of applying Lenz's rule.
Let us assume that the circuit is penetrated by a magnetic field, which increases with time (Fig. (3)). For example, we bring a magnet closer to the contour from below, the north pole of which in this case is directed upward, towards the contour.
The magnetic flux through the circuit increases. The induced current will be in such a direction that the magnetic flux it creates prevents the increase in external magnetic flux. To do this, the magnetic field created by the induction current must be directed against external magnetic field.
The induced current flows counterclockwise when viewed from the direction of the magnetic field it creates. In this case, the current will be directed clockwise when viewed from above, from the side of the external magnetic field, as shown in (Fig. (3)).
Rice. 3. Magnetic flux increases
Now suppose that the magnetic field penetrating the circuit decreases with time (Fig. 4). For example, we move the magnet downward from the loop, and the north pole of the magnet points toward the loop.
Rice. 4. Magnetic flux decreases
The magnetic flux through the circuit decreases. The induced current will have a direction such that its own magnetic flux supports the external magnetic flux, preventing it from decreasing. To do this, the magnetic field of the induction current must be directed in the same direction, as the external magnetic field.
In this case, the induced current will flow counterclockwise when viewed from above, from the side of both magnetic fields.
Interaction of a magnet with a circuit
So, the approach or removal of a magnet leads to the appearance of an induced current in the circuit, the direction of which is determined by Lenz’s rule. But the magnetic field acts on the current! An Ampere force will appear acting on the circuit from the magnetic field. Where will this force be directed?
If you want to have a good understanding of Lenz's rule and the determination of the direction of the Ampere force, try answering this question yourself. This is not a very simple exercise and an excellent task for C1 on the Unified State Exam. Consider four possible cases.
1. We bring the magnet closer to the circuit, the north pole is directed towards the circuit.
2. We remove the magnet from the circuit, the north pole is directed towards the circuit.
3. We bring the magnet closer to the circuit, the south pole is directed towards the circuit.
4. We remove the magnet from the circuit, the south pole is directed towards the circuit.
Do not forget that the magnetic field is not uniform: the field lines diverge from the north pole and converge towards the south. This is very important for determining the resulting Ampere force. The result is as follows.
If you bring the magnet closer, the circuit is repelled from the magnet. If you remove the magnet, the circuit is attracted to the magnet. Thus, if the circuit is suspended on a thread, then it will always deviate in the direction of the movement of the magnet, as if following it. The location of the magnet poles does not matter in this case..
In any case, you should remember this fact - suddenly such a question comes across in part A1
This result can be explained from completely general considerations - using the law of conservation of energy.
Let's say we bring the magnet closer to the circuit. An induction current appears in the circuit. But to create a current, work must be done! Who does it? Ultimately, we are moving the magnet. We perform positive mechanical work, which is converted into positive work of external forces arising in the circuit, creating an induced current.
So our job of moving the magnet should be positive. This means that when we approach the magnet, we must overcome the force of interaction of the magnet with the circuit, which, therefore, is the force repulsion.
Now remove the magnet. Please repeat these arguments and make sure that an attractive force should arise between the magnet and the circuit.
Faraday's Law + Lenz's Rule = Module Removal
Above we promised to remove the modulus in Faraday’s law (5). Lenz's rule allows us to do this. But first we will need to agree on the sign of the induced emf - after all, without the module on the right side of (5), the magnitude of the emf can be either positive or negative.
First of all, one of two possible directions for traversing the contour is fixed. This direction is announced positive. The opposite direction of traversing the contour is called, respectively, negative. Which direction of traversal we take as positive does not matter - it is only important to make this choice.
The magnetic flux through the circuit is considered positive class="tex" alt="(\Phi > 0)"> !}, if the magnetic field penetrating the circuit is directed there, looking from where the circuit is traversed in the positive direction in a counterclockwise direction. If, from the end of the magnetic induction vector, the positive direction of the round is seen clockwise, then the magnetic flux is considered negative.
