Lenz's rule for electromagnetic.
Finance
Lenz's rule allows you to determine the direction of the induced current in the circuit. It says: “the direction of the induced current is always such that its action weakens the action of the cause causing this induced current.”
For example, if you take a small ring of copper suspended on a thread, and try to introduce a strong enough north pole into it, then as the magnet approaches the ring, the ring will begin to repel from the magnet.
It looks as if the ring begins to behave like a magnet, turned by the same pole (in this example, the north) pole towards the magnet introduced into it, and thus tries to weaken the introduced magnet. And if the magnet is stopped in the ring and begins to move out of the ring, then the ring, on the contrary, will follow the magnet, as if manifesting itself as the same magnet, but now facing the opposite pole to the magnet being pulled out (we move North Pole
magnet - the south pole that appears on the ring is attracted), this time trying to strengthen the magnetic field weakened due to the extension of the magnet.
If you do the same with an open ring, then the ring will not react to the magnet, although an EMF will be induced in it, but since the ring is not closed, there will be no induced current, and therefore there is no need to determine its direction.
What's really going on here? By moving a magnet into the whole ring, we increase the magnetic flux penetrating the closed circuit, and this means (since the EMF generated in the ring is proportional to the rate of change of the magnetic flux) an EMF is generated in the ring.
The direction of the induction lines of the magnetic field generated in the current ring can be determined by the gimlet rule, and they will be directed precisely in such a way as to interfere with the behavior of the induction lines of the introduced magnet: the lines of the external source enter the ring, and the lines of the external source leave the ring, respectively leave the ring, and are directed into the ring accordingly.
Lenz's rule in a transformer
Now let’s remember how a loaded one behaves in accordance with Lenz’s rule. Let's say that in the primary winding of the transformer the current increases, therefore the magnetic field in the core increases. The magnetic flux penetrating the secondary winding of the transformer increases.
Since the secondary winding of the transformer is closed through the load, the EMF generated in it will generate an induced current, which will create its own magnetic field of the secondary winding. The direction of this magnetic field will be such as to weaken the magnetic field of the primary winding. This means that the current in the primary winding will increase (since an increase in the load in the secondary winding is equivalent to a decrease in the inductance of the primary winding of the transformer, and therefore a decrease in the impedance of the transformer for the network). And the network will begin to perform work in the primary winding of the transformer, the magnitude of which will depend on the load in the secondary winding.
Electromagnetic induction is a physical phenomenon consisting of the appearance of an electric current in a closed circuit when the flux of magnetic induction changes through the surface limited by this circuit.2. A change in what physical quantities can lead to a change in magnetic flux?
A change in magnetic flux can result from a change over time in the surface area that is limited by the contour; magnetic induction vector module; the angle formed by the induction vector and the area vector of this surface.3. In which case is the direction of the induction current considered positive, and in which - negative?
If the selected direction of bypassing the circuit coincides with the direction of the induction current, then it is considered positive. If the selected direction of bypassing the circuit is opposite to the direction of the induction current, then it is considered negative.4. Formulate the law of electromagnetic induction. Write down its mathematical expression.
The EMF of electromagnetic induction in a closed circuit is equal in magnitude and opposite in sign to the rate of change of magnetic flux through the surface, which is limited by this circuit.5. Formulate Lenz’s rule. Give examples of its application
The induced current arising in the circuit, with its magnetic field, counteracts the change in the magnetic flux that caused this current. For example, as the magnetic flux through the circuit increases, the magnetic flux of the induced current will be negative, and the resulting flux, equal to their sum, will decrease. And when the magnetic flux through the circuit decreases, the magnetic flux of the induced current will support the resulting flux, preventing it from sharply decreasing.In 1834, the Russian academician E. H. Lenz, known for his numerous studies in the field of electromagnetic phenomena, gave a universal rule for determining the direction of the induced electromotive force (EMF) in a conductor. This rule, known as Lenz's rule, can be stated as follows:
The direction of the induced EMF is always such that the current caused by it and it have such a direction that they tend to interfere with the cause that generates this induced EMF.
The validity of the formulation of Lenz’s rule is confirmed by the following experiments:
| Figure 1. Resistance of a conductor with an induced current to its movement |
1. If positioned as shown in Figure 1, then when moving down the conductor will cross this magnetic field. Then an emf is induced in the conductor, the direction of which can be determined by. In our case, the direction of the induced EMF, and therefore the current, will be “towards us”. Let's now see how our conductor will behave with current in a magnetic field. From previous articles we know that a current-carrying conductor will be pushed out of a magnetic field. The direction of ejection is determined by the left-hand rule. In our case, the buoyancy force is directed upward. Thus, the induced current, interacting with the magnetic field, interferes with the movement of the conductor, that is, it counteracts the cause that caused it.
