As we have already found out, electric current is capable of generating magnetic fields. The question arises: can a magnetic field cause the appearance electric current? This problem was solved by the English physicist Michael Faraday, who discovered the phenomenon of electromagnetic induction in 1831 ^ A conductor twisted into a coil is closed on a galvanometer (Fig. 3.19). If a permanent magnet is inserted into the coil, the galvanometer will indicate the presence of current during the entire period of time while the magnet moves relative to the coil. When pulling the magnet out of the coil, the galvanometer shows the presence of a current in the opposite direction. Changes in the direction of the current occur when the retractable or retractable pole of the magnet changes.
Similar results were observed when replacing permanent magnet electromagnet (coil with current). If both coils are fixed motionless, but in one of them the current value is changed, then at this moment an induction current is observed in the other coil.
THE PHENOMENON OF ELECTROMAGNETIC INDUCTION consists in the appearance of an electromotive force (emf) of induction in a conducting circuit, through which the flux of the magnetic induction vector changes. If the circuit is closed, then an induction current arises in it.
Discovery of the phenomenon of electromagnetic induction:
1) showed relationship between electric and magnetic fields;
2) suggested method of generating electric current by using magnetic field.
Basic properties of induction current:
1. Induction current occurs whenever there is a change in the magnetic induction flux coupled to the circuit.
2. The strength of the induction current does not depend on the method of changing the flux of magnetic induction, but is determined only by the rate of its change.
Faraday's experiments found that the magnitude of the electromotive force of induction is proportional to the rate of change magnetic flux penetrating the contour of the conductor (Faraday's law of electromagnetic induction)
Or, (3.46)
where (dF) is the change in flow over time (dt). MAGNETIC FLUX or FLOW MAGNETIC INDUCTION is called the value, which is determined on the basis of the following relationship: ( magnetic flux through a surface of area S): Ф = ВScosα, (3.45), angle a is the angle between the normal to the surface under consideration and the direction of the magnetic induction vector
unit of magnetic flux in the SI system is called weber- [Wb = T × m 2].
The sign "-" in the formula means that the emf induction causes an induction current, the magnetic field of which counteracts any change in the magnetic flux, i.e. at> 0 emf induction e AND<0 и наоборот.
emf induction is measured in volts
To find the direction of the induction current, there is the Lenz rule (the rule was established in 1833): the induction current has such a direction that the magnetic field it creates tends to compensate for the change in magnetic flux that caused this induction current.
For example, if you push the north pole of a magnet into the coil, that is, increase the magnetic flux through its turns, an induction current arises in the coil in such a direction that a north pole appears at the end of the coil closest to the magnet (Figure 3.20). So, the magnetic field of the induction current tends to neutralize the change in the magnetic flux that caused it.
Not only an alternating magnetic field generates an induction current in a closed conductor, but also when a closed conductor of length l moves in a constant magnetic field (B) at a speed v, an emf arises in the conductor:
a (B Ùv) (3.47)
As you already know, electromotive force in the chain is the result of the action of outside forces. When the conductor moves in a magnetic field the role of external forces fulfills Lorentz force(which acts from the side of the magnetic field on a moving electric charge). Under the action of this force, a separation of charges occurs and a potential difference arises at the ends of the conductor. E.m.s. induction in a conductor is the work of moving unit charges along the conductor.
Induction current direction can be determined according to the right hand rule:Vector B enters the palm, the abducted thumb coincides with the direction of the speed of the conductor, and 4 fingers will indicate the direction of the induction current.
Thus, the alternating magnetic field causes the appearance of an induced electric field... It not potentially(as opposed to electrostatic), because Work on the movement of a single positive charge equal to the emf induction, not zero.
Such fields are called vortex. Vortex lines of force electric field - closed on themselves, as opposed to the lines of tension electrostatic field.
E.m.s. induction occurs not only in adjacent conductors, but also in the conductor itself when the magnetic field of the current flowing through the conductor changes. The emergence of electromotive force in any conductor when the current strength itself changes (hence, the magnetic flux in the conductor) is called self-induction, and the current induced in this conductor is called self-induction current.
