After studying the capacitors, we will now analyze the third fundamental component of electrical circuits : the coil. This component involves electrical and magnetic phenomena.
The analysis of existing links between electrical and magnetic phenomena is called electromagnetism.
We already know what magnetism depends on, how it manifests itself, and the basic laws that govern it. We will now operate the same electromagnetism.
1. 1. MAGNETIC EFFECT OF THE CURRENT
The Danish physicist Hans Christian OERSTED (1777 - 1851) is the first to establish the correlation between electrical and magnetic phenomena, thanks to an experiment of the kind shown in Figure 1. From this experience, he notes that By suspending a magnetised needle parallel to a conductor (Figure 1-a), we find that when a current flows through it, the magnetized needle pivots and is placed perpendicular to the conductor (Figure 1-b).
AMPER (1775 - 1836) subsequently notes that the direction in which the needle pivots depends on the direction of movement of the current in the conductor.
When the current passes through the conductor from the left to the right as in Figure 1-b, the north pole of the magnetized needle goes to one side of the conductor, if the current, as Figure 1-c, runs the driver from the right to the left, the north pole of the magnetic needle is on the other side of the conductor.
This experiment shows that the electric current acts in a definite way on the magnetic needle. This way is similar to the effect produced by a magnetic field on this same magnetic needle. Indeed, previously, we saw that a magnetic needle is always aligned according to the lines of force of a magnetic field. We can thus attribute to the electric current a magnetic effect which consists of the creation of a magnetic field around the conductors traversed by this current.
To determine the shape of the magnetic field of force generated by the electric current, it suffices, as shown in Figure 2-a, to place the magnetized needle in various places around the vertically placed conductor. We then note that the positions taken by the needle at different points equidistant from the driver roughly describe a circle whose center is the driver.
We can deduce the shape of the magnetic field around the driver and represent his lines of force as shown in Figure 2-b.
The influence of the magnetic field created by the driver is felt at any point in the space surrounding the driver. However, in order not to complicate Figure 2-b, only a few lines of force are drawn, which is enough for us to get an idea of the magnetic field. By observing Figure 2-a, we note that the poles of the magnetized needle are positioned in two opposite positions according to the direction of movement of the current in the conductor. From this observation, we deduce that according to the direction of the current, the lines of force of the magnetic field created are oriented differently.
It is therefore necessary that, knowing the direction of the current, we can determine the direction of the lines of force. This need is the subject of the MAXWELL rule, also known as the corkscrew rule.
According to this rule, let us imagine having a corkscrew arranged along the conductor, and rotating it so that it moves in the same direction as the current (conventional sense). The direction of rotation of the corkscrew thus determined indicates the direction of the lines of force of the magnetic field.
To highlight the remarks of this rule, let us refer to figure 3 in which are reported the two cases of the experiment previously carried out.
1. 2. - THE COIL
After having considered the magnetic field generated by an electric current traversing a rectilinear conductor, let us now analyze the case of the coil. A coil is simply made of the same conductor, but wound on itself and no longer rectilinear.
Take the driver of Figures 2 and 3 and fold it to obtain Figure 4. The driver thus folded constitutes a turn.
Figure 4 shows the lines of force of the magnetic field created by the current flowing through the coil. The lines of force are, as in the case of the rectilinear driver, circular but unlike the case above, their center is no longer the driver but is located outside the turn.
In the views of Figure 4, we find that the turn and the lines of force are linked together as the links of a chain and, for this reason, we say that the lines of force are embraced by the turn. The turn is the most basic type of coil that can exist.
As a rule, the coils consist of several contiguous turns. With the help of figure 5, let us analyze what becomes the magnetic field created by current I, when we add a second turn to the previous one.
Each of the two turns produces its own magnetic field, some lines of force appear in Figure 5-a.
