When you pass near a speed camera, it detects your speed and even tells you whether or not you will be fined. This speed detection technology is only possible because the structure of cars contains steel, a ferromagnetic material. This type of material, when passed over a current coil, causes an appreciable and detectable increase in an important property of the coils: inductance.
And it is this property that this video will deal with. Hello, welcome to Verve Científica. In this series you are learning about electromagnetism.
If you think this content will help you better understand how the world works, subscribe to the channel and activate the bell. INDUCTORS If you take a piece of copper wire and wrap it around a pen, you will get a coil. The interesting thing now is that if you put this coil in an electrical circuit, it will behave differently than a straight piece of wire!
To be more specific, this coil will now be able to store energy in the magnetic field. It does this in a similar way to the capacitor, which we discussed in this video here and which is capable of storing electrical potential energy. In circuits, a coil is called an inductor because, as I will show here, the potential difference that it applies to the circuit is precisely the electromotive force that it induces.
Just like resistors and capacitors, inductors are among the indispensable circuit elements of modern electronics. Its purpose is to oppose any variations in current through the circuit. In an alternating current circuit, an inductor tends to suppress current variations that are faster than those desired.
There are several important applications for inductors. In a gasoline car, for example, it is the inductor that allows the car's battery of just 12 volts to supply thousands of volts to the spark plugs, which, in turn, allows the spark plugs to fire and make the engine run. In domestic lighting, inductors keep fluorescent lamps shining.
Larger inductors placed under city streets are used to control the operation of traffic signals. In the same way that a capacitor is characterized by its capacitance, in an inductor the relationship between the current and the induced electromotive force is described by the inductance of the coil. SELF-INDUCTION In all the examples of induced electromotive forces that I have discussed so far, the magnetic field was produced by an external source, such as a permanent magnet, for example, or an electromagnet.
But it doesn't have to be that way. The magnetic field does not necessarily need to arise from an external source. An electromotive force can be induced in an inductor by changing the electric field that its own current produces.
Note that an inductor is no fun when the current passing through it is continuous and constant. He would be nothing more than a tangled thread. Inductors become important circuit elements when currents are changing, which is the case with alternating currents.
In this way, an inductor connected to a voltage source is passed through by an alternating current that creates a variable flux through its coil. And according to Faraday's Law, the change in flux induces electromotive force in the inductor itself. This effect, where a varying current in a circuit induces an electromotive force in the same circuit, is called self-induction.
Because of the direction of the induced electromotive force, it is also called the reverse electromotive force, similar to the one we discussed for a motor. Note here that to increase the current in the inductor, it is necessary to force the current against an opposing electromotive force. And this is a very interesting result!
It tells us that even if the wire of an inductor is ideal, with no resistance at all, work would still need to be done to increase the current through it. On the other hand, if there is already a current in the inductor and it decreases over time, Lenz's law guarantees that the self-induced current will also oppose this change, in an attempt to keep the current constant. Thus, an inductor tends to resist changes in its current, regardless of whether it is increasing or decreasing.
INDUCTION To deal with self-induction, it is convenient to rewrite Faraday's Law in a form, in which the electromotive force is proportional to the change in current in the coil and not to the change in flux. Thus, as the flux is proportional to the magnetic field, and the magnetic field is proportional to the current, then the flux will be proportional to the current. The constant of proportionality in this relationship is precisely the inductance of the coil.
NΦ ∝ LI >> L = NΦ / I In this case, strictly speaking, this constant is self-inductance. Through self-induction, we can write the electromotive force given by Faraday's Law in terms of current and inductance. Thus, we replace flux with current.
The unit of inductance in the international system is the henry, named after the American physicist Joseph Henry. APPLICATION OF SELF-INDUCTION Inductance depends only on the geometry of the inductor, its size, its shape and the number of turns. If a magnetic material is inside the coil, the inductance will also depend on the magnetic properties of that material.
Winding the coil around a ferromagnetic core increases the magnetic flux and, consequently, the inductance by thousands of times. This is useful for example for an automatic traffic light system. Since automobiles contain steel in their structure, which is a ferromagnetic material, driving an automobile over a coil causes an appreciable increase in the coil's inductance.
This effect is reflected in traffic light sensors, which use a large current-carrying coil embedded under the road surface near an intersection. The circuit connected to the coil detects the change in inductance when a car passes by. When a pre-programmed number of cars pass over the coil, the traffic light changes to green to allow other cars to pass through the same intersection.