The current in a closed loop creates a magnetic field in the surrounding space, the strength of which is proportional to the strength of the current I. Therefore, the magnetic flux Ф, penetrating the loop, is proportional to the current strength in the loop
Ф = L × I, (3.48).
L is the coefficient of proportionality, which is called the coefficient of self-induction, or, simply, inductance. The inductance depends on the size and shape of the circuit, as well as on the magnetic permeability of the medium surrounding the circuit.
In this sense, the inductance of the circuit is analogue the electrical capacitance of a solitary conductor, which also depends only on the shape of the conductor, its dimensions and the dielectric constant of the medium.
The unit of inductance is henry (H): 1H is the inductance of such a circuit, the self-induction magnetic flux of which at a current of 1A is equal to 1Vb (1H = 1Vb / A = 1V s / A).
If L = const, then the emf self-induction can be represented as follows:
, or 
, (3.49)
where DI (dI) is the change in the current in the circuit containing the inductor (or circuit) L during the time Dt (dt). The sign "-" in this expression means that the emf self-induction prevents a change in the current (i.e., if the current in a closed loop decreases, then the self-induction emf leads to the appearance of a current in the same direction and vice versa).
One of the manifestations of electromagnetic induction is the emergence of closed induction currents in continuous conducting media: metal bodies, electrolyte solutions, biological organs, etc. Such currents are called eddy currents or Foucault currents. These currents arise when a conducting body moves in a magnetic field and / or when the induction of the field in which the bodies are placed changes with time. The strength of Foucault's currents depends on the electrical resistance of bodies, as well as on the rate of change of the magnetic field.
Foucault currents also obey Lenz's rule : Their magnetic field is directed to counteract the change in magnetic flux that induces eddy currents.
Therefore, massive conductors are inhibited in a magnetic field. In electrical machines, in order to minimize the effect of Foucault currents, the cores of transformers and the magnetic circuits of electrical machines are assembled from thin plates isolated from each other with a special varnish or scale.
Eddy currents cause intense heating of the conductors. Joule heat generated by Foucault currents, used in induction metallurgical furnaces for melting metals, according to the Joule-Lenz law.
9.5. Induction current
9.5.1. Thermal action induction current
The emergence of an EMF leads to the appearance in the conducting circuit induction current, the strength of which is determined by the formula
I i = | ℰ i | R,
where ℰ i - EMF of induction arising in the circuit; R is the loop resistance.
When the induction current flows in the circuit, heat is released, the amount of which is determined by one of the expressions:
Q i = I i 2 R t, Q i = ℰ i 2 t R, Q i = I i | ℰ i | t,
where I i - the strength of the induction current in the circuit; R is the loop resistance; t is time; ℰ i - EMF of induction arising in the circuit.
Induction current power calculated by one of the formulas:
P i = I i 2 R, P i = ℰ i 2 R, P i = I i | ℰ i | ,
where I i - the strength of the induction current in the circuit; R is the loop resistance; ℰ i - EMF of induction arising in the circuit.
When an induction current flows in a conducting loop, a charge is transferred through the cross-sectional area of the conductor, the value of which is calculated by the formula
q i = I i ∆t,
where I i - the strength of the induction current in the circuit; Δt is the time interval during which the induction current flows along the circuit.
Example 21. A ring made of a wire with a resistivity of 50.0 ⋅ 10 −10 Ohm ⋅ m is in a uniform magnetic field with an induction of 250 mT. The length of the wire is 1.57 m and its cross-sectional area is 0.100 mm 2. What is the maximum charge that will pass through the ring when the field is turned off?
Solution . The appearance of the EMF of induction in the ring is caused by a change in the flux of the induction vector penetrating the plane of the ring when the magnetic field is turned off.
The flux of magnetic induction through the area of the ring is determined by the formulas:
- before turning off the magnetic field
Ф 1 = B 1 S cos α,
where B 1 - the initial value of the modulus of magnetic field induction, B 1 = 250 mT; S is the area of the ring; α is the angle between the directions of the magnetic induction vector and the normal vector (perpendicular) to the plane of the ring;
- after turning off the magnetic field
Ф 2 = B 2 S cos α = 0,
where B 2 is the value of the induction modulus after turning off the magnetic field, B 2 = 0.
