Let us get into the topic.
Let us discuss electrodynamics and matter.
So first, I want to discuss here the polarization of matter.
So this all starts by considering the charge density.
So previously, we have always assumed a vacuum with individual charges in this vacuum.
So you could say you only have external charges, so to say.
But now, since we have matter and since we want to apply an electric and magnetic field, it means
that the charges in this material will also move.
And we will get, for example, charged separation where we have positive charges on one side and negative
charges on the other side of our piece of metal, for example.
So what we what we can write down is that the total charged density is given by these charges that correspond
to our piece of matter, which are called polarisation charges.
And then we also have the external charges, for example, if we take a wire and apply it to our piece
of matter.
So these are then the charges that we have previously discussed.
This could also be, for example, some kind of defect or atom that we put on top of our piece of metal.
Now, the polarisation charges here.
It's very important to realize that one, that when you integrate over them over the whole piece of
matter, it will give zero.
So this is because that before you apply the electric and magnetic fields, our piece of matter is charged
neutral.
And when you apply these fields, you can move these charges and separate them.
But it still means that overall, if you integrate over the whole piece of metal, it will still be
neutral.
And this is already the whole trick, and you will hopefully soon see why, so the first thing that
we do now is we use our continuity equation, which corresponds to charge conservation.
It means that when we have a temporal change in the charge density, this means we have currents.
So the time derivative of Roe is equal to minus the divergence of the current density.
And now in one of the previous lectures on the on the dipoles, we have already introduced that to the
current and total current is equal to the time derivative of the electric dipole moment.
So now we can transform this year to a current density and can transform this one here to a density
of electric dipole moments.
And this actually is called the electric dipole density or the polarization.
So now we can take this polarization or better to say the time derivative of the polarization and put
it in here instead of the current.
So this means the time derivative of Roe is equal to minus divergence of the time derivative of Pete.
And now we have here ten derivatives in both cases.
So we can just integrate and get rid of the time derivative.
So we have that.
Our polarization charges are equal to minus the divergence of the polarization, which is the electric
dipole density.
And in the second next lecture, you will see how this can really help us to define actual equations
in matter, because we have now expressed our polarisation charges that were absent previously in terms
of a divergence which already fits the mathematical shape of the Maxwell equations.