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So welcome back.



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You already made it quite far in this course.



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So good job and congratulations.



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So we have already discussed three special cases we have started with.



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Light is an electromagnetic wave.



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So this was where in fields where time dependent.



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But we consider the vacuum where we did not have charges and currents.



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And thereafter we consider the static case where we had time independent electric and magnetic fields,



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but we did not it that vacuum.



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But we consider charges and currents.



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So let's combine both of them and let's discuss the more general case.



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So these will really be time dependent problems.



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And the reason why I did not start with this section in the very beginning is, of course, because



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it's the most difficult case, but also because we can use our results from electrostatic and Magneto's



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tactics.



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So it's really a cool thing, I think, because you can see that we can slightly rewrite our Maxwell's



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equations and then they will look quite similar to electrostatic and Magneto's techniques.



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So this means we can just take our solutions and carry them over.



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And the only thing that we have to account for is a so-called retardation.



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So we will introduce -- potentials instead of our vector potential and the electrostatic potential.



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So you will soon see how this works.



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And even though it may be a bit difficult mathematically, I think physically it's quite clear and you



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can often refer to the electrostatic and the magnetic static case.



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So then we will discuss the most prominent example of a time dependent problem, this, the so-called



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Hartzband dipole.



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So this is an electric dipole, for example, where the two charges plus minus that we have discussed



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before, where they move, they they move.



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So what this gives rise to is a time dependent electric field.



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And we will calculate this field and that's quite difficult.



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But I think also it's really satisfying because you will see that also when we take our frequency and



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make it really, really long so that effectively these charges do not move anymore, we can reestablish



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our solution from electrostatic.



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So I think it's really cool.



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So let's go ahead and talk about the time dependent problems.