In the material, we will understand the concept of EMF induction in situations of its occurrence. We also consider inductance as a key parameter for the occurrence of magnetic flux when electric field in the conductor.
Electromagnetic induction is the generation electric current magnetic fields that change over time. Thanks to the discoveries of Faraday and Lenz, patterns were formulated into laws, which introduced symmetry into the understanding of electromagnetic flows. Maxwell's theory brought together knowledge about electric current and magnetic fluxes. Thanks to the discovery of Hertz, humanity learned about telecommunications.
An electromagnetic field appears around a conductor with an electric current, however, in parallel, the opposite phenomenon also occurs - electromagnetic induction. Consider the magnetic flux as an example: if a conductor frame is placed in an electric field with induction and moved from top to bottom along magnetic field lines or to the right or left perpendicular to them, then the magnetic flux passing through the frame will be constant.
When the frame rotates around its axis, then after a while the magnetic flux will change by a certain amount. As a result, an EMF of induction arises in the frame and an electric current appears, which is called induction.
EMF induction
Let us examine in detail what the concept of EMF of induction is. When a conductor is placed in a magnetic field and it moves with the intersection of field lines, an electromotive force appears in the conductor called induction EMF. It also occurs if the conductor remains stationary, and the magnetic field moves and intersects with the conductor lines of force.
When the conductor, where the emf occurs, closes to the external circuit, due to the presence of this emf, an induction current begins to flow through the circuit. Electromagnetic induction involves the phenomenon of EMF induction in a conductor at the moment it is crossed by lines of force magnetic field.
Electromagnetic induction is reverse process transformation of mechanical energy into electric current. This concept and its laws are widely used in electrical engineering, most electrical machines are based on this phenomenon.
Faraday and Lenz laws
The laws of Faraday and Lenz reflect the patterns of occurrence electromagnetic induction.
Faraday found that magnetic effects appear as a result of changes in the magnetic flux over time. At the moment the conductor crosses the variables magnetic current, an electromotive force arises in it, which leads to the appearance of an electric current. Can generate current permanent magnet, and an electromagnet.
The scientist determined that the intensity of the current increases with rapid change the number of lines of force that cross the contour. That is, the EMF of electromagnetic induction is in direct proportion to the speed of the magnetic flux.
According to Faraday's law, the induction EMF formulas are defined as follows:
The minus sign indicates the relationship between the polarity of the induced emf, the direction of the flow, and the changing speed.
According to Lenz's law, it is possible to characterize the electromotive force depending on its direction. Any change in the magnetic flux in the coil leads to the appearance of an EMF of induction, and with a rapid change, an increasing EMF is observed.
If the coil, where there is an EMF of induction, has a short circuit to an external circuit, then an induction current flows through it, as a result of which a magnetic field appears around the conductor and the coil acquires the properties of a solenoid. As a result, a magnetic field is formed around the coil.
E.Kh. Lenz established a pattern according to which the direction of the induction current in the coil and the induction EMF are determined. The law states that the induction EMF in the coil, when the magnetic flux changes, forms a directional current in the coil, in which the given magnetic flux of the coil makes it possible to avoid changes in the extraneous magnetic flux.
Lenz's law applies to all situations of electric current induction in conductors, regardless of their configuration and the method of changing the external magnetic field.
The movement of a wire in a magnetic field
The value of the induced emf is determined depending on the length of the conductor crossed by the field lines of force. At more field lines, the value of the induced emf increases. With an increase in the magnetic field and induction, a greater value of EMF occurs in the conductor. Thus, the value of the EMF of induction in a conductor moving in a magnetic field is directly dependent on the induction of the magnetic field, the length of the conductor and the speed of its movement.
This dependence is reflected in the formula E = Blv, where E is the induction emf; B - the value of magnetic induction; I - conductor length; v is the speed of its movement.
Note that in a conductor that moves in a magnetic field, the induction EMF appears only when it crosses the magnetic field lines. If the conductor moves along the lines of force, then no EMF is induced. For this reason, the formula applies only in cases where the movement of the conductor is directed perpendicular to the lines of force.
