Flow of induction |
Electric
inductance and its calculation |
Nature
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Created it, 05/10/16
Update it, 05/10/17
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After having studied the condensers, We now will analyze the third fundamental component of the electric circuits : the reel. This component brings into play electric and magnetic phenomena.
The analysis of the existing bonds between the electric and magnetic phenomena is called electromagnetism.
We know already what depends magnetism, the manner whereby it appears and the fundamental laws which govern it. We now will operate in the same way electromagnetism.
1. 1. MAGNETIC EFFECT OF THE CURRENT
The Danish physicist Hans Christian OERSTED (1777 - 1851) is the first to establish the correlation between the electric and magnetic phenomena, and this thanks to an experiment like that represented on figure 1. From this experiment, it notes that by suspending a needle magnetized a driver parallel to (figure 1-a), we note that when a current traverses this one, the magnetized needle swivels and places itself perpendicularly with the driver (figure 1-b).
Thereafter, AMP (1775 - 1836) notes that the direction in which the needle swivels depends on the direction of displacement of the current in the driver.
When the current crosses the driver of the left towards the line as on the figure 1-b, the North Pole of the magnetized needle is put on a side of the driver, if the current, like appears 1-c, traverses the driver of the right-hand side towards the left, the North Pole of the magnetized needle puts on the other side of the driver.
This experiment shows that the electrical current acts in a way well defined on the magnetized needle. This way is connected with the effect produced by a magnetic field on this same magnetized needle. Indeed, previously, we saw that a magnetized needle is always aligned according to tension fields' of a magnetic field. We can thus allot to the electrical current a magnetic effect which consists of the creation of a magnetic field around the drivers traversed by this current.
To determine the pace of the tension fields of the magnetic field generated by the electrical current, it is enough for us, as shows it the figure with, to place the needle magnetized in various places all around the driver placed vertically. We note whereas the positions taken by the needle in various points located at equal distance of the driver roughly describe a circle whose center is the conductive.
We can deduce the pace from the magnetic field around the driver and represent its tension fields from it as the figure 2-b shows it.
The influence of the magnetic field created by the driver is felt in any point of space surrounding the driver. However, with an aim of not complicating the figure 2-b, only some tension fields are drawn, which is sufficient for us to have an idea of the aspect of the magnetic field. By observing the figure with, we note that the poles of the magnetized needle position in two positions opposed according to direction's of the displacement of the current in the driver. From this observation, we deduce that according to the direction of the current, the tension fields of the magnetic field created are directed differently.
It is thus necessary that, knowing the direction of the current, we can determine the direction of the tension fields. This need is the subject of the rule of MAXWELL called also rule of the corkscrew.
According to this rule, imagine we to have a corkscrew laid out along the driver, and to make it turn so that it moves in the same direction as the current (conventional direction). The direction of rotation of the corkscrew thus determined indicates the direction of the tension fields of the magnetic field.
To highlight the remarks of this rule, we defer on the figure 3 in which the two cases of the experiment previously carried out are deferred.
1. 2. - THE REEL
After having considered the magnetic field generated by an electrical current traversing a rectilinear driver, let us analyze the case of the reel now. A reel is simply consisted of the same driver, but rolled up on itself and either rectilinear.
Let us take again the driver of figures 2 and 3 and fold up it so as to obtain figure 4. The driver thus folded up constitutes a whorl.
Figure 4 are represented the fields tension of the magnetic field created by the current which traverses the whorl. The tension fields are, as for the case of the rectilinear driver, circulars but contrary to the above mentioned case, their center is not any more the conductive but is outside the whorl.
With the sights of figure 4, we note that the tension whorl and fields are dependent between them as the links of a chain and, for this reason, we say that the tension fields are embraced by the whorl. The whorl is the most elementary type of reel being able to exist.
In general, the reels consist of several jointed whorls. Using figure 5, analyze what becomes the magnetic field created by current I, when we associate one second whorl with the preceding one.
Each of the two whorls produces its own magnetic field whose some tension fields appear figure 5-a.