At point A shown in Figure 5-a and in the vicinity of it, we can consider that the magnetic field is zero. Indeed, the magnetic field at point A is the field resulting from the fields of each turn, but at this point, the lines of force of each turn being in the opposite direction, the resulting field is zero. In practice, in the points we have just considered (point A and its surroundings), the lines of force cancel each other out and their general appearance for the two turns takes the form illustrated in figure 5-b. The lines of force are common to both turns.
This demonstrates that two neighboring turns do not produce two distinct magnetic fields, but a single magnetic field.
The same magnetic field can be produced differently. Instead of running the two turns by two distinct currents of the same intensity as in figure 5-a and 5-b, we can feed the two turns by the same current and this by connecting them to each other. series as illustrated in figure 5-c.
In this arrangement, the same current passes successively through each turn and the magnetic field thus created is identical to the case of Figure 5-b.
Each turn contributes to the production of the magnetic field and we deduce that :
The magnetic field produced by a coil is all the more important as the number of turns of this coil is large.
To illustrate this, consider the two coils of Figure 6.
The coil of Figure 6-a has six turns while the coil of Figure 6-b has 30 turns, that is to say five times more. If two coils are traversed by a current (I) of the same intensity, the field produced by the coil of Figure 5-b is five times greater than that of the coil shown in Figure 6-a. However, if in the latter we apply a current of intensity five times greater than the initial current I, then the magnetic field produced by this coil becomes equal to that of the coil of Figure 6-a. We deduce that :
The magnetic field produced by a coil is all the more important as the intensity of the current flowing through it is high.
From the two deductions we have just made, we can say that the magnetic field depends on the product of the number of turns (N) by the current I.
To 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 A-t.
f.m.m. = N x I
In general, the conductor is wound on a cylindrical support made of insulating material. The turns may not be joined but they must remain very close. If the wire is insulated, it can be wound in several superimposed layers, provided not to change the direction of the winding (condition of which we will see the cause later).
On the other hand, if the length of the coil exceeds ten times its diameter, we are in the presence of a solenoid or long coil.
As can be seen in Figure 6, the main effect of winding the conductor is to concentrate the lines of force of the magnetic field inside the coil. The magnetic field inside the coil is thus much more intense than outside where the lines of force are dispersed. The result of this concentration appears clearly in figure 6-b. The lines of force inside the coil are practically parallel to one another, thus giving rise to a uniform magnetic field.
In the case of a coil, as in that of the single conductor, it is possible to determine the direction of the lines of force according to the direction of flow of the electric current. For this, we will have recourse, once again, to the rule of the corkscrew, but applied differently.
The application of the rule of the corkscrew to a spool is illustrated in figure 7.
The corkscrew is arranged along the axis of the coil. By turning the corkscrew in the direction of the current in the coil, the direction in which the corkscrew moves indicates the direction of the lines of force inside the coil.
We deduce that the pole from which the lines of force come out is a north pole and that the pole through which they enter the coil is a south pole. This completes the similarity with the natural magnet.
We now know how to get a magnetic field from a current coil, let's see how this field can be used.
Introduce inside a coil a ferromagnetic metal bar, as shown in Figure 8-a.
The bar is then called the core of the coil
From the theory relating to magnetism, we know that any ferromagnetic material placed in a magnetic field acquires magnetic properties because the small elementary magnets which constitute it, are oriented along the lines of force of the magnetic field. The bar placed in the magnetic field of the coil does not escape this rule, and as we see in figure 8-a, the core magnetizes by induction and becomes a real magnet. It then has a north pole and a south pole at its ends. If the core is made of steel, it keeps the magnetization even when the current stops flowing the coil, it is also with this method that are obtained permanent magnets. If, on the other hand, the core is of soft iron, it is magnetized or demagnetized according to whether the current flows in the coil or not. Soft iron cores are used for the realization of electromagnets.
Since the core of the coil magnetizes by becoming a magnet, it in turn produces its own magnetic field which is added to that produced by the coil. What must be noted is that the magnetic field of the nucleus can become several hundred times higher than that produced by the coil alone.