∆Ф = Ф 2 - Ф 1 = −Ф 1,
or, taking into account the explicit form Ф 1,
∆Ф = −B 1 S cos α.
The average value of the EMF of induction arising in the ring when the field is turned off,
| ℰ i | = | Δ Ф Δ t | = | - B 1 S cos α Δ t | = B 1 S | cos α | Δ t,
where ∆t is the time interval during which the field is switched off.
The presence of an EMF induction leads to the appearance of an induction current; the strength of the induction current is determined by Ohm's law:
I i = | ℰ i | R = B 1 S | cos α | R Δ t,
where R is the resistance of the ring.
When an induction current flows through the ring, an induction charge is transferred
q i = I i Δ t = B 1 S | cos α | R.
The maximum value of the charge corresponds to the maximum value of the cosine function (cos α = 1):
q i max = I i Δ t = B 1 S R.
The resulting formula determines the maximum value of the charge that will pass through the ring when the field is turned off.
However, to calculate the charge, it is necessary to obtain expressions that will allow us to find the area of the ring and its resistance.
The area of the ring is the area of a circle of radius r, the perimeter of which is determined by the formula for the circumference and coincides with the length of the wire from which the ring is made:
l = 2πr,
where l is the length of the wire, l = 1.57 m.
Hence it follows that the radius of the ring is determined by the ratio
r = l 2 π,
and its area is
S = π r 2 = π l 2 4 π 2 = l 2 4 π.
Ring resistance is given by the formula
R = ρ l S 0,
where ρ is the resistivity of the wire material, ρ = 50.0 × 10 −10 Ohm ⋅ m; S 0 - cross-sectional area of the wire, S 0 = = 0.100 mm 2.
We substitute the obtained expressions for the area of the ring and its resistance into the formula that determines the required charge:
q i max = B 1 l 2 S 0 4 π ρ l = B 1 l S 0 4 π ρ.
Let's calculate:
q i max = 250 ⋅ 10 - 3 ⋅ 1.57 ⋅ 0.100 ⋅ 10 - 6 4 ⋅ 3.14 ⋅ 50.0 ⋅ 10 - 10 = 0.625 C = 625 mC.
When the field is turned off, a charge equal to 625 mC passes through the ring.
Example 22. A loop with an area of 2.0 m 2 and a resistance of 15 mOhm is in a uniform magnetic field, the induction of which increases by 0.30 mT per second. Find the maximum possible power of the induction current in the circuit.
Solution . The appearance of the EMF of induction in the circuit is caused by a change in the flux of the induction vector penetrating the plane of the circuit, when the magnetic induction changes over time.
The change in the flux of the magnetic induction vector is determined by the difference
∆Ф = ∆BS cos α,
where ∆B is the change in the magnetic field induction modulus for the selected time interval; S is the area bounded by the contour, S = 2.0 m 2; α is the angle between the directions of the magnetic induction vector and the normal vector (perpendicular) to the plane of the contour.
The average value of the EMF of the induction arising in the circuit, when the induction of the magnetic field changes:
| ℰ i | = | Δ Ф Δ t | = | Δ B S cos α Δ t | = Δ B S | cos α | Δ t,
where ∆B / ∆t is the rate of change in the modulus of the magnetic field induction vector over time, ∆B / ∆t = 0.30 mT / s.
The appearance of an induction EMF leads to the appearance of an induction current; the strength of the induction current is determined by Ohm's law:
I i = | ℰ i | R = Δ B S | cos α | R Δ t,
where R is the loop resistance.
Induction current power
P i = I i 2 R = (Δ B Δ t) 2 S 2 R cos 2 α R 2 = (Δ B Δ t) 2 S 2 cos 2 α R.
The maximum value of the power of the induction current corresponds to the maximum value of the cosine function (cos α = 1):
P i max = (Δ B Δ t) 2 S 2 R.
Let's calculate:
P i max = (0.30 ⋅ 10 - 3) 2 (2.0) 2 15 ⋅ 10 - 3 = 24 ⋅ 10 - 6 W = 24 μW.
