So welcome back.
You already made it quite far in this course.
So good job and congratulations.
So we have already discussed three special cases we have started with.
Light is an electromagnetic wave.
So this was where in fields where time dependent.
But we consider the vacuum where we did not have charges and currents.
And thereafter we consider the static case where we had time independent electric and magnetic fields,
but we did not it that vacuum.
But we consider charges and currents.
So let's combine both of them and let's discuss the more general case.
So these will really be time dependent problems.
And the reason why I did not start with this section in the very beginning is, of course, because
it's the most difficult case, but also because we can use our results from electrostatic and Magneto's
tactics.
So it's really a cool thing, I think, because you can see that we can slightly rewrite our Maxwell's
equations and then they will look quite similar to electrostatic and Magneto's techniques.
So this means we can just take our solutions and carry them over.
And the only thing that we have to account for is a so-called retardation.
So we will introduce -- potentials instead of our vector potential and the electrostatic potential.
So you will soon see how this works.
And even though it may be a bit difficult mathematically, I think physically it's quite clear and you
can often refer to the electrostatic and the magnetic static case.
So then we will discuss the most prominent example of a time dependent problem, this, the so-called
Hartzband dipole.
So this is an electric dipole, for example, where the two charges plus minus that we have discussed
before, where they move, they they move.
So what this gives rise to is a time dependent electric field.
And we will calculate this field and that's quite difficult.
But I think also it's really satisfying because you will see that also when we take our frequency and
make it really, really long so that effectively these charges do not move anymore, we can reestablish
our solution from electrostatic.
So I think it's really cool.
So let's go ahead and talk about the time dependent problems.