The introduction of a core into a coil makes it possible to obtain a strong magnetic field with a low current intensity.
The shape of the lines of force produced by the coil and its core are drawn in figure 8-b. These lines of force are also called induction lines because they are precisely due to the induction magnetization of the nucleus. The set of all the induction lines constitutes the induction flux produced by the coil.
The symbol of the induction flux is the Greek letter phi :Ø
A coreless coil also has the property of producing an induction flux if we consider the lines of force to be induction lines.
In the case of a single coil, we can say that the core of it, although not existing is in fact the air encompassed by the winding of the coil. Naturally, in the latter case, since the air does not have the magnetizing power of a core, the induction flux produced is far inferior : In conclusion, we can say that the induction flux of a coil depends largely on the material placed in its winding.
We must now consider the coil no longer as an element capable of exerting a force of attraction on ferromagnetic materials, but as an element capable of magnetizing, by induction, the material placed in its winding. The coil thus creates an induction flux that depends on the particular type of material used.
The induction flux is measured in Weber (symbol Wb). This unit of measure owes its name to the German physicist Wihlem WEBER (1804 - 1891).
To produce an induction flux, we must circulate a current in the turns of the coil thus creating a magnetomotive force.
We can attribute to this magnetomotive force the production of the induction flux on the part of the coil.
Each coil is characterized according to its ability to produce an embraced flow when its turns are traversed by a current, just as a capacitor is characterized by its ability to accumulate electrical charges between its armatures when they are subject to a potential difference.
This capacitance of the coil is called electrical inductance (symbol L).
A coil is therefore characterized by the value of its inductance L, as a resistor is characterized by its resistive value R and a capacitor by its capacitance value C.
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 difference of potential existing between this one : C = Q / V
Similarly, the inductance of a coil is indicated by the induction flux embraced by its turns as a function of the current flowing through them. In this case too, we obtain the inductance of a given coil by dividing the total flux embraced by the current that produces it :
L = Ø /I
Measuring the Weber flux and the current in ampere, the inductance is measured in Weber / ampere. At this unit, Henry (H) is named in memory of the American physicist Joseph HENRY (1797 - 1878) to whom we owe important studies, especially on self-induction.
In many cases, henry is too large a unit, so we use millihenry (symbol mH) which is one thousandth of a henry, or microhenry (symbol µH) which is worth one millionth of a henry.
Between the capacitor and the coil, there are other analogies that are worth highlighting.
By applying a voltage across a capacitor, its dielectric is electrically polarized to the extent that appear at its ends a north pole and a south pole. So, since the capacitance of a capacitor depends on its dielectric, so the inductance of a coil depends on the nature of its core, which we already know because a coil in which we introduce a core produces a flux more important induction.
In the case of the capacitor, we introduced the notion of absolute dielectric constant (ε). For the air capacitor, this constant takes the name of dielectric constant of air or vacuum (εo), whereas in the case of a solid dielectric capacitor we have introduced the notion of dielectric constant relative to the air (εr). εr expresses how many times the capacity of a capacitor increases when we replace the air with a solid dielectric. From there, we deduced the following formula :
e = eo x er
In the same way for a coil, we take into account the influence of the material constituting its core and we then consider the absolute magnetic permeability of the material whose symbol and the Greek letter µ (reads "mu"). Absolute of a material is expressed in henry per meter (symbol H / m).
Magnetic permeability is the coefficient that characterizes the magnetic properties of a body. Its ability to guide the magnetic induction flux increases with its permeability.
For a coreless coil, which therefore only has air in the middle, we will take into account the magnetic permeability of the air or the vacuum designated by the symbol µo and which has the value 4 π x 10-7 H / m either to facilitate calculations 1,256 µH / m.
If we introduce a material inside the coil, we then multiply the magnetic permeability of the air or vacuum µo by a coefficient called relative magnetic permeability with respect to air or vacuum and symbolized by µr.