The maximum power of the induction current in this circuit is 24 μW.
Themes of the USE codifier: the phenomenon of electromagnetic induction, magnetic flux, Faraday's law of electromagnetic induction, Lenz's rule.
Oersted's experiment showed that an electric current creates a magnetic field in the surrounding space. Michael Faraday came to the idea that there could be an opposite effect: a magnetic field, in turn, generates an electric current.
In other words, let a closed conductor be in a magnetic field; will not an electric current arise in this conductor under the influence of a magnetic field?
After ten years of searching and experimenting, Faraday finally managed to detect this effect. In 1831 he made 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 leads of the first coil were connected to a current source, the leads of the second coil were connected to a galvanometer (a galvanometer is a sensitive device for measuring low 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 first coil was closed, the galvanometer recorded a short and weak current pulse in the second coil.
When a direct current was flowing through the first coil, no current was generated in the second coil.
When the first coil was opened, a short and weak current pulse arose again in the second coil, but this time in the opposite direction compared to the current when the circuit was closed.
Output.
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 induction current.
If the magnetic field of the first coil increases (at the moment the current rises when the circuit is closed), then the induction 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 induction current in the second coil flows in the other direction.
If the magnetic field of the first coil does not change (constant current through it), then there is no induction current in the second coil.
The discovered phenomenon Faraday called electromagnetic induction(ie, "induction of electricity by magnetism").
2. To confirm the guess that the induction current is generated variable 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 the movement (approach or removal), the second coil ended up 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, and the other when they were removed. In this case, the strength of the induction current was the greater, the faster the coils moved..
3. The first coil was replaced with a permanent magnet. When a magnet was introduced into the second coil, an induction current was generated. When the magnet was pulled out, a 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 have shown that the induction current in the conducting circuit occurs in all cases when the "number of lines" of the magnetic field penetrating the circuit changes. The strength of the induction current turns out to be the greater, the faster this number of lines changes. The direction of the current will be one with an increase in the number of lines through the contour, and another - with a 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, penetrating the stationary contour, changes, or the contour moves from an area with one density of lines to an area with a different 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 the contour."
Magnetic flux
The concept of magnetic flux is precisely the characteristic of the number of magnetic field lines penetrating the contour.
For simplicity, we restrict ourselves to the case of a uniform magnetic field. Consider a contour of an area in a magnetic field with induction.
First, let the magnetic field be perpendicular to the plane of the contour (Fig. 1).
Rice. 1.
In this case, the magnetic flux is determined very simply - as the product of the magnetic field induction by the area of the circuit:
(1)
Now consider the general case when the vector makes an angle with the normal to the plane of the contour (Fig. 2).
Rice. 2.
We see that now only the perpendicular component of the magnetic induction vector "flows" through the contour (and the component that is parallel to the contour 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 contour (that is), then the magnetic flux becomes zero.
And how to determine the magnetic flux if the field is not uniform? We will only indicate an 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 our 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 you can see,
Wb = Tl m = V s. (3)
Why does the magnetic flux characterize the "number of lines" of the magnetic field, penetrating the contour? Very simple. The "number of lines" is determined by their density (and hence, by their size - after all, the greater the induction, the denser the lines) and the "effective" area penetrated by the field (and this is nothing else but). But the factors actually 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 appearance of an electric current in a closed conducting circuit when the magnetic flux permeating the circuit changes.
EMF induction
What is the mechanism of induction current generation? 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 the circuit is called electromotive force (EMF):. In our case, when the magnetic flux through the circuit changes, the corresponding EMF is called EMF induction and is indicated by.
So, EMF of induction is the work of external forces arising from a change in the magnetic flux through the circuit, by 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 the greater, the faster the magnetic flux through the circuit changed.
If in a short time the change in the magnetic flux is equal, then speed changes in the magnetic flux are a fraction (or, which is the same, the time derivative of the magnetic flux).
