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So in the previous lecture, we've introduced the polarisation as a density of electric dipole moments



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and we have separated our charge into two parts, and we've also shown that this new part of this polarization



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charge can be expressed as the divergence of this polarization, which will later help us to introduce



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a new Maxwell formulation for dimensional equations in matter.



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But for that, we also need to do a similar thing and introduce to magnetization this because we need



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to separate also the currents.



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So maybe you already have a good feeling about this, because as you probably know by the Maxwell equations,



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all of the electric properties are related mainly to charges and all of the magnetic properties are



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mainly related to currents.



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And this is why when we want to introduce democratization, we need to separate our charges and not



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our charges, but our current densities, so we have now three terms for the current densities.



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So first of all, we have J zero, which are, you could say, the external currents.



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These are the currents that we have considered so far.



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These are the currents in the vacuum and not in our piece of matter.



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In the matter, we get two types of additional currents.



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So one of them we have already introduced in the previous lecture about depolarization.



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So when we apply an electric or magnetic fields, the charges will start moving and especially it can



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lead to some charge separation, which is a polarisation.



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And if this happens, we get these polarisation currents, JP.



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But in this lecture, we are more interested in the and the other type, which are, for example, circular



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currents, these are currents where the charge moves, but it moves on a close trajectory and there



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is no real charged separation.



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So this means and when you look on the average of all of these charges, the time the relative is zero.



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So on average, they stay where they are.



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There's no charge separation.



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And so these are called circular currents.



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And these are also the currents that cause the magnetic moments.



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Just if you remember from the magnetic dipole moment, this was defined as a year as a closed loop of



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a wire.



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And in the most simple case, it was just a circularly lid closed wire.



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And when we have these circular currents, we get a magnetic moments.



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OK, so once again, we can write down the continuity equation, which is in fact just charged conservation.



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And now we can separate our charge into the two previous parts and the currents in the three parts here.



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So just, yeah, we could also separate the charge into these three parts, but then you would say that



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Roedad is zero.



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So what we get is we get five times here and now.



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We also must realize that the continuity equation is also fulfilled for the individual parts here.



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So we can write down this continuity equation for the polarisation currents and for the polarization



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charges.



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This is the continuity equation that we had in the previous lecture about the polarization.



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And we can also write down the continuity equation for the external currents.



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So this was the continuity equation that we have used throughout this whole course.



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So essentially, what it means is that the external charges conserved, that the polarized charges conserved



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and that the magnetised charges conserved, but it's also zero.



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So it means we cannot simply transform an external charging to a polarized charge and so on and so on.



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And what this means is these two terms cancel the zero, these to cancel, they give zero.



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So this means there's one here.



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We'll give zero.



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So we have now the fact that the divergence of the circular current is zero.



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So what we can do is we can introduce a new vector and write down this circular current density in terms



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of a rotation of this vector.



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And from the dimensionality, you find out that this has the units of a magnetic dipole density.



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And so this is called the magnetization.



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So as you can see, we have now separated our charges into two parts of occurrence, into three parts,



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and we have introduced the electric dipole density, polarisation and the magnetic dipole density to



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magnetization.



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And we were able to write down this new polarization charge as the divergence of Pete and this new circular



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magnetization, current density in terms of a rotation of M.



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And in the next lecture, we will use these equations and derive the maximal equations and matter.