The induced emf is considered positive class="tex" alt="(\mathcal E_i > 0)"> !}, if the induced current flows in a positive direction. In this case, the direction of external forces arising in the circuit when the magnetic flux through it changes coincides with the positive direction of bypassing the circuit.
On the contrary, induced emf is considered negative if the induced current flows in a negative direction. In this case, external forces will also act along the negative direction of the circuit bypass.
So, let the circuit be in a magnetic field. We fix the direction of the positive circuit bypass. Let's assume that the magnetic field is directed there, looking from where the positive detour is made counterclockwise. Then the magnetic flux is positive: class="tex" alt="\Phi > 0"> .!}
Rice. 5. Magnetic flux increases
Therefore, in this case we have . The sign of the induced emf turned out to be opposite to the sign of the rate of change of the magnetic flux. Let's check this in another situation.
Namely, let us now assume that the magnetic flux decreases. According to Lenz's rule, the induced current will flow in the positive direction. That is, class="tex" alt="\mathcal E_i > 0"> !}(Fig. 6).
Rice. 6. Magnetic flux increases class="tex" alt="\Rightarrow \mathcal E_i > 0"> !}
This is actually the general fact: with our agreement on signs, Lenz's rule always leads to the fact that the sign of the induced emf is opposite to the sign of the rate of change of magnetic flux:
(6)
Thus, the modulus sign in Faraday’s law of electromagnetic induction is eliminated.
Vortex electric field
Let us consider a stationary circuit located in an alternating magnetic field. What is the mechanism for the occurrence of induction current in the circuit? Namely, what forces cause the movement of free charges, what is the nature of these external forces?
Trying to answer these questions, the great English physicist Maxwell discovered a fundamental property of nature: a time-varying magnetic field generates an electric field. It is this electric field that acts on free charges, causing an induced current.
The lines of the resulting electric field turn out to be closed, which is why it was called vortex electric field. The vortex electric field lines go around the magnetic field lines and are directed as follows.
Let the magnetic field increase. If there is a conducting circuit in it, then the induced current will flow in accordance with Lenz’s rule - clockwise, when viewed from the end of the vector. This means that the force acting from the vortex electric field on the positive free charges of the circuit is also directed there; This means that the vector of the vortex electric field intensity is directed exactly there.
So, the lines of intensity of the vortex electric field are directed in this case clockwise (looking from the end of the vector , (Fig. 7).
Rice. 7. Vortex electric field with increasing magnetic field
On the contrary, if the magnetic field decreases, then the lines of intensity of the vortex electric field are directed counterclockwise (Fig. 8).
Rice. 8. Vortex electric field with decreasing magnetic field
Now we can better understand the phenomenon of electromagnetic induction. Its essence lies precisely in the fact that an alternating magnetic field generates a vortex electric field. This effect does not depend on whether a closed conducting circuit is present in the magnetic field or not; With the help of a circuit we only detect this phenomenon by observing the induced current.
The vortex electric field differs in some properties from the electric fields already known to us: the electrostatic field and the stationary field of charges that form a direct current.
1. The vortex field lines are closed, while the electrostatic and stationary field lines begin on positive charges and end on negative ones.
2. The vortex field is nonpotential: its work on moving a charge along a closed loop is not zero. Otherwise, the vortex field could not create an electric current! At the same time, as we know, electrostatic and stationary fields are potential.
So, Induction emf in a stationary circuit is the work of a vortex electric field to move a single positive charge around the circuit.
Let, for example, the circuit be a ring of radius and penetrated by a uniform alternating magnetic field. Then the intensity of the vortex electric field is the same at all points of the ring. The work force with which the vortex field acts on the charge is equal to:
Therefore, for the induced emf we obtain:
Induction emf in a moving conductor
If a conductor moves in a constant magnetic field, then an induced emf also appears in it. However, the reason now is not the vortex electric field (it does not arise - after all, the magnetic field is constant), but the action of the Lorentz force on the free charges of the conductor.