The absolute magnetic permeability µ is obtained by the product of µo per µr.
µ = µo x µr
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
Argent
0,999981
Air
1,0000004
Silicon iron
7 000 maximum
NICKEL ALLOYS
Permalloy
NICKEL ALLOYS
23 000 à 600 000
Anhyster
2 000 à 5 000
Mumetal
100 000 maximum
Permimphy
150 000 à 250 000
.Fig. 9. - Relative magnetic permeability µr of materials.
In principle, the value of 1 is given to µr for all substances that are not ferromagnetic, ie air and to winding supports such as bakelite, plastics, glass, quartz , ceramics, etc ...
It should be noted that in the case of the capacitor, the dielectric occupies all the space between its armatures, that is to say all the space traversed by the lines of force of the electric field. On the other hand, in the case of the coil, the core is only inside the coil and does not occupy all the space traversed by the lines of force of the magnetic field because this one, as represented in Figure 10 also outside the winding.
In summary, in order for the analogy between the capacitor and the coil to be complete, it would be necessary for the core to occupy the entire space traversed by the induction lines, in other words that the core should be outside the winding.
In such a configuration, the core also called magnetic circuit is said closed. This is the case, for example, transformers. Conversely, a coil such as that of Figure 10 to an open magnetic circuit.
It is therefore only in the case of a closed magnetic circuit where the entire induction flux passes into the ferromagnetic core that we can say, as in the case of the capacitor, that the magnetic permeability relative to the air indicates by how much many times the inductance of the coil increases when it is provided with a core.
In the case of an open magnetic circuit, the influence of the nucleus is less but remains predominant.
In this lesson, we will limit ourselves to considering the calculation of the inductance of a coreless coil, putting the computation relating to the coils provided with nucleus, when we will meet the practical applications.
Let's see which elements depend on the inductance of a coreless coil.
In the first place, the inductance depends on the section of the turns constituting the coil. This section is the area circumscribed by the driver as we see it for a turn in Figure 11 where this surface hatched.
It is understandable that the larger the section of the coil, the greater the induction flux embraced.
The inductance of a coil is therefore proportional to its section :
L = f (S)
The inductance of a coil also depends on the square of the number of its turns. To be aware of this, consider Figure 12 where two coils are drawn. The first has a turn (Figure 12-a) and the second five turns (Figure 12-b).
If the two coils are traversed by a current (I) of the same intensity, the coil with five turns produces a magnetic field five times greater than the field produced by the single turn coil. On the other hand, we introduced in the first lines of this lesson the notion of the flow embraced by the spiral. The more the induction flux is embraced by the current, the more its lines of force are concentrated, so the greater the intensity of the flux.
The multi-turn coil of Figure 12-b embraces the flux five times more than the coil of Figure 12-a.
In conclusion, the intensity of the flux produced by a coil depends on the square of the number of turns. Since the inductance is related to the flux, we can say :
The inductance of a coil is proportional to the square of the number of its turns.
L = f (N2)
In the last resort, the inductance depends on the length of the coil. To understand how the length of the coil can influence its inductance, consider Figure 13.
In Figure 13 are shown two coils having the same number of turns, in this case 6. These two coils have the same section but their winding is such that the coil of Figure 13-a ; has a length of 3 cm while that of Figure 13-b is twice as long and measures 6 cm. If the two coils are traversed by a current (I) of the same intensity, the latter having the same number of turns, the magnetomotive force that they generate is identical.
The f.m.m. being the cause of the production of the flow, we can rightly think that they embrace the same flow therefore has the same inductance. But the reality is much more complex and the induction flux depends not only on the magnetomotive force but also on how this force is distributed along the coil.
Take again our two coils of figure 13, that of figure 13-a ; has two turns per centimeter of length, while the coil of Figure 13-b has only one turn per centimeter. As a result, the flux produced by the first coil is twice that produced by the second coil. We can conclude that the flux embraced by the turns of a coil (and therefore not inductance) depends on the length of the coil.