At point A represented figure 5-a and in the surroundings of this one, we can consider that the magnetic field is null. Indeed, the magnetic field at point A is the field resulting from the fields of each whorl, but, in this point, the fields tension of each whorl being opposite direction, the resulting field is null. In practice, in the points which we have just considered (not A and its surroundings), the tension fields are cancelled and their general pace for the two whorls takes the form illustrated appears 5-b. The tension fields are common to both whorls.
This shows that two close whorls do not produce two distinct magnetic fields, but a single magnetic field.
The same magnetic field can be produced differently. Instead of making traverse the two whorls by two distinct currents of the same intensity as in the figure 5-a and 5-b, we can feed the two whorls by the same current and this by connecting them one to the other in series like illustrated appears 5-c.
In this provision, the same current crosses successively each whorl and the magnetic field thus created is identical to the case of the figure 5-b.
Each whorl contributes its share to the production of the magnetic field and we deduce that :
The magnetic field produced by a reel is all the more important as the number of whorls of this reel is large.
To illustrate this, let us consider the two reels of figure 6.
The reel of the figure 6-a has six whorls while the reel of the figure 6-b has 30 of them, i.e. five times more. If they is two reels are traversed by a current (I) of the same intensity, the field produced by the reel of the figure 5-b is of five times superior to that of the reel represented figure 6-a. On the other hand, if in the latter we apply a current of intensity five times superior to the initial current I, then the magnetic fields produced by this reel becomes equal to that of the reel of the figure 6-a. We deduce that :
The magnetic field produced by a reel is all the more important as the intensity of the current which it cross-piece is high.
Of the two deductions which we have just made, we can say that the magnetic field depends on the product of the number of whorls (N) by current I.
This product, it is given the number of magnetomotive force symbol f.m.m.
The unit of the magnetomotive force is the ampere turn symbol At.
Generally, the driver is rolled up on an insulating material cylindrical component. The whorls can not be jointed but they must remain very close. If the wire is insulated, it can be rolled up in several superimposed layers, with the proviso of not changing the direction of the rolling up (condition whose we will see the cause further).
In addition, if the length of the reel exceeds ten times its diameter, we are in the presence of a solenoid or winds long.
As we see it on figure 6, the rolling up of the driver has for principal incidence to concentrate the tension fields of the magnetic field inside the reel. The magnetic field inside the reel is thus much more intense than outside where the tension fields disperse. The result of this concentration appears figure 6-b clearly. The tension fields inside the reel are practically parallel between them thus giving rise to a uniform magnetic field.
In the case of a reel, as in that of the simple driver, it is possible to determine the direction of the tension fields according to the direction of circulation of the electrical current. For this, we will have recourse, once again, with the rule of the corkscrew, but observed differently.
The application of the rule of the corkscrew to a reel is illustrated figure 7.
The corkscrew is laid out along the axis of the reel. While turning the corkscrew in the direction where the current in the reel turns, the direction in which the corkscrew moves indicates the direction of the tension fields inside the reel.
We deduce from it that the pole by where leave the tension fields is a North Pole and that the pole by where they return in the reel is a South Pole. This supplements the similarity with the natural magnet.
1. 3. - FLOW
OF INDUCTION
We now know to obtain a magnetic field starting from a reel traversed by a current, see now how this field can be used.
Let us introduce inside a reel a ferromagnetic metal bar, as represented figure 8-a.
The bar is then called core of the reel
Theory relating to magnetism, we know that any ferromagnetic material placed in a magnetic field acquires magnetic properties owing to the fact that the small elementary magnets which constitute it, are directed according to tension fields' of the magnetic field. The bar placed in the magnetic field of the reel does not escape from this rule, and as we see it figure 8-a, the core is magnetized by induction and becomes a genuine magnet. It then presents a North Pole and a South Pole at its ends. If the core is made out of steel, it preserves magnetizing even when the current ceases traversing the reel, it is besides with this method that the permanent magnets are obtained. So on the other hand, the core is out of soft iron, it is magnetized or demagnetized according to whether the current circulates or not in the reel. The soft iron cores are used for the realization of electro-magnets.
Since the core of the reel is magnetized while becoming loving, it produces in its turn its own magnetic field which is added to that produced by the reel. What it is necessary to note, it is that the magnetic field of the core can become several hundreds of times superior to that produced by the reel alone.