The direction of the induced EMF and electric current in the conductor is determined by the direction of movement of the conductor itself. To identify the direction, the right hand rule has been developed. If you hold the palm of your right hand so that the field lines enter in its direction, and the thumb indicates the direction of movement of the conductor, then the remaining four fingers indicate the direction of the induced emf and the direction of the electric current in the conductor.
Rotating coil
The functioning of the electric current generator is based on the rotation of the coil in a magnetic flux, where there is a certain number of turns. EMF is induced in an electric circuit always when it is crossed by a magnetic flux, based on the magnetic flux formula Ф \u003d B x S x cos α (magnetic induction multiplied by the surface area through which the magnetic flux passes, and the cosine of the angle formed by the direction vector and the perpendicular plane lines).
According to the formula, F is affected by changes in situations:
- when the magnetic flux changes, the direction vector changes;
- the area enclosed in the contour changes;
- angle changes.
It is allowed to induce EMF with a stationary magnet or a constant current, but simply when the coil rotates around its axis within the magnetic field. In this case, the magnetic flux changes as the angle changes. The coil in the process of rotation crosses the lines of force of the magnetic flux, as a result, an EMF appears. With uniform rotation, a periodic change in the magnetic flux occurs. Also, the number of field lines that cross every second becomes equal to the values at regular intervals.
In practice, in alternating current generators, the coil remains stationary, and the electromagnet rotates around it.
EMF self-induction
When an alternating electric current passes through the coil, an alternating magnetic field is generated, which is characterized by a changing magnetic flux that induces an EMF. This phenomenon is called self-induction.
Due to the fact that the magnetic flux is proportional to the intensity of the electric current, then the self-induction EMF formula looks like this:
Ф = L x I, where L is the inductance, which is measured in H. Its value is determined by the number of turns per unit length and the value of their cross section.
Mutual induction
When two coils are located side by side, they observe the EMF of mutual induction, which is determined by the configuration of the two circuits and their mutual orientation. With increasing separation of the circuits, the value of mutual inductance decreases, since there is a decrease in the total magnetic flux for the two coils.
Let us consider in detail the process of the emergence of mutual induction. There are two coils, current I1 flows through the wire of one with N1 turns, which creates a magnetic flux and goes through the second coil with N2 number of turns.
The value of the mutual inductance of the second coil in relation to the first:
M21 = (N2 x F21)/I1.
Magnetic flux value:
F21 = (M21/N2) x I1.
The induced emf is calculated by the formula:
E2 = - N2 x dФ21/dt = - M21x dI1/dt.
In the first coil, the value of the induced emf:
E1 = - M12 x dI2/dt.
It is important to note that the electromotive force provoked by mutual inductance in one of the coils is in any case directly proportional to the change in electric current in the other coil.
Then the mutual inductance is considered equal to:
M12 = M21 = M.
As a consequence, E1 = - M x dI2/dt and E2 = M x dI1/dt. M = K √ (L1 x L2), where K is the coupling coefficient between the two inductance values.
Mutual inductance is widely used in transformers, which make it possible to change the value of an alternating electric current. The device is a pair of coils that are wound on a common core. The current in the first coil forms a changing magnetic flux in the magnetic circuit and a current in the second coil. With fewer turns in the first coil than in the second, the voltage increases, and, accordingly, with a greater number of turns in the first winding, the voltage decreases.
Beyond generating and transforming electrical energy, the phenomenon of magnetic induction is used in other devices. For example, in magnetic levitation trains moving without direct contact with the current in the rails, but a couple of centimeters higher due to electromagnetic repulsion.
What's happened EMF(electromotive force) in physics? Electric current is not understood by everyone. Like space distance, only under the very nose. In general, it is not fully understood by scientists either. Enough to remember Nikola Tesla with his famous experiments, centuries ahead of their time and even today remaining in a halo of mystery. Today we are not solving big mysteries, but we are trying to figure out what is emf in physics.
Definition of EMF in physics
EMF is the electromotive force. Denoted by letter E or the small Greek letter epsilon.
Electromotive force- scalar physical quantity characterizing the work of external forces ( forces of non-electric origin) acting in electrical circuits of alternating and direct current.
EMF, like voltage e, measured in volts. However, EMF and voltage are different phenomena.