2. For the experiment, we will assemble the circuit shown in Figure 2. By lowering it into the coil (with the north pole down), we will notice the deviation of the galvanometer needle. Experience shows that the direction of the induced current in the coil will be as shown by the arrows in Figure 2, A. Let it correspond to the deviation of the arrow to the left from the average zero position. Consequently, the coil seems to have turned into and the indicated direction of the current creates its north pole at the top, and the south pole at the bottom. Since like poles of the magnet and solenoid will repel each other, the induced current in the coil will interfere with the movement of the permanent magnet, that is, it will counteract the reason that caused it.
Figure 2. Solenoid resistance to magnet movement:
A- down, b- up
If we remove the permanent magnet from the coil, the galvanometer needle will deviate to the right (Figure 2, b). This deflection of the galvanometer needle, as experience shows, corresponds to the direction of the induced current, shown by the arrows in Figure 2, b, and opposite to the direction of current in Figure 2, A.
Determining the poles of the coil using the “gimlet rule”, we find that the south pole will now be at the top of the coil, and the north pole at the bottom. The opposite poles of the magnet and solenoid, attracting, will slow down the movement of the magnet. This means that the induced current will again counteract the cause that caused it.
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| Figure 3. Occurrence of induced current II: A- at the moment of circuit closure I, b- at the moment of opening the circuit |
3. Completing the circuit I(Figure 3, A), let's pass current through the conductor AB. The direction of the current is shown in the figure by arrows. Magnetic field of a conductor AB, created by the emerging current, spreading in all directions, will cross the conductor VG, and in the chain II an induced emf occurs. Since circuit II is closed to the galvanometer, a current will appear in it. The galvanometer in this case is turned on in the same way as in the previous experiment.
The galvanometer needle, deviating to the left, will show that the current through the device is flowing from top to bottom. Comparing the direction of currents in conductors AB and VG, we see that their currents are directed in different directions.
As we already know, conductors in which the currents are directed in different directions, one from the other. Therefore the conductor VG with an induced current will tend to push away from the conductor AB(same as conductor AB from VG), eliminate the influence of the conductor field AB and thereby interfere with the cause that caused the induced current.
Induced current in a circuit II will take a short time. As soon as the conductor AB will be established, the intersection of the conductor will stop VG magnetic field of the conductor AB, current in the circuit II will disappear.
When the circuit opens I the disappearing current will cause a decrease in the magnetic field, the induction lines of which, crossing the conductor VG, will create in it an induced current in the same direction as in the conductor AB(Figure 3, b).
We know that conductors in which current flows in one direction are one to the other. Therefore the conductor VG will tend to reach out to the conductor AB to maintain its decreasing magnetic field.
4. For the next example, let’s take a coil that has a round core made of chopped steel wire, on which a light aluminum ring is loosely placed (Figure 4). At the moment the circuit is closed, a magnetic field begins to pass through the coil winding, creating a magnetic field, the induction lines of which, crossing the aluminum ring, induce a current in it. At the moment the coil is turned on, an induced current appears in the aluminum ring, directed oppositely to the current in the turns of the coil. Conductors having different direction induced current are repelled. Therefore, when the coil is turned on, the aluminum ring jumps up.
We now know that with any change in time of the magnetic flux penetrating the circuit, an induced emf appears in it, determined by the equality:
The expression in this formula represents the average rate of change of magnetic flux over time. The shorter the time period Δ t, the less the above EMF differs from its actual value in this moment time. The minus sign in front of the expression shows the direction of the induced emf, that is, it takes into account Lenz’s rule.
As the magnetic flux increases, the expression will be positive and the emf will be negative. This is Lenz's rule: The EMF and the current it creates counteract the cause that caused it.
If the magnetic flux changes uniformly over time, the expression will be constant. Then the absolute value of the EMF in the conductor will be equal to:
The dimension of the magnetic flux will be:
[F] = [ e × t] = V × sec or weber.
If we have not one conductor, but a coil consisting of w turns, then the magnitude of the induced EMF will be:
The product of the number of turns of a coil and the magnetic flux associated with them is called the flux linkage of the coil and is denoted by the letter ψ. Therefore, the law can be written in another form:
In 1834, the Russian academician E. H. Lenz, known for his numerous studies in the field of electromagnetic phenomena, gave a universal rule for determining the direction of the induced electromotive force (EMF) in a conductor. This rule, known as Lenz's rule, can be stated as follows:
The direction of the induced EMF is always such that the current caused by it and it have such a direction that they tend to interfere with the cause that generates this induced EMF.