MUTUAL INDUCTION Now consider two coils of wire: one that I will call the primary coil, which has a generator or battery connected to it. And another, which I will call the secondary coil, which is not connected to any voltage source, but to a voltmeter. The primary coil, as it is connected to a voltage source, becomes an electromagnet and therefore creates a magnetic field in its vicinity.
If the two coils are close to each other, a significant fraction of this magnetic field will penetrate the secondary coil and produce a magnetic flux. Due to the variation in this flux, an electromotive force will be induced in the secondary coil. This effect, where a varying current in one circuit induces an electromotive force in another circuit, is called mutual induction.
According to Faraday's law, the average electromotive force induced in the secondary coil is proportional to the change in magnetic flux. But note that this flux variation is no longer produced by the coil itself, but by the change in current that occurs in the primary coil! And this time the proportionality constant is M, which is the mutual inductance.
Writing Faraday's law in this way, it is clear that the average electromotive force induced in the secondary coil is due to the change in current in the primary coil. Mutual inductance can be a nuisance in electrical circuits, since variations in current in one circuit can induce unwanted electromotive forces in nearby circuits. To minimize these effects, multiple circuit systems must be designed so that two coils are placed as far apart as possible or with their planes orthogonal to each other.
On the other hand, mutual inductance also has many useful applications. A transformer, for example, used in alternating current circuits to raise or lower voltages, is nothing more than two coils interacting with each other. By the end of this series I will discuss how a transformer works.
MAGNETIC ENERGY An inductor, like a capacitor, can store energy. This stored energy arises because the voltage source, whether a generator or a battery, will work to establish a current in the inductor, forcing charge to flow through it. But what happens to this energy that was spent to increase the current?
We know that part of this energy is lost as heat in the internal resistance of the circuit. But what about the rest? The remainder is stored in the inductor's magnetic field, of the same were that electrical energy is stored in the electric field of a capacitor.
To see this, suppose that an inductor is connected to a generator whose voltage can vary continuously from zero to some final value. As the voltage increases, the current does not reach its maximum value abruptly, but rather gradually. Thus, while the current is increasing, an induced electromotive force, proportional to the average variation of current in the circuit, will manifest itself in the inductor.
And according to Lenz's law, the polarity of the induced electromotive force must be opposite to the polarity of the generator, and thus oppose the increase in current. Therefore, the generator must do a certain amount of work to push the charges through the inductor against this induced electromotive force. If we substitute the electromotive force of self-induction into this relationship, and remember that the current is the rate at which the charge varies, we see that the work done by the generator to induce the current in the inductor will depend on the square of the current.
Note that this quantity is just one element, a tiny fraction of the total work, whose integral value is obtained by the sum of all these elements. By doing this we can find that the work is proportional to the square of the current, and in this expression the factor ½ arises due to the integration process. This work is stored as energy in the inductor, or more specifically the magnetic energy stored in the magnetic field.
Note the similarity in the expression between the magnetic potential energy stored in an inductor and that of other potential energy storage systems, such as the capacitor or the mass-spring mechanical system. They all have the same mathematical form. ENERGY DENSITY The important thing now is to write the energy density in an inductor in terms of the magnetic field.
To do this, we employ the inductance of a solenoid which is proportional to its length, its area and the number of turns in the wire. We also use the expression for its magnetic field, which is proportional to the current, the number of turns of the wire and inversely proportional to the length of the solenoid. Inverting this expression, we obtain the current as a function of the field and substitute it into the expression for energy, together with the expression for inductance.
This leads us to an expression for energy stored in the inductor. Note that it is proportional to the volume of the solenoid and we can think of this energy as the energy contained in a volume delimited by the device's winding. If we divide this expression by the volume, we obtain an energy density.
We finally see that the magnetic energy density in an inductor is proportional to the square of the magnetic field. Although this formula was derived for the special case of a solenoid, it is valid for any region of empty space where a magnetic field exists. This expression is analogous to the one we saw earlier when discussing the electrical energy stored in a capacitor.
Later in this series, I will show that magnetic energy density is fundamental to understanding how an electromagnetic wave is capable of transporting energy. One of the most important applications of self-induction and mutual induction occurs in a transformer, a device that is used to increase or decrease an alternating voltage. This will be the subject of our next video!
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