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Now we come to the last early concept in electrodynamics that we want to discuss in this section, and



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this is induction.



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So the electromagnetic induction was first described by Faraday in the 1930s and later also violence



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and Norman.



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And everything is condensed here in this equation, so what happens here is that when you have time,



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change of a magnetic flux, I will later explain to you what this is.



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But if you have a time change of the magnetic flux, this will lead to a voltage induction voltage.



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And the reason is that we have some electric field that is generated.



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So let me first explain to you what a magnetic fluxes like the magnetic flux fire is calculated by this



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integral here.



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So we have a magnetic field that depends on the position and we integrate this year a a surface element.



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We integrate over a certain area.



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So when our magnetic field is constant, then this whole integral will just give the magnetic field



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times the size of this area.



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So it will just be A times B, for example, if you have a square, then this would give a square.



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So the length of the square, A squared times B.



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However, we can also have change in the area that we consider and we can have a change in the magnetic



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field.



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So this can change the magnetic flux.



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And if this happens over time, then this generates a voltage because we induce here an electric field



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actually distillation.



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He is related to basic concepts of mathematics.



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This is called the Stokes law.



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And we will later in a later section, we will discuss this in more detail.



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And you will understand it much better, I think.



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But for now, let's just keep in mind that the experimentalists of the time knew that when you have



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a change in the magnetic flux, this gives rise to an induction voltage.



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So an experiment that you can do is you can take such a closed loop of a wire and then you move it through



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such a magnetic field back and forth.



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And what happens here is that the magnetic flux changes because here in the initial state, we have



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a magnetic flux of zero because the magnetic field inside of this area here, a magnetic flux, the



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magnetic field is zero and therefore also Democratic Fluxus zero.



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However, as you have seen, we have moved this this close wire here into this magnetic field.



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And so over time, the integral over the magnetic field inside the wire has increased.



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So this means our time derivative of PHY is different to zero, and therefore we have this induction



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voltage.



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So the effect of electromagnetic induction is very famous and very much used in technology.



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Still today, for example, you can charge a battery, for example, if you take a magnet and move it



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through a coil back and forth, because the magnet exhibits a magnetic field.



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And when you push it through the coil, then you basically change the flux over time.



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So this generates a induction voltage which can be used to charge some device, for example.



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Also, it's used for detecting cars on motorcycles in the street, for example, often there is such



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a closed wire here inside of the road when you have a red light so that people or the police can detect



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if you have crossed the red line or not, because then when your car is moving through the wire, it



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will give rise to a change in the magnetic flux and therefore it generates an induction voltage.



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So it's still used to this day.