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Let us get into the topic.



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Let us discuss electrodynamics and matter.



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So first, I want to discuss here the polarization of matter.



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So this all starts by considering the charge density.



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So previously, we have always assumed a vacuum with individual charges in this vacuum.



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So you could say you only have external charges, so to say.



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But now, since we have matter and since we want to apply an electric and magnetic field, it means



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that the charges in this material will also move.



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And we will get, for example, charged separation where we have positive charges on one side and negative



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charges on the other side of our piece of metal, for example.



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So what we what we can write down is that the total charged density is given by these charges that correspond



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to our piece of matter, which are called polarisation charges.



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And then we also have the external charges, for example, if we take a wire and apply it to our piece



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of matter.



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So these are then the charges that we have previously discussed.



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This could also be, for example, some kind of defect or atom that we put on top of our piece of metal.



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Now, the polarisation charges here.



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It's very important to realize that one, that when you integrate over them over the whole piece of



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matter, it will give zero.



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So this is because that before you apply the electric and magnetic fields, our piece of matter is charged



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neutral.



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And when you apply these fields, you can move these charges and separate them.



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But it still means that overall, if you integrate over the whole piece of metal, it will still be



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neutral.



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And this is already the whole trick, and you will hopefully soon see why, so the first thing that



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we do now is we use our continuity equation, which corresponds to charge conservation.



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It means that when we have a temporal change in the charge density, this means we have currents.



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So the time derivative of Roe is equal to minus the divergence of the current density.



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And now in one of the previous lectures on the on the dipoles, we have already introduced that to the



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current and total current is equal to the time derivative of the electric dipole moment.



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So now we can transform this year to a current density and can transform this one here to a density



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of electric dipole moments.



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And this actually is called the electric dipole density or the polarization.



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So now we can take this polarization or better to say the time derivative of the polarization and put



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it in here instead of the current.



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So this means the time derivative of Roe is equal to minus divergence of the time derivative of Pete.



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And now we have here ten derivatives in both cases.



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So we can just integrate and get rid of the time derivative.



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So we have that.



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Our polarization charges are equal to minus the divergence of the polarization, which is the electric



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dipole density.



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And in the second next lecture, you will see how this can really help us to define actual equations



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in matter, because we have now expressed our polarisation charges that were absent previously in terms



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of a divergence which already fits the mathematical shape of the Maxwell equations.