The introduction of a core into a reel makes it possible to extremely obtain a magnetic field with a low intensity of current.
The pace of the tension fields produced by the reel and its core are drawn figure 8-B These fields tension are also called lines of induction because they are precisely due to magnetizing by induction of the core. The whole of all the lines of induction constitutes the flow of induction produced by the reel.
The symbol of the flow of induction is the Greek letter phi : Ø
A reel without core also has the property to produce a flow of induction if we regard the tension fields as being lines of induction.
In the case of a reel alone, we can say that the core of this one, although not existing is actually the air included by the rolling up of the reel. Naturally, in this last case, the air not having the capacity of magnetizing of a core, the produced flow of induction is lower by far : In conclusion, we can say that the flow of induction of a reel depends mainly on material placed in its rolling up.
It is now necessary to regard the reel either an element able to exert a force of attraction on ferromagnetic materials, but as an element able to magnetize, by induction, material placed in its rolling up. The reel thus creates a flow of induction which depends on the particular type of material used.
The flow of induction is measured in Weber (Wb symbol). This measuring unit owes its name to the German physicist Wihlem WEBER (1804 - 1891).
To produce a flow of induction, we must make circulate a current in the whorls of the reel thus to create a magnetomotive force.
We can allot to this magnetomotive force the production of the flow of induction on behalf of the reel.
1. 4. - ELECTRIC INDUCTANCE AND ITS CALCULATION
Each reel is characterized according to its aptitude to just like produce a flow embraced when its whorls are traversed by a current, a condenser is characterized by its aptitude to accumulate electric charges between its reinforcements when they are subjected to a potential difference.
This aptitude of the reel is called electric inductance (symbol L).
A reel is thus characterized by the value of its inductance L, as a resistance is characterized by its resistive value R and a condenser by its value capacity C.
Let us recall that the capacitance of a capacitor is indicated by the quantity of electricity present on one or the other of its reinforcements according to the existing potential difference between this one : C = Q / V
In a similar way, the inductance of a reel is indicated by the flow of induction embraced by its whorls according to the current which crosses them. In this case also, we obtain the inductance of a reel given by dividing the total flow embraced by the current which produces it :
Measuring flow in Weber and the current in amp, inductance is measured in Weber/amp. With this unit, it is given the name of Henry (symbol H) in memory to the American physicist Joseph HENRY (1797 - 1878) with whom we must of important studies in particular on the self-induction.
In many cases, Henry represents a too important unit, also we have recourse to the millihenry (symbol mH) which is worth thousandths of Henry, or to the microhenry (symbol µH) which is worth one millionth of Henry.
Between the condenser and the reel, there are other analogies which it is wise to highlight.
By applying a terminal voltage of a condenser, its dielectric polarizes electrically insofar as at its ends a North Pole and a South Pole appear. Thus, as the capacitance of a capacitor depends on its dielectric, in the same way the inductance of a reel depends on the nature of its core, which we already know considering that a reel into which we introduce a core produced a more important flow of induction.
Into the case of the condenser, we introduced the concept of absolute permittivity (µr). For the condenser with air, this constant takes the name of permittivity of the air or vacuum (µo), while into the case of a condenser with dielectric solid, we introduced the concept of permittivity relating to the air (µr). µr expresses by how much time the capacitance of a capacitor increases when we replace the air by a dielectric solid. From there, we deduced the following formula from it :
In the same way for a reel, we hold account of the influence of material constituting its core and we then consider the absolute magnetic permeability of the material of which the symbol and the Greek letter µ (is read ''driven"). The absolute magnetic permeability of a material is expressed as a Henry per meter (symbol H / m).
The magnetic permeability is the coefficient which characterizes the magnetic properties of a body. Its aptitude to guide the flow of magnetic induction increases with its permeability.
For a reel without core, therefore having only air in its medium, we will hold account of the magnetic permeability of the air or of the vacuum indicated by the symbol µo and which has as a value 4 Õ x 10-7 H / m, that is to say to facilitate calculations 1,256 µH / m.