Experiments have shown that the strength of the induction current is directly proportional to the modulus of the rate of change of the magnetic flux:
The module was installed in order not to associate with negative values for now (after all, with a decrease in the magnetic flux 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 EMF of induction is directly proportional to the rate of change of the magnetic flux:
(4)
EMF is measured in volts. But the rate of change in magnetic flux is also measured in volts! Indeed, from (3) we see that Wb / s = B. Therefore, the units of measurement of both parts of proportionality (4) coincide, therefore the coefficient of proportionality is a dimensionless quantity. In the SI system, it is assumed to be equal to one, and we get:
(5)
That's what it is electromagnetic induction law or Faraday's law... Let's give it a verbal formulation.
Faraday's law of electromagnetic induction. When the magnetic flux penetrating the circuit changes, an EMF of induction arises in this circuit, which is equal to the modulus of the rate of change of the magnetic flux.
Lenz's rule
The magnetic flux, a change in which leads to the appearance of an induction current in the circuit, we will call external magnetic flux... And the very magnetic field that 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 magnetic field, which, according to the principle of superposition, is added to the external magnetic field.
Accordingly, along with the external magnetic flux, own the magnetic flux created by the magnetic field of the induction current.
It turns out that these two magnetic fluxes - own and external - are linked in a strictly defined way.
Lenz's rule. The induction current always has such a direction that its own magnetic flux prevents a change in the external magnetic flux.
Lenz's rule allows you to find the direction of the induction current in any situation.
Let's consider some examples of the application of Lenz's rule.
Suppose that the contour 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 is directed upward in this case, to the contour.
The magnetic flux through the circuit increases. The induction current will have such a direction that the magnetic flux it creates prevents an increase in the external magnetic flux. For this, the magnetic field created by the induction current must be directed against external magnetic field.
The induction current flows counterclockwise when viewed from the side 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. The magnetic flux increases
Now suppose that the magnetic field that penetrates the loop decreases with time (Fig. 4). For example, we are removing the magnet downward from the path and the north pole of the magnet is pointing towards the path.
Rice. 4. The magnetic flux decreases
The magnetic flux through the circuit is reduced. The induction current will have such a direction that its own magnetic flux supports the external magnetic flux, preventing it from decreasing. For this, the magnetic field of the induction current must be directed in the same direction as the external magnetic field.
In this case, the induction 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 induction current in the circuit, the direction of which is determined by Lenz's rule. But the magnetic field acts on the current! The Ampere force will appear, acting on the contour from the side of the magnet field. Where will this force be directed?
If you want to get a good understanding of Lenz's rule and in determining the direction of the Ampere force, try to answer this question yourself. This is not a very simple exercise and a great C1 exam task. Consider four possible cases.
1. The magnet is brought closer to the contour, the North Pole is directed to the contour.
2. The magnet is removed from the contour, the north pole is directed to the contour.
3. The magnet is brought closer to the contour, the south pole is directed to the contour.
4. The magnet is removed from the contour, the south pole is directed to the contour.
Do not forget that the field of a magnet is not uniform: the field lines diverge from the north pole and converge towards the south. This is very important for determining the net Ampere force. The result is as follows.
If the magnet is brought closer, the contour is repelled from the magnet. If you remove the magnet, the loop is attracted to the magnet. Thus, if the contour 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 poles of the magnet does not play a role in this..
In any case, you should remember this fact - suddenly such a question will fall into part A1
This result can also be explained from completely general considerations - with the help of the law of conservation of energy.
Let's say we bring the magnet closer to the contour. An induction current appears in the circuit. But to create a current, you have to do some work! Who is doing 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 induction current.
So our job of moving the magnet should be positive... This means that we, bringing the magnet closer, must overcome the force of interaction of a magnet with a circuit, which, therefore, is a force repulsion.
Now we remove the magnet. Please repeat this reasoning and make sure that a force of attraction should arise between the magnet and the circuit.
Faraday's Law + Lenz's Rule = Module Removal
Above, we promised to remove the module in Faraday's law (5). Lenz's rule allows you to do this. But first, we will need to agree on the sign of the EMF of induction - after all, without the module on the right-hand side of (5), EMF value can be both positive and negative.
First of all, one of the 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 detour we take as positive does not matter - it is only important to make this choice.