The inductance of a coil is inversely proportional to its length.
We now have all the elements to state the formula for calculating the inductance :
For a coreless coil, the inductance is obtained by multiplying the magnetic permeability of the air by the section of the turns and by the square of the number of turns and dividing the product by the length of the coil. In summary, we get the following formula :
L :
Inductance in H
µo : Magnetic permeability of air or vacuum in H/m
N2 :
Number of turns squared
S : Section of the turn inm2
l : Length in m
NOTE: In a coil having air as a core, the absolute magnetic permeability (µ) is equal to the magnetic permeability of the air or vacuum, ie, in this case, the magnetic permeability relative to air or empty µo equals 1. The formula can be written as :
This formula for calculating the inductance is, however, valid only when all the induction lines are embraced by all the turns, as in the case of the coil represented in Figure 14-a.
When the turns are, on the contrary, discarded as in the case of the coil drawn Figure 14-b, it happens that some lines of force are not embraced by all the turns of the coil. In this case, the flux embraced and consequently, the inductance of the coil are smaller.
Moreover, the calculation formula of (L) that we have just seen is no longer applicable and in practice, we must take into account this feature by introducing correction coefficients as we will see in the forms.
Finally, you must know that the inductance (L) of a coil is also called the coefficient of self-induction.
In the table of figure 15, are grouped the quantities introduced in this lesson devoted explicitly to the coil as well as their unit and their formula if necessary.
GREATNESS
UNIT OF MEASUREMENT
FORMULA
Denomination
Symbol
Denomination
Symbol
Magnetomotive force
f.m.m.
ampere-turn
A-t
F.m.m. = N x I
Absolute magnetic permeability
µ
Henry by meter
H / m
Inductance
L
henry
H
L =µ x (N2) / l
Induction flow
Ф
Weber
Wb
Ф =L x I
Fig. 15. - Quantities related to electromagnetism.
In the lesson devoted to magnetism, we have not given a concrete and admitted explanation to the fact that certain substances possess magnetic properties.
There are two theories on this subject ; however, as one of them does not rest on any notion of real existence, we will opt for the one advocated by AMPERE.
This theory is based on the existence of particulate currents and does not distinguish between magnetism proper and electromagnetism. She found her interpretation in the movement of the electrons of atoms.
We know that a turn traversed by an electric current produces a magnetic field ; we also know that this current is due to a displacement of electrons. We can therefore attribute the magnetic field to the fact that the electrons derive a gyration along the turn.
If we now remember the structure of an atom, we see that in this case too, electrons gravitate in circular orbits around a nucleus. Consequently, there is no reason for the electrons of a body not to produce a magnetic field similar to that caused by the electrons circulating in a coil.
Atoms can be considered, or more precisely their electronic orbit as a tiny turn.
Figure 16 shows the analogy between a turn traveled by a current and an electronic orbit of an atom.
In a piece of demagnetized ferromagnetic material, the electronic orbits of each of its atoms are arranged in a disordered manner as illustrated in Figure 17-a.
As a result, each field thus created is oriented in a different direction. Magnetic fields can not combine their effects and the overall effect remains non-existent. On the other hand, if the body is magnetized, this is the case of FIG. 17-b, all the electronic orbits align themselves with respect to each other in a coherent manner thus generating a magnetic field.
Note after these explanations relating to magnetism that all phenomena considered so far are due to electrons.
For the conductors, the electric current is due to a displacement of electrons.
For capacitors, the polarization of the dielectric is due to the deceleration of the electronic orbits relative to their nucleus.
For magnets and coils, the magnetic polarization is due to the particular orientation of the electronic orbits.
Having already seen that the passage of electric current, as the polarization of the dielectric cause a consumption of electrical energy, it is easy to understand that the magnetic polarization of a core also requires some energy. This energy is provided by the coil and we will deal in the next lesson this phenomenon at the same time we will see the use of coils in electronic circuits.
Induction flow
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