If we introduce a material inside the reel, we then multiply the magnetic permeability of the air or the vacuum µo by a coefficient called relative magnetic permeability compared to the air or to the vacuum and symbolized by µr.
The absolute magnetic permeability µ is obtained by the product of µo by µr.
The magnetic permeability relating to the air or the vacuum µr does not have any unit since it acts of a report/ratio as in the case of µo seen for the condenser.
In the table of figure 9 are given the relative magnetic permeabilities of materials used for the design of cores.
|
MATERIAL |
Relative magnetic permeability µr |
||
|
Water |
0,999991 |
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|
Money |
0,999981 |
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|
air |
1,0000004 |
||
|
Iron with silicon |
7 000 maximum |
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|
|
|
||
|
Anhyster |
2 000 to 5 000 |
||
|
Mumétal |
100 000 maximum |
||
|
Permimphy |
150 000 to 250 000 |
In theory, the value of 1 is given to µr for all the substances which are not ferromagnetic, i.e. the air and to the supports of windings such as bakelite, the plastics, glass, quartz, ceramics, etc...
That in the case of the condenser, the dielectric one occupies all the space ranging between its reinforcements, i.e. all should be noted the space crossed by the tension fields of the electric field. On the other hand, in the case of the reel, the core is only inside winding and does not occupy all the space crossed by the tension fields of the magnetic field because this one, as represented figure 10 also pass outside winding.
In short, so that the analogy between the condenser and the reel is total, it would be necessary that the core occupies the totality of the space crossed by the lines of induction, in other words that the core is in more external with winding.
In such a configuration, the core called also magnetic circuit known as is closed. It is the case, for example, of the transformers. Conversely, a reel such as that of figure 10 with an open magnetic circuit.
It is thus only in the case of a closed magnetic circuit where the totality of the flow of induction passes in the ferromagnetic core which we can say as in the case of the condenser that the magnetic permeability relating to the air indicates by how much time the inductance of the reel increases when it is provided with a core.
In the case of an open magnetic circuit, the influence of the core is less but remains dominating.
In this lesson, we will limit ourselves to consider the calculation of the inductance of a reel without core, giving calculation relating to the reels provided with core, when we meet the practical applications of them.
Let us see on which elements inductance depends on a reel without core.
Initially, inductance depends on the section of the whorls constituting the reel. This section is the surface circumscribed by the driver as we see it for a whorl on figure 11 where this hatched surface.
It is comprehensible that more the section of the reel is important plus the embraced flow of induction is important.
The inductance of a reel is thus proportional to its section:
The inductance of a reel also depends on the square of the number of its whorls. To realize of this, let us consider figure 12 where two reels are drawn. The first has a whorl (figure 12-a) and the second five whorls (figure 12-b).
If the two reels are traversed by a current (I) of the same intensity, the reel with five whorls produces magnetic fields five times superior with the field produced by the reel with single whorl. In addition, we had introduced into the first lines above of this lesson, the notion of the flow embraced by the whorl. The more flow of induction is embraced by the current, plus its tension fields are thus concentrated more is important the intensity of flow.
The reel multispires of the figure 12-b embraces five times plus flow that the reel of the figure 12-a.
In conclusion, the intensity of the flow produced by a reel, depends on the square of the number of whorls. Since inductance is related to flow, we can say :
The inductance of a reel is proportional to the square of the number of its whorls.
As a last chief, inductance depends on the length of the reel. To include/understand how the length of the reel can influence its inductance, let us consider figure 13.
On figure 13 are represented two reels having an identical number of whorls, in fact 6. These two reels have the same section but their winding is such as the reel of the figure 13-a ; a 3 cm has length while that of the figure 13-b is twice longer and measures 6 cm. If the two reels are traversed by a current (I) of the same intensity, those having the same number of whorls, the magnetomotive force that they generate is identical.
The f.m.m. being the cause of the production of flow, we can think rightly which they thus embrace same flow has same inductance. But reality is much more complex and the flow of induction depends not only on the magnetomotive force but also on way in which this force is distributed along the reel.
Let us take again our two reels of figure 13, that of the figure 13-a ; is two whorls per centimetre length, while the reel of the figure 13-b has only one whorl with the centimetre. Consequently, the flow produced by the first reel is double among that produced by the second. We can conclude that the flow embraced by the whorls of a reel (thus not inductance) depends on the length of the reel.