Voltage(between points A and B) - physical quantity, equal to work effective electric field produced by the transfer of a unit test charge from one point to another.
We explain the essence of EMF "on the fingers"
To understand what is what, we can give an analogy example. Imagine that we have a water tower completely filled with water. Compare this tower with a battery.
Water exerts maximum pressure on the bottom of the tower when the tower is full. Accordingly, the less water in the tower, the weaker the pressure and pressure of the water flowing from the tap. If you open the tap, the water will gradually flow out at first under strong pressure, and then more and more slowly until the pressure weakens completely. Here stress is the pressure that the water exerts on the bottom. For the level of zero voltage, we will take the very bottom of the tower.
It's the same with the battery. First, we include our current source (battery) in the circuit, closing it. Let it be a watch or a flashlight. While the voltage level is sufficient and the battery is not discharged, the flashlight shines brightly, then gradually goes out until it goes out completely.
But how to make sure that the pressure does not run out? In other words, how to maintain a constant water level in the tower, and a constant potential difference at the poles of the current source. Following the example of the tower, the EMF is presented as a pump, which ensures the influx of new water into the tower.
The nature of the emf
The reason for the occurrence of EMF in different current sources is different. According to the nature of occurrence, the following types are distinguished:
- Chemical emf. Occurs in batteries and accumulators due to chemical reactions.
- Thermo EMF. Occurs when contacts of dissimilar conductors at different temperatures are connected.
- EMF of induction. Occurs in a generator when a rotating conductor is placed in a magnetic field. EMF will be induced in a conductor when the conductor crosses the lines of force of a constant magnetic field or when the magnetic field changes in magnitude.
- Photoelectric EMF. The occurrence of this EMF is facilitated by the phenomenon of an external or internal photoelectric effect.
- Piezoelectric emf. EMF occurs when a substance is stretched or compressed.
Dear friends, today we have considered the topic "EMF for Dummies". As you can see, the EMF force of non-electric origin, which maintains the flow of electric current in the circuit. If you want to know how problems with EMF are solved, we advise you to contact our authors– scrupulously selected and proven specialists who will quickly and clearly explain the course of solving any thematic problem. And by tradition, at the end we invite you to watch the training video. Happy viewing and good luck with your studies!
Themes USE codifier : electromotive force, current source internal resistance, Ohm's law for a complete electrical circuit.
Until now, in the study of electric current, we have considered the directed motion of free charges in external circuit, that is, in conductors connected to the terminals of the current source.
As we know, positive charge:
Goes into the external circuit from the positive terminal of the source;
Moves in an external circuit under the influence of a stationary electric field created by other moving charges;
It comes to the negative terminal of the source, completing its path in the external circuit.
Now our positive charge needs to close its trajectory and return to the positive terminal. To do this, he needs to overcome the final segment of the path - inside the current source from the negative terminal to the positive. But think about it: he doesn’t want to go there at all! The negative terminal attracts it to itself, the positive terminal repels it from itself, and as a result, an electric force acts on our charge inside the source, directed against charge movement (i.e. against the direction of the current).
third party force
However, current flows through the circuit; therefore, there is a force that “drags” the charge through the source despite the opposition of the electric field of the terminals (Fig. 1).
Rice. 1. Third party power
This force is called outside force; It is thanks to her that the current source functions. An external force has nothing to do with a stationary electric field - it is said to have non-electric origin; in batteries, for example, it arises due to the flow of appropriate chemical reactions.
Denote by the work of an external force to move the positive charge q inside the current source from the negative terminal to the positive one. This work is positive, since the direction of the external force coincides with the direction of charge movement. The work of an external force is also called current source operation.
There is no external force in the external circuit, so the work of the external force to move the charge in the external circuit is zero. Therefore, the work of an external force in moving the charge around the entire circuit is reduced to the work of moving this charge only inside the current source. Thus, this is also the work of an external force in moving the charge throughout the chain.
We see that the external force is non-potential - its work when moving a charge along a closed path is not equal to zero. It is this non-potentiality that ensures the circulation of electric current; the potential electric field, as we said earlier, cannot support a constant current.