The magnetic flux through the loop is considered positive. class = "tex" alt = "(! LANG: (\ Phi> 0)"> !}, if the magnetic field penetrating the contour is directed there, looking from where the contour is traversed in the positive direction counterclockwise. If, from the end of the magnetic induction vector, the positive direction of the bypass is seen clockwise, then the magnetic flux is considered negative.
EMF of induction is considered positive class = "tex" alt = "(! LANG: (\ mathcal E_i> 0)"> !} if the induction 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 the circuit bypass.
On the contrary, the EMF of induction is considered negative if the induction current flows in the negative direction. In this case, external forces will also act along the negative direction of the contour traversal.
So, let the circuit be in a magnetic field. We fix the direction of the positive traversal of the contour. Suppose that the magnetic field is directed there, looking from where the positive traversal is made counterclockwise. Then the magnetic flux is positive: class = "tex" alt = "(! LANG: \ Phi> 0"> .!}
Rice. 5. The magnetic flux increases
Therefore, in this case we have. The sign of the induction EMF turned out to be opposite to the sign of the rate of change of the magnetic flux. Let's check this in a different situation.
Namely, let us now assume that the magnetic flux is decreasing. According to Lenz's rule, the induction current will flow in a positive direction. That is, class = "tex" alt = "(! LANG: \ mathcal E_i> 0"> !}(fig. 6).
Rice. 6. The magnetic flux increases class = "tex" alt = "(! LANG: \ Rightarrow \ mathcal E_i> 0"> !}
This is actually a general fact: with our agreement on the signs, the Lenz rule always leads to the fact that the sign of the EMF of induction is opposite to the sign of the rate of change of the magnetic flux:
(6)
Thus, the modulus sign in the Faraday law of electromagnetic induction has been eliminated.
Vortex electric field
Consider a stationary circuit in an alternating magnetic field. What is the mechanism 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... Exactly this electric field and acts on free charges, causing an induction current.
The lines of the arising electric field turn out to be closed, in connection with which it was called vortex electric field... The lines of the vortex electric field go around the lines of the magnetic field and are directed as follows.
Let the magnetic field increase. If there is a conducting circuit in it, then the induction 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 side of 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 strength is directed exactly there.
So, the lines of intensity of the vortex electric field are directed in this case clockwise (we look 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 intensity lines of the vortex electric field are directed counterclockwise (Fig. 8).
Rice. 8. Vortex electric field with decreasing magnetic field
We can now gain a deeper understanding of 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 loop is present in the magnetic field or not; with the help of the circuit, we only detect this phenomenon by observing the induction current.
The vortex electric field differs in some properties from the electric fields already known to us: an electrostatic field and a stationary field of charges that form a direct current.
1. The lines of the vortex field are closed, while the lines of the electrostatic and stationary fields start at positive charges and end at negative ones.
2. The vortex field is non-potential: its work to move the charge along a closed loop is not equal to zero. Otherwise, the vortex field could not create an electric current! At the same time, as we know, the electrostatic and stationary fields are potential.
So, EMF of induction in a stationary circuit is the work of a vortex electric field to move a single positive charge around the circuit.
For example, let the contour 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 of the force with which the vortex field acts on the charge is equal to:
Therefore, for the EMF induction we obtain:
EMF of induction in a moving conductor
If the conductor moves in a constant magnetic field, then the EMF of induction also appears in it. However, the reason now is not a 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.
Consider a situation that often occurs in tasks. V horizontal plane parallel rails are located, the distance between which is equal. The rails are in a vertical uniform magnetic field. A thin conductive rod moves along the rails at a speed; it remains perpendicular to the rails all the time (Fig. 9).
Rice. 9. The movement of a conductor in a magnetic field
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 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 the charge moves from point to point, our external force will do the work:
(We also consider the length of the rod to be equal.) Therefore, the EMF of induction in the rod will be equal to:
(7)
Thus, the rod is similar to a current source with a positive terminal and a negative terminal. Inside the rod, due to the action of the external Lorentz force, the charges are separated: positive charges move to the point, negative ones - to the point.
