Now we come to the last early concept in electrodynamics that we want to discuss in this section, and
this is induction.
So the electromagnetic induction was first described by Faraday in the 1930s and later also violence
and Norman.
And everything is condensed here in this equation, so what happens here is that when you have time,
change of a magnetic flux, I will later explain to you what this is.
But if you have a time change of the magnetic flux, this will lead to a voltage induction voltage.
And the reason is that we have some electric field that is generated.
So let me first explain to you what a magnetic fluxes like the magnetic flux fire is calculated by this
integral here.
So we have a magnetic field that depends on the position and we integrate this year a a surface element.
We integrate over a certain area.
So when our magnetic field is constant, then this whole integral will just give the magnetic field
times the size of this area.
So it will just be A times B, for example, if you have a square, then this would give a square.
So the length of the square, A squared times B.
However, we can also have change in the area that we consider and we can have a change in the magnetic
field.
So this can change the magnetic flux.
And if this happens over time, then this generates a voltage because we induce here an electric field
actually distillation.
He is related to basic concepts of mathematics.
This is called the Stokes law.
And we will later in a later section, we will discuss this in more detail.
And you will understand it much better, I think.
But for now, let's just keep in mind that the experimentalists of the time knew that when you have
a change in the magnetic flux, this gives rise to an induction voltage.
So an experiment that you can do is you can take such a closed loop of a wire and then you move it through
such a magnetic field back and forth.
And what happens here is that the magnetic flux changes because here in the initial state, we have
a magnetic flux of zero because the magnetic field inside of this area here, a magnetic flux, the
magnetic field is zero and therefore also Democratic Fluxus zero.
However, as you have seen, we have moved this this close wire here into this magnetic field.
And so over time, the integral over the magnetic field inside the wire has increased.
So this means our time derivative of PHY is different to zero, and therefore we have this induction
voltage.
So the effect of electromagnetic induction is very famous and very much used in technology.
Still today, for example, you can charge a battery, for example, if you take a magnet and move it
through a coil back and forth, because the magnet exhibits a magnetic field.
And when you push it through the coil, then you basically change the flux over time.
So this generates a induction voltage which can be used to charge some device, for example.
Also, it's used for detecting cars on motorcycles in the street, for example, often there is such
a closed wire here inside of the road when you have a red light so that people or the police can detect
if you have crossed the red line or not, because then when your car is moving through the wire, it
will give rise to a change in the magnetic flux and therefore it generates an induction voltage.
So it's still used to this day.