The validity of the formulation of Lenz’s rule is confirmed by the following experiments:
| Figure 1. Resistance of a conductor with an induced current to its movement |
1. If positioned as shown in Figure 1, then when moving down the conductor will cross this magnetic field. Then an emf is induced in the conductor, the direction of which can be determined by. In our case, the direction of the induced EMF, and therefore the current, will be “towards us”. Let's now see how our conductor will behave with current in a magnetic field. From previous articles we know that a current-carrying conductor will be pushed out of a magnetic field. The direction of ejection is determined by the left-hand rule. In our case, the buoyancy force is directed upward. Thus, the induced current, interacting with the magnetic field, interferes with the movement of the conductor, that is, it counteracts the cause that caused it.
2. For the experiment, we will assemble the circuit shown in Figure 2. By lowering it into the coil (with the north pole down), we will notice the deviation of the galvanometer needle. Experience shows that the direction of the induced current in the coil will be as shown by the arrows in Figure 2, A. Let it correspond to the deviation of the arrow to the left from the average zero position. Consequently, the coil seems to have turned into and the indicated direction of the current creates its north pole at the top, and the south pole at the bottom. Since like poles of the magnet and solenoid will repel each other, the induced current in the coil will interfere with the movement of the permanent magnet, that is, it will counteract the reason that caused it.
Figure 2. Solenoid resistance to magnet movement:
A- down, b- up
If we remove the permanent magnet from the coil, the galvanometer needle will deviate to the right (Figure 2, b). This deflection of the galvanometer needle, as experience shows, corresponds to the direction of the induced current, shown by the arrows in Figure 2, b, and opposite to the direction of current in Figure 2, A.
Determining the poles of the coil using the “gimlet rule”, we find that the south pole will now be at the top of the coil, and the north pole at the bottom. The opposite poles of the magnet and solenoid, attracting, will slow down the movement of the magnet. This means that the induced current will again counteract the cause that caused it.
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| Figure 3. Occurrence of induced current II: A- at the moment of circuit closure I, b- at the moment of opening the circuit |
3. Completing the circuit I(Figure 3, A), let's pass current through the conductor AB. The direction of the current is shown in the figure by arrows. Magnetic field of a conductor AB, created by the emerging current, spreading in all directions, will cross the conductor VG, and in the chain II an induced emf occurs. Since circuit II is closed to the galvanometer, a current will appear in it. The galvanometer in this case is turned on in the same way as in the previous experiment.
The galvanometer needle, deviating to the left, will show that the current through the device is flowing from top to bottom. Comparing the direction of currents in conductors AB and VG, we see that their currents are directed in different directions.
As we already know, conductors in which the currents are directed in different directions, one from the other. Therefore the conductor VG with an induced current will tend to push away from the conductor AB(same as conductor AB from VG), eliminate the influence of the conductor field AB and thereby interfere with the cause that caused the induced current.
Induced current in a circuit II will take a short time. As soon as the conductor AB will be established, the intersection of the conductor will stop VG magnetic field of the conductor AB, current in the circuit II will disappear.
When the circuit opens I the disappearing current will cause a decrease in the magnetic field, the induction lines of which, crossing the conductor VG, will create in it an induced current in the same direction as in the conductor AB(Figure 3, b).
We know that conductors in which current flows in one direction are one to the other. Therefore the conductor VG will tend to reach out to the conductor AB to maintain its decreasing magnetic field.
4. For the next example, let’s take a coil that has a round core made of chopped steel wire, on which a light aluminum ring is loosely placed (Figure 4). At the moment the circuit is closed, a magnetic field begins to pass through the coil winding, creating a magnetic field, the induction lines of which, crossing the aluminum ring, induce a current in it. At the moment the coil is turned on, an induced current appears in the aluminum ring, directed oppositely to the current in the turns of the coil. Conductors having different directions of induction current repel each other. Therefore, when the coil is turned on, the aluminum ring jumps up.
We now know that with any change in time of the magnetic flux penetrating the circuit, an induced emf appears in it, determined by the equality:
The expression in this formula represents the average rate of change of magnetic flux over time. The shorter the time period Δ t, the less the above EMF differs from its actual value at a given time. The minus sign in front of the expression shows the direction of the induced emf, that is, it takes into account Lenz’s rule.