Let us first assume that the rails do not conduct current, then the movement of charges in the rod will gradually stop. After all, as you accumulate positive charges at the end and negative charges at the end, the Coulomb force will increase, with which the positive free charge is repelled from and attracted to - and at some moment this Coulomb force will balance the Lorentz force. A potential difference will be established between the ends of the rod, equal emf induction (7).
Now, suppose the rails and the jumper are conductive. Then an induction current will appear in the circuit; it will go in the direction (from "source plus" to "minus" N). Suppose that the resistance of the rod is equal to (this is an analogue of the internal resistance of the current source), and the resistance of the section is equal to (the resistance of the external circuit). Then the strength of the induction current is found according to Ohm's law for a complete circuit:
It is remarkable that expression (7) for the EMF of induction can also be obtained using Faraday's law. Let's do it.
During the time, our rod passes the path and takes the position (Fig. 9). The area of the contour increases by the size of the area of the rectangle:
The magnetic flux through the circuit increases. The increment of the magnetic flux is equal to:
The rate of change of the magnetic flux is positive and equal to the EMF of induction:
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, then its magnetic field is directed opposite to the external field and, therefore, prevents an increase in the magnetic flux through the circuit.
In this example, we see that in situations where a conductor moves in a magnetic field, you can act in two ways: either with the involvement of the Lorentz force as an external force, or with the help of 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 conductive loop moves in a constant magnetic field, which also causes a change in the magnetic flux of the penetrating loop.
Figure 1 - The conductor moves in a constant magnetic field
The induction current is caused by a vortex electric field, which is generated by a magnetic field. This electric field acts on free charges in a conductor placed in this vortex electric field.
Figure 2 - vortex electric field
You can also find such a definition. Induction current is an electric current that occurs due to the action of electromagnetic induction. If he does not 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 a current in a conductive circuit under the influence of an alternating magnetic field.
Using this law, you can also determine the magnitude of the induction current. Since he gives us the value of the EMF, which arises in the circuit under the action of an alternating magnetic field.
Formula 1 - EMF of magnetic field induction.
As can be seen from formula 1, the value of the induction EMF, and hence the induction current, depends on the rate of change of the magnetic flux penetrating the circuit. That is, the faster the magnetic flux changes, the higher the induction current can be obtained. In the case when we have a constant magnetic field in which the conducting circuit moves, then the EMF value will depend on the speed of the circuit.
Lenz's rule is used to determine the direction of the induction current. Which says that the induction current is directed towards the current that caused it. Hence the minus sign in the formula for definition of EMF induction.
Induction current plays an important role in modern electrical engineering. For example, the induction current arising in the rotor asynchronous motor, interacts with the current supplied from the power source in its stator, as a result of which the rotor rotates. Modern electric motors are built on this principle.
Figure 3 - asynchronous motor.
In the 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 parameters of the transformer.
Figure 4 - electrical transformer.
Finally, induction currents can also occur in massive conductors. These are the so-called Foucault currents. Thanks to them, it is possible to produce 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 may heat up above its melting point.
Figure 5 - Induction melting of metals.
So, we found out that induction current can provide mechanical, electrical and thermal action... All of these effects are commonly used in modern world, both on an industrial scale and at the household level.
The relationship between electric and magnetic fields has been noticed for a very long time. This connection was discovered back in the 19th century by the English physicist Faraday and gave it a name. It appears at the moment when the magnetic flux penetrates the surface of the closed loop. After a change in the magnetic flux occurs for a certain time, the appearance of an electric current is observed in this circuit.
Relationship between electromagnetic induction and magnetic flux
The essence of the magnetic flux is displayed by the well-known formula: Ф = BS cos α. In it, Ф is the magnetic flux, S is the surface of the contour (area), B is the vector of magnetic induction. The angle α is formed due to the direction of the magnetic induction vector and the normal to the surface of the contour. Hence it follows that the maximum threshold of the magnetic flux will reach at cos α = 1, and the minimum at cos α = 0.
