A Lei da Indução de Faraday: Campos magnéticos induzem campos elétricos.

The phenomenon of magnetic induction reveals an impressive feature of nature: an electric field can be induced by a magnetic field. This discovery revolutionized the world and now I will explain the law that governs this phenomenon and also explain how this induced electric field behaves. Hello everyone, I'm Eudes Fileti, welcome to Verve Cientifica!

Here I teach the basic principles that govern the world, such as Faraday's Law, for example. If you think this is important for your intellect, subscribe to the channel and activate the bell to follow all our content closely. FARADAY'S LAW The Law of induction, or as I think it is better: Faraday's Law, is the law that describes the phenomena of magnetic induction, providing us with a mathematical relationship for the intensity of the induced electromotive force.

It states that whenever there is a change in the flow through a loop, an electromotive force will be induced in that loop. And more specifically, it also states that this electromotive force will be proportional to the average variation of the magnetic flux through the loop. In this relationship, the minus sign indicates that the electromotive force opposes the change in magnetic flux.

I will discuss this in detail in the next video. Now, if instead of a single turn, we employ a coil of N turns, the flux will pass through each one of them and Faraday's Law looks like this, that is, the total induced electromotive force will be N times the electromotive force of a single breathe. Regarding Faraday's law there is a subtlety that you should pay close attention to!

The induced electromotive force is caused by CHANGES in flow. As magnetic flux plays a central role in Faraday's law, it is tempting to think that this flux is the cause of the induced electromotive force, that this force will always appear in the circuit when it is immersed in a magnetic field. But not!

Faraday 's Law shows that only a CHANGE in the flux through a circuit can induce an electromotive force in that circuit, not the flow itself. If the flux through a circuit is constant, whether positive, negative or zero, it will not be able to induce electromotive force. So, to emphasize: the electromotive force is induced not by the flow, but by the temporal variation of the flow.

THE TWO WAYS OF INDUCING ELECTROMOTIVE FORCE In the previous video I showed that the current induced in a mobile circuit can be understood as an electromotive force of movement, due to electromagnetic forces on charges that are moving. To understand and explain this phenomenon, new laws of physics were not necessary, and one way to make flow vary is to simply move or change the geometry of the loop in the field where it is immersed. But I also commented in the previous video that the induced currents that arise in a motionless, stationary loop can only be explained by the appearance of an induced electric field.

This becomes clear if you think in cascade, about what we have already learned: 1) a variable field results in a variable magnetic flux through the loop, this is what the definition of flux says. 2) by Faday's law we know that the change in flux causes an electromotive force in the loop. 3) We also know that an electromotive force causes a current in the loop.

4) And since we talked about electrostatics, way back, we know that an electric current in a conductor is driven by an electric field in the loop. So at this point, we are forced to conclude that there must indeed be an induced electric field in the conductor caused by the variation in magnetic flux. Faraday recognized that all induced currents are associated with one of these two forms of varying magnetic flux.

One is due to the movement or change of shape of the circuit, which leads to the action of a magnetic force on the charges. Another, due to the variation of the magnetic field over time, which leads to a variation in the flow and, consequently, the induction of an electric field. If we take the flux to be the product of the field times the area, we can decompose the flux variation into two different terms.

This procedure in differential calculus is nothing more than the derivation of a product function. By doing this we can write Faraday's law like this. Here, the first term on the right-hand side represents the electromotive force of movement, whose magnetic flux associated is due to changes or movements of the loop itself.

Here, it is the movement that causes the magnetic forces on the charges in the loop. The second term, in turn, is the new physics that Faraday's law brings us. This term tells us that it is possible to create an electromotive force simply by changing the magnetic field across the loop.

Even if she's not moving. Here an induced electromotive force is simply the rate of change of magnetic flux through the area of ​​the loop. At this point, Faraday's Law is completely described.

But we can still go deeper, and put it in an even more general form. But to do this we need to better understand the nature of the induced electric field. INDUCED ELECTRIC FIELD A pertinent question in this discussion is the following: What happens if we simply remove the conducting loop from the analysis?