As the magnetic flux increases, the expression will be positive and the emf will be negative. This is Lenz's rule: The EMF and the current it creates counteract the cause that caused it.
If the magnetic flux changes uniformly over time, the expression will be constant. Then the absolute value of the EMF in the conductor will be equal to:
The dimension of the magnetic flux will be:
[F] = [ e × t] = V × sec or weber.
If we have not one conductor, but a coil consisting of w turns, then the magnitude of the induced EMF will be:
The product of the number of turns of a coil and the magnetic flux associated with them is called the flux linkage of the coil and is denoted by the letter ψ. Therefore, the law can be written in another form:
>> Direction of induction current. Lenz's rule
By connecting the coil in which the induced current occurs to a galvanometer, you can find that the direction of this current depends on whether the magnet is approaching the coil (for example, with the north pole) or moving away from it (see Fig. 2.2, b).
Emerging induced current of one direction or another somehow interacts with a magnet (attracts or repels it). A coil with current passing through it is like a magnet with two poles - north and south. The direction of the induction current determines which end of the coil acts as the north pole (the magnetic induction lines come out of it). Based on the law of conservation of energy, it is possible to predict in which cases the coil will attract a magnet and in which cases it will repel it.
Interaction of induction current with a magnet. If the magnet is brought closer to the coil, then an induced current appears in it in such a direction that the magnet is necessarily repelled. To bring the magnet and coil closer together, positive work must be done. The coil becomes like a magnet, with its pole of the same name facing the magnet approaching it. Poles of the same name repel each other.
When the magnet is removed, on the contrary, a current appears in the coil in such a direction that a force attracting the magnet appears.
What is the difference between the two experiments: bringing a magnet closer to the coil and moving it away? In the first case, the number of lines of magnetic induction penetrating the turns of the coil, or, what is the same, the magnetic flux, increases (Fig. 2.5, a), and in the second case it decreases (Fig. 2.5, b). Moreover, in the first case, the induction lines of the magnetic field created by the induction current that arises in the coil come out of the upper end of the coil, since the coil repels the magnet, and in the second case, on the contrary, they enter this end. These magnetic induction lines are shown in black in Figure 2.5. In case a, the coil with current is similar to a magnet, the north pole of which is located at the top, and in case b, at the bottom.
Similar conclusions can be drawn using the experiment shown in Figure 2.6. At the ends of the rod, which can rotate freely around a vertical axis, two conductive aluminum rings are fixed. One of them has a cut. If you bring a magnet to the ring without a cut, then an induction current will arise in it and it will be directed so that this ring will push away from the magnet and the rod will rotate. If you remove the magnet from the ring, then, on the contrary, it will be attracted to the magnet. The magnet does not interact with the cut ring, since the cut prevents the occurrence of induction current in the ring. Whether a magnet repels or attracts a coil depends on the direction of the induction current in it. Therefore, the law of conservation of energy allows us to formulate a rule that determines the direction of the induction current.
Now we come to the main thing: with an increase in the magnetic flux through the turns of the coil, the induced current has such a direction that the magnetic field it creates prevents the increase in the magnetic flux through the turns of the coil. After all, the induction lines of this field are directed against the induction lines of the field, a change in which generates an electric current. If the magnetic flux through the coil weakens, then the induction
the current creates a magnetic field with induction, increasing the magnetic flux through the turns of the coil.
This is the essence of the general rule for determining the direction of the induction current, which is applicable in all cases. This rule was established by the Russian physicist E. H. Lenz.
According to Lenz's rule The induced current arising in a closed circuit with its magnetic field counteracts the change in the magnetic flux that causes it. More briefly, this rule can be formulated as follows: the induced current is directed so as to interfere with the cause that causes it.
To apply Lenz's rule to find the direction of the induction current in the circuit, it is necessary to do this:
1. Determine the direction of the magnetic induction lines of the external magnetic field.
2. Find out whether the flux of the magnetic induction vector of this field through the surface bounded by the contour increases (Ф > 0) or decreases (Ф< 0).
3. Set the direction of the magnetic induction lines of the magnetic field of the induced current. According to Lenz's rule, these lines must be directed opposite to the lines of magnetic induction at Ф > 0 and have the same direction as them at Ф< 0.
4. Knowing the direction of the magnetic induction lines, find the direction of the induction current using the gimlet rule.
The direction of the induction current is determined using the law of conservation of energy. In all cases, the induced current is directed so that its magnetic field prevents the change in the magnetic flux causing the given induced current.
1. How is the direction of the induction current determined?
2. Will an electric field appear in a ring with a cut if you bring a magnet to it?