Experience shows that work is directly proportional to the charge being moved. Therefore, the ratio is no longer dependent on the charge and is a quantitative characteristic of the current source. This relationship is indicated by:
(1)
This value is called electromotive force(EMF) current source. As you can see, EMF is measured in volts (V), so the name "electromotive force" is extremely unfortunate. But it has long been rooted, so you have to put up with it.
When you see the inscription on the battery: "1.5 V", then know that this is exactly the EMF. Is this value equal to the voltage that the battery creates in the external circuit? It turns out not! Now we will understand why.
Ohm's law for a complete circuit
Any current source has its own resistance, which is called internal resistance this source. Thus, a current source has two important characteristics: EMF and internal resistance.
Let a current source with an EMF equal to , and an internal resistance is connected to a resistor (which in this case is called external resistor, or external load, or payload). All this together is called complete chain(Fig. 2).
Rice. 2. Complete chain
Our task is to find the current in the circuit and the voltage across the resistor.
In time, a charge passes through the circuit. According to formula (1), the current source does the work:
(2)
Since the current strength is constant, the work of the source is entirely converted into heat, which is released at the resistances and. This amount of heat is determined by the Joule–Lenz law:
(3)
So, , and we equate the right parts of formulas (2) and (3) :
After reducing to we get:
So we found the current in the circuit:
(4)
Formula (4) is called Ohm's law for a complete circuit.
If you connect the source terminals with a wire of negligible resistance, then you get short circuit. In this case, the maximum current will flow through the source - short circuit current:
Due to the smallness of the internal resistance, the short-circuit current can be very large. For example, a penlight battery heats up at the same time so that it burns your hands.
Knowing the current strength (formula (4)), we can find the voltage across the resistor using Ohm's law for the circuit section:
(5)
This voltage is the potential difference between the points and (Fig. 2). The potential of the point is equal to the potential of the positive terminal of the source; the potential of the point is equal to the potential of the negative terminal. Therefore, stress (5) is also called voltage at the source terminals.
We see from formula (5) what will happen in a real circuit - after all, it is multiplied by a fraction less than one. But there are two cases where .
1. Ideal current source. This is the name of a source with zero internal resistance. At , formula (5) gives .
2. Open circuit. Consider the current source itself, outside the electrical circuit. In this case, we can assume that the external resistance is infinitely large: . Then the value is indistinguishable from , and formula (5) again gives us .
The meaning of this result is simple: if the source is not connected to the circuit, then the voltmeter connected to the poles of the source will show its EMF.
Electric circuit efficiency
It's not hard to see why a resistor is called a payload. Imagine it's a light bulb. The heat generated by a light bulb is useful, because thanks to this warmth, the light bulb fulfills its purpose - it gives light.
Let us denote the amount of heat released on the payload during the time .
If the current in the circuit is , then
A certain amount of heat is also released at the current source:
The total amount of heat released in the circuit is:
Electric circuit efficiency is the ratio of useful heat to total:
The efficiency of the circuit is equal to unity only if the current source is ideal.
Ohm's law for a heterogeneous area
Ohm's simple law is valid for the so-called homogeneous section of the circuit - that is, the section on which there are no current sources. Now we will obtain more general relations, from which both Ohm's law for a homogeneous section and the Ohm's law obtained above for a complete chain follow.
The section of the circuit is called heterogeneous if it has a current source. In other words, an inhomogeneous section is a section with an EMF.
On fig. 3 shows an inhomogeneous section containing a resistor and a current source. The EMF of the source is , we consider its internal resistance zero(if the internal resistance of the source is , you can simply replace the resistor with a resistor).
Rice. 3. EMF "helps" the current:
The current strength in the section is equal, the current flows from point to point. This current is not necessarily caused by a single source. The area under consideration, as a rule, is part of a circuit (not shown in the figure), and other current sources may be present in this circuit. Therefore, the current is the result of the cumulative action all sources in the circuit.
Let the potentials of the points and be equal to and , respectively. We emphasize once again that we are talking about the potential of a stationary electric field generated by the action of all sources of the circuit - not only the source belonging to this section, but also, possibly, available outside this section.
The voltage in our area is: In time, a charge passes through the section, while the stationary electric field does the work:
In addition, the positive work is done by the current source (after all, the charge has passed through it!):
The current strength is constant, therefore, the total work to advance the charge, performed on the site by a stationary electric field and external source forces, is completely converted into heat:.
