Roadmap for Electrodynamics
Electrodynamics isn’t appreciated enough! Lots of people find it stuffed with tedious computations and tricks, but the fact is that it remains one of the most practical, wide-ranging subjects and a key cornerstone of one’s physics learning journey.
A big disclaimer that I should add is that my viewpoint is skewed towards high energy physics, so I am not aware of the details of electrodynamical applications to say plasma physics. Sorry.
Also before I commence, I just want to put it out there: Griffiths’ Electrodynamics book is a national treasure.
Definite prerequisites
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The mathematical prerequisites are, on the whole, very similar to those for quantum mechanics - with the sole exception of linear algebra. So an understanding of multivariable calculus and differential equations is necessary to commence. Knowledge of basic PDE and Fourier series is also helpful, but can be learned concurrently.
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Most electrodynamics sources provide an overview of the requisite vector calculus, which is probably the largest mathematical hurdle. It’s possible to pick it up simultaneously after a brief overview of vector fields, vector operators and Gauss’ and Stokes’ theorems: don’t waste your time solving too many abstract problems beforehand, since you’ll have to apply them anyway while doing E&M problems. It’s good to be able to visualise all of these mathematical notions clearly (they’re really quite intuitive once you get the hang of it)
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Wave optics: Essentially just the high school coverage of light and waves, this goes without saying. A qualitative understanding of the key optical phenomena should be coupled with knowledge of non-rigorous derivations of the key formulae. Don’t worry, the motivation behind all the seemingly ad hoc rules that pervade high school physics will become clear in due course.
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Newtonian mechanics: Duh.
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High school electromagnetism: now this varies hugely from one education system to another, I’ve seen some high school physics syllabi extend right until Maxwell’s equations, while some go up only to electric force, potentials and some basic electromagnetic relations. My advice: make sure you at least know the latter. In fact, you can specialise to electric fields and potentials only, the high school/pop-sci explanations of magnetism are generally not great, and so you can rely on a solid electrodynamics textbook to teach you this.
Learn it along the way (or before, for a better understanding):
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Try performing some computational electrodynamics! There are lots of finite element methods, discretisation schemes and numerical methods to be played with here, and these all serve as a robust introduction to more advanced simulations, for example in quantum chemistry
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Quantum mechanics: There are a few historical routes that you can use to enter the quantum domain! First is spontaneous emission á la Einstein, and the other (more famous one) is Planck’s radiation curve - see if you can find some more conflicts between the two.
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Special relativity: A lot of E&M textbooks are bundled together with a chapter or two on special relativity anyway, but it’s fun to start exploring and thinking about early on!
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Classical field theory: You get to put to the test all of your field theoretic knowledge! Sadly, most of the content is not very helpful for practical electrodynamics, but it assumes utmost importance if you want to probe the theoretical features of Maxwell’s equations, and electrodynamics as a gauge theory.