Let's consider a situation that often occurs in problems. Parallel rails are located in a horizontal plane, the distance between them is equal to . The rails are in a vertical uniform magnetic field. A thin conductive rod moves along the rails at a speed of ; it remains perpendicular to the rails all the time (Fig. 9).
Rice. 9. Movement of a conductor in a magnetic field
Let's take a positive free charge inside the rod. Due to the movement of this charge together with the rod at a speed, the Lorentz force will act on the charge:
This force is directed along the axis of the rod, as shown in the figure (see this for yourself - do not forget the clockwise or left-hand rule!).
The Lorentz force plays in this case the role of an external force: it sets in motion the free charges of the rod. When moving a charge from point to point, our external force will do work:
(We also consider the length of the rod to be equal to .) Therefore, the induced emf in the rod will be equal to:
(7)
Thus, a rod is similar to a current source with a positive terminal and a negative terminal. Inside the rod, due to the action of an external Lorentz force, a separation of charges occurs: positive charges move to point , negative charges move to point .
Let us first assume that the rails do not conduct current. Then the movement of charges in the rod will gradually stop. Indeed, as positive charges accumulate at the end and negative charges at the end, the Coulomb force with which the positive free charge is repelled from and attracted to will increase - and at some point this Coulomb force will balance the Lorentz force. A potential difference equal to the induced emf (7) will be established between the ends of the rod.
Now assume that the rails and jumper are conductive. Then an induced current will appear in the circuit; it will go in the direction (from the “plus source” to the “minus” N). Let's assume that the resistance of the rod is equal (this is an analogue of the internal resistance of the current source), and the resistance of the section is equal (the resistance of the external circuit). Then the strength of the induction current will be found according to Ohm’s law for the complete circuit:
It is remarkable that expression (7) for the induced emf can also be obtained using Faraday’s law. Let's do it.
Over time, our rod travels a path and takes a position (Fig. 9). The area of the contour increases by the area of the rectangle:
The magnetic flux through the circuit increases. The magnetic flux increment is equal to:
The rate of change of magnetic flux is positive and equal to the induced emf:
We got the same result as in (7). The direction of the induction current, we note, obeys Lenz's rule. Indeed, since the current flows in the direction, its magnetic field is directed opposite to the external field and, therefore, prevents the increase in magnetic flux through the circuit.
In this example, we see that in situations where a conductor moves in a magnetic field, we can act in two ways: either using the Lorentz force as an external force, or using Faraday’s law. The results will be the same.
Induction current is a current that occurs in a closed conductive circuit located in an alternating magnetic field. This current can occur in two cases. If there is a stationary circuit penetrated by a changing flux of magnetic induction. Or when a conducting circuit moves in a constant magnetic field, which also causes a change in the magnetic flux penetrating the circuit.
Figure 1 - A conductor moves in a constant magnetic field
The cause of the induction current is the vortex electric field, which is generated by the magnetic field. This electric field acts on free charges located in a conductor placed in this vortex electric field.
Figure 2 - vortex electric field
You can also find this definition. Induction current is an electric current that arises due to the action of electromagnetic induction. If you don’t delve into the intricacies of the law of electromagnetic induction, then in a nutshell it can be described as follows. Electromagnetic induction is the phenomenon of the occurrence of current in a conducting circuit under the influence of an alternating magnetic field.
Using this law, you can determine the magnitude of the induction current. Since it gives us the value of the EMF that occurs in the circuit under the influence of an alternating magnetic field.
Formula 1 - EMF of magnetic field induction.
As can be seen from formula 1, the magnitude of the induced emf, and therefore the induced current, depends on the rate of change of the magnetic flux penetrating the circuit. That is, the faster the magnetic flux changes, the greater the induction current can be obtained. In the case when we have a constant magnetic field in which the conducting circuit moves, the magnitude of the EMF will depend on the speed of movement of the circuit.
To determine the direction of the induction current, Lenz's rule is used. Which states that the induced current is directed towards the current that caused it. Hence the minus sign in the formula for determining the induced emf.