We substitute here the expressions for , and the Joule–Lenz law:
Reducing by , we get Ohm's law for an inhomogeneous section of a circuit:
(6)
or, which is the same:
(7)
Notice the plus sign in front of it. We have already indicated the reason for this - the current source in this case performs positive work, "dragging" the charge inside itself from the negative terminal to the positive. Simply put, the source "helps" current flow from point to point.
We note two consequences of the derived formulas (6) and (7) .
1. If the site is homogeneous, then . Then from formula (6) we obtain - Ohm's law for a homogeneous section of the chain.
2. Suppose that the current source has an internal resistance. This, as we already mentioned, is equivalent to replacing with:
Now let's close our section by connecting the points and . We obtain the complete chain discussed above. In this case, it turns out that the previous formula will also turn into Ohm's law for a complete chain:
Thus, Ohm's law for a homogeneous section and Ohm's law for a complete circuit both follow from Ohm's law for an inhomogeneous section.
There may be another case of connection, when the source "prevents" the current from flowing through the section. Such a situation is shown in Fig. 4 . Here, the current coming from to is directed against the action of external forces of the source.
Rice. 4. EMF "interferes" with the current:
How is this possible? It's very simple: other sources available in the circuit outside the section under consideration "overpower" the source in the section and force the current to flow against. This is exactly what happens when you put the phone on charge: the adapter connected to the outlet causes the movement of charges against the external forces of the phone's battery, and the battery is thereby charged!
What will change now in the derivation of our formulas? Only one thing - the work of external forces will become negative:
Then Ohm's law for an inhomogeneous section will take the form:
(8)
where, as before, is the voltage on the section.
Let's put formulas (7) and (8) together and write Ohm's law for the section with EMF as follows:
The current flows from point to point. If the direction of the current coincides with the direction of external forces, then a “plus” is placed in front; if these directions are opposite, then "minus" is put.
Electric current does not flow in a copper wire for the same reason that water remains stationary in a horizontal pipe. If one end of the pipe is connected to a tank in such a way that a pressure difference is formed, liquid will flow out of one end. Similarly, to maintain a constant current, an external force is needed to move charges. This effect is called electromotive force or EMF.
Between late XVIII And early XIX centuries of work by scientists such as Coulomb, Lagrange and Poisson laid the mathematical foundations for determining electrostatic quantities. Progress in the understanding of electricity at this historical stage is obvious. Franklin had already introduced the concept of "quantity of electrical substance", but so far neither he nor his successors have been able to measure it.
Following the experiments of Galvani, Volta tried to find evidence that the "galvanic fluids" of the animal were of the same nature with static electricity. In search of the truth, he discovered that when two electrodes made of different metals are in contact through an electrolyte, both are charged and remain charged despite the circuit being closed by a load. This phenomenon did not correspond to the existing ideas about electricity, because the electrostatic charges in such a case had to recombine.
Volta introduced a new definition of force acting in the direction of separation of charges and maintaining them in this state. He called it electromotive. Such an explanation of the description of the operation of the battery did not fit into theoretical basis physics of that time. In the Coulomb paradigm of the first third of the 19th century e. d.s. Volta was determined by the ability of some bodies to generate electricity in others.
The most important contribution to the explanation of the operation of electrical circuits was made by Ohm. The results of a number of experiments led him to construct a theory of electrical conductivity. He introduced the value of "voltage" and defined it as the potential difference across the contacts. Like Fourier, who in his theory distinguished between the amount of heat and temperature in heat transfer, Ohm created a model by analogy relating the amount of charge transferred, voltage and electrical conductivity. Ohm's law did not contradict the accumulated knowledge about electrostatic electricity.
The electromotive force, in the people of EMF, as well as the voltage is measured in volts, but is of a completely different nature.
EMF in terms of hydraulics
I think you are already familiar with the water tower from the last article about
Assume that the tower is completely filled with water. We drilled a hole at the bottom of the tower and cut a pipe into it, through which water runs to your house.