In the second variant, vector B will be perpendicular to the normal. It turns out that the flow lines do not cross the contour, but only slide along its plane. Consequently, the characteristics will be determined by the lines of the vector B intersecting the surface of the contour. For the calculation, weber is used as a unit of measurement: 1 wb = 1v x 1s (volt-second). Another, smaller unit of measurement is Maxwell (μs). It is: 1 wb = 108 μs, that is, 1 μs = 10-8 wb.
For research, Faraday used two wire coils, isolated from each other and placed on a coil of wood. One of them was connected to an energy source, and the other was connected to a galvanometer designed to register low currents. At the moment when the circuit of the original spiral was closed and opened, in another circuit the arrow of the measuring device was deflected.
Research of the phenomenon of induction
In the first series of experiments, Michael Faraday inserted a magnetized metal bar into a coil connected to a current, and then took it out (Fig. 1, 2).
1 
2 
When a magnet is placed in a coil connected to a measuring device, an induction current begins to flow in the circuit. If the magnetic bar is removed from the coil, the induction current still appears, but its direction is already opposite. Consequently, the parameters of the induction current will be changed in the direction of movement of the bar and depending on the pole with which it is placed in the coil. The current strength is influenced by the speed of movement of the magnet.
The second series of experiments confirms the phenomenon in which a changing current in one coil causes an induction current in another coil (Fig. 3, 4, 5). This happens at the moments of closing and opening the circuit. The direction of the current will also depend on whether the electrical circuit is closed or opened. In addition, these actions are nothing more than ways of changing the magnetic flux. When the circuit is closed, it will increase, and when it is opened, it will decrease, while simultaneously penetrating the first coil.
3 
4 
5 
As a result of the experiments, it was found that the occurrence of an electric current inside a closed conducting circuit is possible only when they are placed in an alternating magnetic field. At the same time, the flow can change in time by any means.
The electric current that appears under the influence of electromagnetic induction is called induction, although it will not be a current in the conventional sense. When a closed loop is in a magnetic field, EMF is generated with an exact value, and not a current that depends on different resistances.
This phenomenon is called the EMF of induction, which is reflected by the formula: Eind = - ∆F / ∆t. Its value coincides with the speed of changes in the magnetic flux penetrating the surface of the closed loop, taken with a negative value. Minus present in this expression, is a reflection of Lenz's rule.
Lenz's rule for magnetic flux
The well-known rule was derived after a series of studies in the 30s of the 19th century. It is formulated as follows:
The direction of the induction current, excited in a closed loop by a changing magnetic flux, affects the magnetic field created by it in such a way that it, in turn, creates an obstacle to the magnetic flux that causes the induction current to appear.
When the magnetic flux increases, that is, it becomes Ф> 0, and the EMF of induction decreases and becomes Eind< 0, в результате этого появляется электроток с такой направленностью, при которой под влиянием его магнитного поля происходит изменение потока в сторону уменьшения при его прохождении через плоскость замкнутого контура.
If the flow decreases, then the reverse process occurs, when Ф< 0 и Еинд >0, that is, the action of the magnetic field of the induction current, there is an increase in the magnetic flux passing through the circuit.
The physical meaning of Lenz's rule is to reflect the law of conservation of energy, when with a decrease in one quantity, the other increases, and, conversely, with an increase in one quantity, the other will decrease. Various factors also affect the EMF of induction. When a strong and weak magnet is inserted into the coil alternately, the device will respectively show a higher value in the first case, and a lower value in the second. The same happens when the speed of the magnet changes.
The figure shows how the direction of the induction current is determined using Lenz's rule. Blue color corresponds to power lines magnetic fields of induction current and permanent magnet. They are located in the direction of the poles from north to south, which are found in each magnet.
The changing magnetic flux leads to the emergence of an inductive electric current, the direction of which causes opposition from its magnetic field, which prevents changes in the magnetic flux. In this regard, the lines of force of the magnetic field of the coil are directed in the direction opposite to the lines of force of the permanent magnet, since its movement occurs in the direction of this coil.
Used with a right-hand thread to determine the direction of current. It must be screwed in so that the direction of its translational movement coincides with the direction of the induction lines of the coil. In this case, the directions of the induction current and rotation of the gimbal handle will coincide.