The inductance of a reel is inversely proportional to its length.
We now have all the elements to state the formula of computation of inductance :
For a reel without core, inductance is obtained by multiplying the magnetic permeability of the air by the section of the whorls and the square of the number of whorls and by dividing the product by the length of the reel. In short, we obtain the following formula :
L: Inductance out of H
µo: Magnetic permeability of the air or the vacuum out of H / m
N2 : A number of whorls squared
S: Section of the whorl in m2
L: Length in m
NOTE : In a reel having the air like core, the absolute magnetic permeability (µ) is equal to the magnetic permeability of the air or of the vacuum is µo, since in this case, the magnetic permeability relating to the air or the vacuum µo is equal to 1. The formula can thus be written :
This formula of computation of inductance is however valid only when all the lines of induction are embraced by all the whorls as in the case of the reel represented figure 14-a.
When the whorls are, on the contrary, isolated as in the case of the drawn reel figure 14-b, it arrives that certain tension fields are not embraced by the totality of the whorls of the reel. In this case, the flow embraced and consequently, the inductance of the reel is less.
Moreover, the formula of computation of (L) which us has just seen is not more applicable and in practice, it is necessary to hold account of this characteristic by introducing coefficients of correction as we will see it in the forms.
To finish, you must know that the inductance (L) of a reel is also called coefficient of self-induction.
In the table of figure 15, are gathered the sizes introduced into this lesson devoted explicitly to the reel like their unit and their formula so necessary.
|
SIZE |
MEASURING UNIT |
FORMULATE |
|
Denomination |
Symbol |
Denomination |
Symbol |
|
|
Magnetomotive force |
f.m.m. |
amp-turn |
At |
f.m.m. = N x I |
|
Absolute magnetic permeability |
µ |
Henry per meter |
H / m |
|
|
Inductance |
L |
henry |
H |
L = µ x (N2) / l |
|
Flux d'induction |
Ø |
Weber |
Wb |
Ø = L x I |
2. - NATURE
OF MAGNETISM
In the lesson devoted to magnetism, we did not bring a concrete and allowed explanation to the fact that certain substances have magnetic properties.
There are two theories on this subject; however, one of it resting on no concept equipped with real existence, we will choose that recommended per AMP.
This theory is founded on the existence of particulate currents and does not distinguish magnetism itself from electromagnetism. It found its interpretation in the movement of the electrons of the atoms.
We know that a whorl traversed by an electrical current produces a magnetic field; we also know that this current is due to a displacement of electrons. We can thus allot the magnetic fields to the fact that the electrons derive a gyration along the whorl.
If we remember now the structure of an atom, we see that in this case also, of the electrons revolve on circular orbits around a core. Consequently, there is no reason so that the electrons of a body do not produce a magnetic field similar to that caused by the electrons circulating in a whorl.
The atoms can be considered, or more precisely their electronic orbit like a tiny whorl.
Figure 16 represents the analogy between a whorl traversed by a current and an electronic orbit of an atom.
In a piece of demagnetized material ferromagnetic, the electronic orbits of each one of its atoms are laid out in a disordered way like illustrated appears 17-a.
Consequently, each field thus created is directed in a different direction. The magnetic fields cannot combine their effects and the total effect remains non-existent. On the other hand, if the body is magnetized, it is the case of the figure 17-b, all the electronic orbits align one compared to the other in a coherent way thus generating a magnetic field.
Let us note after these explanations relating to magnetism that all the phenomena considered until now must with the electrons.
For the drivers, the electrical current is due to a displacement of electrons.
For the condensers, the polarization of dielectric must with décalement of the electronic orbits compared to their core.
For the magnets and the reels, magnetic polarization must with the particular orientation of the electronic orbits.
Having already seen that the passage of the electrical current, as the polarization of dielectric involve an electric consumption of power, it is easy to understand that the magnetic polarization of a core also requires a certain energy. This energy is provided by the reel and we will treat in the next lesson this phenomenon at the same time as we will see the use of the reels in the electronic circuits.
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