The neighbor wanted to water the cucumbers, you decided to wash the car, the mother started the laundry and voila! The flow of water became less and less, and soon completely dried up ... What happened? The tower ran out of water...
The time it takes to empty the tower depends on the capacity of the tower itself, as well as how many consumers will use the water.
All the same can be said about the radio element capacitor:
Let's say we charged it from a 1.5 volt battery and it took a charge. Let's draw a charged capacitor like this:
But as soon as we connect a load to it (let the LED be the load) by closing the key S, in the first fraction of seconds the LED will glow brightly, and then fade away quietly ... and until it goes out completely. The extinction time of the LED will depend on the capacitance of the capacitor, as well as on what load we attach to the charged capacitor.
As I said, this is tantamount to a simple filled tower and consumers who use water.
But why then does our towers never run out of water? Yes because it works. water supply pump! Where does this pump get its water from? From a well that was drilled to extract groundwater. Sometimes it is also called artesian.
As soon as the tower is completely filled with water, the pump turns off. In our water towers, the pump always supports maximum level water.
So, let's remember what is stress? By analogy with hydraulics, this is the water level in the water tower. A full tower is the maximum water level, which means the maximum voltage. No water in the tower - zero voltage.
EMF of electric current
As you remember from previous articles, water molecules are “electrons”. For an electric current to occur, the electrons must move in the same direction. But for them to move in the same direction, there must be tension and some kind of load. That is, the water in the tower is a tension, and the people who spend water for their needs are a burden, since they create a flow of water from a pipe located at the foot of the tower. And the flow is nothing but the strength of the current.
The condition must also be observed that the water must always be at the maximum level, regardless of how many people spend it for their needs at the same time, otherwise the tower will be empty. For a water tower, this life-saving tool is a water pump. What about electric current?
For an electric current, there must be some kind of force that would push the electrons in one direction for a long time. That is, this force must move the electrons! Electromotive force! Yes exactly! ELECTROMOTIVE FORCE! You can call it abbreviated EMF - E electro D seeing WITH silt. It is measured in volts, like voltage, and is indicated mainly by the letter E.
Does this mean that our batteries also have such a “pump”? There is, and it would be more correct to call it “electron pump”). But, of course, no one says that. They simply say - EMF. I wonder where this pump is hidden in the battery? This is simply an electrochemical reaction, due to which the “water level” in the battery is kept, but then, nevertheless, this pump wears out and the voltage in the battery begins to sag, because the “pump” does not have time to pump water. In the end, it completely breaks down and the voltage on the battery drops to almost zero.
Real EMF source
The source of electrical energy is a source of EMF with internal resistance R ext. It could be any chemical elements power supplies such as batteries and accumulators
Their internal structure in terms of EMF looks something like this:
Where E is the EMF, and R ext is the internal resistance of the battery
So what conclusions can be drawn from this?
If no load clings to the battery, such as an incandescent lamp, etc., then as a result, the current strength in such a circuit will be zero. A simplified diagram would be:
But if we nevertheless attach an incandescent bulb to our battery, then our circuit will become closed and current will flow in the circuit:
If you draw a graph of the dependence of the strength in the current circuit on the voltage on the battery, then it will look like this:
What is the conclusion? In order to measure the EMF of a battery, we just need to take a good multimeter with a high input resistance and measure the voltage at the battery terminals.
Ideal EMF source
Let's say that our battery has zero internal resistance, then it turns out that R ext \u003d 0.
It is easy to guess that in this case the voltage drop across zero resistance will also be zero. As a result, our graph will look like this:
As a result, we got just an EMF source. Therefore, an EMF source is an ideal power source, in which the voltage at the terminals does not depend on the strength of the current in the circuit. That is, no matter what load we would attach to such an EMF source, in our case it will still give out the required voltage without a drawdown. The EMF source itself is designated as follows:
In practice, there is no ideal source of emf.
EMF types
– electrochemical(EMF of batteries and accumulators)
– photoelectric effect(receiving electric current from solar energy)
– induction(generators using the principle of electromagnetic induction)
– Seebeck effect or thermoEMF(the occurrence of an electric current in a closed circuit consisting of dissimilar conductors connected in series, the contacts between which are at different temperatures)
– piezoEMF(receiving EMF from )