Induction current plays an important role in modern electrical engineering. For example, the induced current generated in the rotor of an induction motor interacts with the current supplied from the power source in its stator, causing the rotor to rotate. Modern electric motors are built on this principle.
Figure 3 - asynchronous motor.
In a transformer, the induction current arising in the secondary winding is used to power various electrical devices. The magnitude of this current can be set by the transformer parameters.
Figure 4 - electrical transformer.
And finally, induced currents can also arise in massive conductors. These are the so-called Foucault currents. Thanks to them, it is possible to perform induction melting of metals. That is, eddy currents flowing in the conductor cause it to heat up. Depending on the magnitude of these currents, the conductor can heat up above the melting point.
Figure 5 - induction melting of metals.
So, we have found that induction current can have mechanical, electrical and thermal effects. All these effects are widely used in the modern world, both on an industrial scale and at the household level.
Most of the electricity in the form of alternating induction current on planet Earth is produced by humanity using induction electric generators. Direct current, also obtained from electric generators, is a special case of alternating current. There are many different designs of electric generators, but their operation is based on the same principle. This is the principle of relative movement (rotation) of the armature in the magnetic field of the inductor, or vice versa, rotation of the magnetic field of the inductor relative to the armature.
The famous Serbian scientist Nikola Tesla made a great scientific and practical contribution to the development of the science of electricity and the creation of equipment for its production. His inventions and discoveries as a physicist, engineer, and designer provided a solid foundation for the development of electrical engineering and radiophysics. Many of his ideas in these areas of science and technology are still in demand today.
Significant mechanical forces are expended to organize and maintain the operation of the electric generator, to overcome the forces of resistance to the rotation of the armature in the magnetic field of the inductor. Basically, these forces are realized in the form of various drives, such as steam, gas turbines, hydraulic turbines, internal combustion engines, etc. Electromagnetic induction is directly (directly) related to the production of electricity.
Let's consider the simplest laboratory diagram of an electric generator, shown in Fig. 1. Most industrial electric generators are constructed according to this scheme, but with a more complex design.
In the magnetic field of a permanent magnet, a conducting frame 2 made of wire rotates between the poles N and S, the ends of which are soldered to conducting rings 1. These rings are connected to contacts 3 and then to the wires of the external circuit, including the galvanometer. The frame rotates in the magnetic field of a magnet, the magnetic flux of which changes all the time. As a result of the influence of magnetic flux F on the microstructure of the frame conductors, an induction current appears in a closed circuit, which is detected by a galvanometer. In almost all physics textbooks, the value of F through a coil-frame is defined as the product of the magnetic field strength (H) by the area of the coil (S) and by the sine of the angle (a) between the direction of the magnetic field and the plane of the frame.
Replacing the angle a through (wхt), where w is the angular velocity of rotation of the coil-frame, and t is time, we obtain the formula
in which the graph of changes in the value of Ф through the frame is a sinusoid (Fig. 2).
The above formula, apart from a mathematical description of the change in the value of F through the area of the coil, does not provide anything in terms of understanding the physical meaning of the process. In this formula, instead of the turn area S, one should indicate the length of the frame conductors, since the magnetic field during the rotation of the frame interacts with the microstructure of its wires.
Similar graphs of changes in current and voltage over time, recorded by an oscilloscope, also represent a sinusoid (Fig. 3). We needed this known information only to remind us that the effect of the external magnetic field of a magnet on the coil-frame rotating in it is nothing more than a sinusoidal, pulsed interaction of the magnetic field with the microstructure of the wires of the coil-frame.
As mentioned earlier, the design of the electric generator is an oscillatory circuit. The magnetic field of the inductor-magnet (Fig. 1), which is an external magnetic field in relation to the armature-frame, affects the microstructure of the frame conductors with a magnetic flux changing according to the law of sine variation, inducing its own magnetic field in the microstructure of the armature conductors. Almost simultaneously with the beginning of the rotation of the frame, a signal-pulse from an external magnetic field passes through the rest of the closed electrical circuit, and throughout the entire volume of the circuit, micro sources repeat this impulse in an image and likeness, creating their own magnetic field throughout the circuit. One more impulse - and again reproduction (repetition). And so on an infinite number of times while the electric generator is running.
