The first lecture of this section, I just want to go ahead and show you the Maxwell's equations that
Maxwell formulated in the 18 60s.
So these are the four equations in differential form.
So we have here their divergence of the electric field and the divergence of the magnetic fields.
So these are the sources of these two fields.
And for the electric field, we get that it's given by one over Epsilon zero, which is a constant called
to vacuum permeability.
And then we multiply here by the charged density, which is a quantity that depends on the position.
So it's actually row of R and that tells us the charges are the sources of the electric field.
The second equation is that the divergence of the magnetic field is zero.
So when we compare the electric field and the magnetic field, this means the magnetic field does not
have any sources.
So it means there are not such things as charges for the magnetic field.
So there are no magnetic monopoles.
Magnets always come in pairs.
So you always have the North and South Pole, but no monopoles.
The other two equations relate the rotation of the electric field to the time derivative of the magnetic
field and vice versa.
So we have year rotation of the electric field is equal to minus one times the time derivative of the
magnetic field.
So it means that when we have a change in the magnetic field over time, this generates electric fields.
And also, it goes the other way around when we have time changes in the electric field.
This gives rise to magnetic fields.
But here we have a factor, which is the product of this vacuum perpetuity and the vacuum permeability.
And then we also have the other term that we have found already in the first section of the Holocaust
where we found that charges.
So basically moving, moving charges that give rise to currents generate magnetic fields.
So remember these rotational symmetric field lines around a wire.
So these are the form Maxwell equations and these are the most important equations of this whole course.
And we were out the following lectures and sections.
We will discuss these equations in much detail and we will solve special cases, for example, where
the fields do not depend on time, but only on the position.
And also, I want to show you how we can find the Coulomb law and the amperes law and the law of electromagnetic
induction in these Maxwell's equations.
Therefore, we also have to formulate these differential versions of the Maxwell equations as integral
versions.
So this is one of the upcoming lectures.
But before I want to start with an optional lecture where I want to show you how we can motivate these
four equation based on symmetry arguments.
So this is a very theoretical lecture.
And if you are not that interested in the topic, that is totally fine.
You can go ahead and skip it.
But I think it's worth giving it a shot and try to understand because it's really rewarding to understand
where to Maxwell's equations come from.