So in the previous lecture, we've introduced the polarisation as a density of electric dipole moments
and we have separated our charge into two parts, and we've also shown that this new part of this polarization
charge can be expressed as the divergence of this polarization, which will later help us to introduce
a new Maxwell formulation for dimensional equations in matter.
But for that, we also need to do a similar thing and introduce to magnetization this because we need
to separate also the currents.
So maybe you already have a good feeling about this, because as you probably know by the Maxwell equations,
all of the electric properties are related mainly to charges and all of the magnetic properties are
mainly related to currents.
And this is why when we want to introduce democratization, we need to separate our charges and not
our charges, but our current densities, so we have now three terms for the current densities.
So first of all, we have J zero, which are, you could say, the external currents.
These are the currents that we have considered so far.
These are the currents in the vacuum and not in our piece of matter.
In the matter, we get two types of additional currents.
So one of them we have already introduced in the previous lecture about depolarization.
So when we apply an electric or magnetic fields, the charges will start moving and especially it can
lead to some charge separation, which is a polarisation.
And if this happens, we get these polarisation currents, JP.
But in this lecture, we are more interested in the and the other type, which are, for example, circular
currents, these are currents where the charge moves, but it moves on a close trajectory and there
is no real charged separation.
So this means and when you look on the average of all of these charges, the time the relative is zero.
So on average, they stay where they are.
There's no charge separation.
And so these are called circular currents.
And these are also the currents that cause the magnetic moments.
Just if you remember from the magnetic dipole moment, this was defined as a year as a closed loop of
a wire.
And in the most simple case, it was just a circularly lid closed wire.
And when we have these circular currents, we get a magnetic moments.
OK, so once again, we can write down the continuity equation, which is in fact just charged conservation.
And now we can separate our charge into the two previous parts and the currents in the three parts here.
So just, yeah, we could also separate the charge into these three parts, but then you would say that
Roedad is zero.
So what we get is we get five times here and now.
We also must realize that the continuity equation is also fulfilled for the individual parts here.
So we can write down this continuity equation for the polarisation currents and for the polarization
charges.
This is the continuity equation that we had in the previous lecture about the polarization.
And we can also write down the continuity equation for the external currents.
So this was the continuity equation that we have used throughout this whole course.
So essentially, what it means is that the external charges conserved, that the polarized charges conserved
and that the magnetised charges conserved, but it's also zero.
So it means we cannot simply transform an external charging to a polarized charge and so on and so on.
And what this means is these two terms cancel the zero, these to cancel, they give zero.
So this means there's one here.
We'll give zero.
So we have now the fact that the divergence of the circular current is zero.
So what we can do is we can introduce a new vector and write down this circular current density in terms
of a rotation of this vector.
And from the dimensionality, you find out that this has the units of a magnetic dipole density.
And so this is called the magnetization.
So as you can see, we have now separated our charges into two parts of occurrence, into three parts,
and we have introduced the electric dipole density, polarisation and the magnetic dipole density to
magnetization.
And we were able to write down this new polarization charge as the divergence of Pete and this new circular
magnetization, current density in terms of a rotation of M.
And in the next lecture, we will use these equations and derive the maximal equations and matter.