Let's take a closer look at this process. Let's start with an inconvenient children's question: “Why does induced current arise in a closed frame (in relation to Fig. 1), which rotates in the magnetic field of a permanent magnet, and does not arise in a stationary frame located in the same magnetic field of the magnet, in whatever position was there a frame? According to quantum physics, electrons-electric charges revolve around the nucleus of an atom at high speed. In this case, electrons have two magnetic moments: orbital and spin, and according to the same quantum laws they must interact with the magnetic field (they must decelerate in the magnetic field of a stationary magnet), emitting microenergy by analogy with the northern lights. But it was not there. No radiation occurs, although the magnetic field lines (MFL) of the magnet penetrate the microstructure of the conductors at the atomic level. Why is it that micro-sources-electrons in the microstructure of conductors are so attracted to a moving magnetic field? To answer this question, let us recall the experiments of the Russian scientist P.N. Lebedev to study the pressure of light on light objects in a vacuum. Copernicus also pointed out that light pressure exists by observing the tail part of comets flying near the Sun.
Let us recall some simple experiments in which the emergence of electric current as a result of electromagnetic induction is observed.
One of these experiments is shown in Fig. 253. If a coil consisting of a large number of turns of wire is quickly put on a magnet or pulled off it (Fig. 253, a), then a short-term induction current arises in it, which can be detected by the throw of the needle of a galvanometer connected to the ends of the coil. The same happens if the magnet is quickly pushed into the coil or pulled out of it (Fig. 253, b). Obviously, only the relative motion of the coil and the magnetic field matters. The current stops when this movement stops.
Rice. 253. With the relative movement of the coil and the magnet, an induced current arises in the coil: a) the coil is put on the magnet; b) the magnet moves into the coil
Let us now consider several additional experiments that will allow us to formulate in a more general form the conditions for the occurrence of an induction current.
The first series of experiments: changing the magnetic induction of the field in which the induction circuit (coil or frame) is located.
The coil is placed in a magnetic field, for example, inside a solenoid (Fig. 254, a) or between the poles of an electromagnet (Fig. 254, b). Let's install the coil so that the plane of its turns is perpendicular to the magnetic field lines of the solenoid or electromagnet. We will change the magnetic induction of the field by quickly changing the current strength in the winding (using a rheostat) or simply turning the current off and on (with a key). With each change in the magnetic field, the galvanometer needle gives a sharp rebound; this indicates the occurrence of an induction electric current in the coil circuit. When the magnetic field strengthens (or appears), a current in one direction will appear, and when it weakens (or disappears), a current in the opposite direction will appear. Let us now perform the same experiment, installing the coil so that the plane of its turns is parallel to the direction of the magnetic field lines (Fig. 255). The experiment will give a negative result: no matter how we change the magnetic induction of the field, we will not detect an induction current in the coil circuit.
Rice. 254. An induced current appears in a coil when the magnetic induction changes if the plane of its turns is perpendicular to the magnetic field lines: a) the coil in the solenoid field; b) a coil in the field of an electromagnet. Magnetic induction changes when the switch is closed and opened or when the current in the circuit changes
Rice. 255. Induction current does not occur if the plane of the coil turns is parallel to the magnetic field lines
The second series of experiments: changing the position of a coil located in a constant magnetic field.
Let's place the coil inside the solenoid, where the magnetic field is uniform, and quickly rotate it through a certain angle around an axis perpendicular to the direction of the field (Fig. 256). With any such rotation, the galvanometer connected to the coil detects an induced current, the direction of which depends on the initial position of the coil and on the direction of rotation. When the coil rotates 360° completely, the direction of the induction current changes twice: each time the coil passes a position in which its plane is perpendicular to the direction of the magnetic field. Of course, if you rotate the coil very quickly, the induced current will change its direction so often that the needle of a conventional galvanometer will not have time to follow these changes and a different, more “obedient” device will be needed.