Well, this will eliminate the charges present on the loop, of course. As a result, there will no longer be any induced current or electromotive force. But something very important will remain.

The induced electric field will still be there! The moving charges in the loop only show that the electric field was always there, but the loop itself is not necessary for this electric field to exist. The existence of this electric field is due solely to changes in magnetic flux.

So this analysis leads us to see that there are two different ways of generating an electric field. The first is an electrostatic form, where the Coulomb electric field is created by static charges and whose field lines always point away from the charges if they are positive and always point towards the charges if they are negative. This is the type of field we discuss in this video here.

Now on the other hand, there is also electromagnetic induction, where a non-Coulomb electric field is created by a changing magnetic field instead of stationary charges. Both types of fields exert a force on a charge. And both create a current in a conducting loop.

But the electric field induced by the variation in magnetic flux is quite peculiar. The first notable feature is that the field lines of the induced electric field are no longer divergent, like those of an electrostatic field, but rather closed lines, centered on the axis that directs the magnetic field. And just like in Ampère's law, where the magnetic field was concentric to a current wire, here the induced electric field will be concentric to the direction of the changing magnetic field.

A second difference is that while the electrostatic field varies with the inverse square of the distance, the induced electric field varies with the inverse of the distance only. This will have important consequences in the context of the production of electromagnetic waves. A last and important difference is that an induced electric field is non-conservative, different from a Coulomb electrostatic field.

We talk about conservative forces in this video here, but it's worth remembering that a conservative force does not do net work on a particle that moves in a closed trajectory. The weight force, for example, is conservative, the negative work that is done on the way up is compensated by the same work, only positive, done on the way down. And just as it is for the gravitational case, in the electrostatic case we can associate an electrical potential energy with a conservative electrical force.

Now in electromagnetic induction it is different. As the induced field is non-conservative, a charge that moves in a closed path under the action of this field is always being pushed in the same direction by the electric force. There is never negative work to balance the positive work, which implies that the total work done in a closed path is not zero.

And furthermore, because it is non-conservative, we cannot associate an electric potential with the induced electric field. The concept of potential has no meaning whatsoever for this type of field. Despite this, we can still associate the field with an electromotive force induced in the circuit.

I will now show how to do this and the end result will be the general form of Faraday's Law. THE GENERAL FORM OF FARADAY'S LAW We saw that a potential difference between two points can be written as a function of the electric field. Now if we add up all the potential differences over small lengths in a closed circuit, which coincides with the conducting loop, we can equate it to the electromotive force induced in the loop.

Keep in mind that the sum can be expressed as an integral, in the same way as we did here for Àmpere's law. Now according to Faraday's law, the electromotive force is also the negative of the average variation of the magnetic flux through the loop. Here we can express this average variation as a rate of change, an instantaneous variation.

With this, we can reformulate Faraday's law and write it in its general form. This form represents all possible situations in which a changing magnetic field generates an electric field: whether in the situation where an electromotive force is induced by magnetic forces on charges when a conductor moves through a magnetic field. In other words, when a time-varying magnetic field induces an electric field in a stationary conductive loop.

THE GENERAL FORM OF FARADAY'S LAW In a series of epoch-making experiments, Michael Faraday discovered the phenomenon of electromagnetic induction and showed that an electric current can be induced in a circuit by simply varying the magnetic flux in its vicinity. The induced electromotive force, described by Faraday's law, is not a mere laboratory curiosity. In fact, it is revolutionary.

From a technological point of view, it enabled the generation and modern and rational use of electrical energy. As if that were not enough, from a conceptual point of view, Faraday's Law also proved to be extremely useful in establishing that a variable magnetic field induces an electric field. I have shown that these “induced” electric fields are very different from the fields produced by electric charges.

And Faraday's law of induction is the key we have to understanding their behavior. Finally, as one of Maxwell's four equations, Faraday's Law is necessary to explain the behavior of electromagnetic waves, whose applications have a profound impact on modern life. This video ends here.

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