At my university the second half of a year long sequence in basic calculus based physics focuses on electrodynamics and magnetism. I am wondering what is the significance of these topics to physics in general? How does it relate/prepare you to study the more advanced subjects like quantum mechanics and the like?
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Motivation: the electromagnetic force is one of the four elementary interactions in Nature. The electromagnetic force is responsible of lots of phenomena: intermolecular bonding in ordinary matter, electromagnetic waves [light], electrons are bound to nucleus by the electromagnetic force etc. Chemistry is basically governed by the electromagnetic interaction.
The difficulty to make compatible classical electrodynamics and classical mechanics [ Maxwell equations predicted that the speed of light is a universal constant in free space which contradicts Galilean invariance] led to the theory of special relativity by Lorentz, Poincaré and Einstein.
One cannot overemphasize the importance of classical electromagnetism. It is one of cornestornes of physics and, even if it does not prepare you to manipulate quantum mechanics (different formalism) it does prepare you to understand it.
Quantum electrodynamics: is the quantum theory of electromagnetism. The theory was born after the seminal works of Planck and Einstein in photons / photoelectric effect respectively. It was completed in the 1940s and is one of the most accurate theories known in physics.