Rice. 256. When a coil rotates in a magnetic field, an induced current arises in it
If, however, the coil is moved so that it does not rotate relative to the direction of the field, but only moves parallel to itself in any direction along the field, across it, or at any angle to the direction of the field, then no induced current will arise. Let us emphasize once again: the experiment of moving the coil is carried out in a uniform field (for example, inside a long solenoid or in the Earth’s magnetic field). If the field is non-uniform (for example, near the pole of a magnet or electromagnet), then any movement of the coil can be accompanied by the appearance of an induction current, with the exception of one case: the induction current does not arise if the coil moves in such a way that its plane remains parallel to the direction of the field all the time (i.e. i.e. no magnetic field lines pass through the coil).
The third series of experiments: changing the area of a circuit located in a constant magnetic field.
A similar experiment can be carried out according to the following scheme (Fig. 257). In a magnetic field, for example, between the poles of a large electromagnet, we place a circuit made of flexible wire. Let the contour initially have the shape of a circle (Fig. 257a). With a quick movement of the hand, you can tighten the contour into a narrow loop, thus significantly reducing the area it covers (Fig. 257, b). The galvanometer will show the occurrence of an induction current.
Rice. 257. An induced current appears in a coil if the area of its circuit, located in a constant magnetic field and located perpendicular to the magnetic field lines, changes (the magnetic field is directed away from the observer)
It is even more convenient to carry out an experiment with changing the contour area according to the scheme shown in Fig. 258. In a magnetic field there is a circuit, one of the sides of which (in Fig. 258) is made movable. Each time it moves, the galvanometer detects the occurrence of an induction current in the circuit. Moreover, when moving to the left (increasing area), the induction current has one direction, and when moving to the right (decreasing area) - in the opposite direction. However, even in this case, changing the area of the circuit does not produce any induced current if the plane of the circuit is parallel to the direction of the magnetic field.
Rice. 258. When the rod moves and, as a result, the area of the circuit located in a magnetic field changes, a current arises in the circuit.
By comparing all the described experiments, we can formulate the conditions for the occurrence of an induced current in a general form. In all the cases considered, we had a circuit placed in a magnetic field, and the plane of the circuit could make one or another angle with the direction of magnetic induction. Let us denote the area limited by the contour by , the magnetic induction of the field by , and the angle between the direction of the magnetic induction and the plane of the contour by . In this case, the component of magnetic induction perpendicular to the plane of the circuit will be equal in magnitude (Fig. 259)
Rice. 259. Decomposition of magnetic induction into a component perpendicular to the plane of the induction loop, and a component parallel to this plane
We will call the product the flux of magnetic induction, or, in short, the magnetic flux through the circuit; We will denote this quantity by the letter . Thus,
. (138.1) through this contour remains unchanged. So:
Whenever there is a change in the magnetic flux through a conducting circuit, an electric current arises in this circuit.
This is one of the most important laws of nature - the law of electromagnetic induction, discovered by Faraday in 1831.
138.1. Coils I and II are located one inside the other (Fig. 260). The first circuit includes a battery, the second circuit contains a galvanometer. If an iron rod is pushed into or out of the first coil, the galvanometer will detect the occurrence of an induction current in the second coil. Explain this experience.
Rice. 260. For exercise 138.1
138.2. The wire frame rotates in a uniform magnetic field around an axis parallel to the magnetic induction. Will an induced current appear in it?
138.3. Does e. d.s. induction at the ends of the steel axle of a car when it moves? In what direction is the car moving? d.s. largest and at what point is it smallest? Does it depend? d.s. induction from car speed?
138.4. The car chassis, together with its two axles, forms a closed conductive circuit. Is current induced in it when the car moves? How can the answer to this problem be reconciled with the results of Problem 138.3?
138.5. Why did lightning strikes sometimes cause damage to sensitive electrical measuring instruments several meters from the point of impact, and melt fuses in the lighting network?