What are some practical things one can do with classical electrodynamics and QED? Many basic types of physics have ready and obvious everyday applications. For instance, basic electromagnetism vector calculus can give great insights into how something as simple as a bar magnate works. And obviously the more people understand the science the easier it is to apply it.  
My Question: 
What are some examples of useful or practical applications of  classical electrodynamics and  quantum electrodynamics? 
I'm hoping that by getting some examples it will help me better understand why physicist seek these elaborate tools to describe physical phenomena.  
 A: Quantum mechanics and classical E&M have created a whole bunch of fruit. In no particular order:


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*Light is an electromagnetic wave. This means that we are routinely making light with LEDs and the like. It's pretty cool that you can design better antennas, or waveguides, or what have you. While we're at it, knowing why Stefan-Boltzmann radiation goes like T4 and having the formula for Larmor radiation are both huge wins.

*Photomultiplier tubes. These tubes always begin with a bunch of electric fields shaping the first generation of electrons to hit a smallish target and kick off even more electrons, until we can get a current out of there.

*Mother-effing magnets. Magnetic fields are used in particle accelerators to get particles moving in a big circle, but also in smaller (but crazier) fusion reactors called tokamaks, to try to keep this surface-of-the-Sun substance from touching the walls. 

*Even if you don't understand the mechanism by which a material is superconducting, you can confirm that it must expel almost all of its magnetic field, and you can thereby work out a lot of the properties that it must have.

*It's a nice springboard to think about special relativity.

*A good understanding of E&M reveals why your pet perpetual motion device doesn't work.
Magnets might look pretty magical but it turns out they're not that magical. While we're at it, you can prove that there's no way to permanently levitate something with fixed, nonadaptive, nonsuperconducting magnets -- you have to have a mechanism which dynamically adjusts the magnetic field because every equilibrium is some form or another of saddle point.

*Circuits make more sense. How does electricity get through a capacitor if electrons can't? How do inductors work? What are those diode and transistor things anyway? Sure, once you get to digital logic gates these laws get far-removed; but when you want to peek inside the components' real-world characteristics, like using diodes in their crossover regimes, you benefit from understanding how the world is not ideal.

*Once you get to QED you have a springboard for getting into quantum field theories, which allow us to bring symmetries and group theory and all sorts of other great pieces of mathematics to simple questions about "what particles could exist?". Then people who work in solid-state physics (who steal your methods shamelessly but do not have particle accelerators) then find electronic excitations in semiconductors which behave just like your exotic "Majorana fermions". (This happened; these strange "particles" were discovered at the TU Delft while I worked there.) Those devices might later go on to enable a new technological revolution, or might not. Lots of people are using quantum mechanics to try and build quantum computers, for example.

