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  1. What topics do I need to study (in order) so that I can study electromagnetics on the quantum scale?

  2. What is the name of the discipline studying electromagnetism on the quantum scale?

  3. Do I need to know nuclear physics?

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    $\begingroup$ Seems you're looking for Quantum electrodynamics (usually abbreviated as QED). $\endgroup$ – Kyle Kanos Dec 21 '14 at 21:38
  • $\begingroup$ AS well as the link Kyle gave you, see the Quantization of the electromagnetic field Wiki article for a brief "flavour" of the quantum field. That article is essentially Dirac's legacy and is the "field" side of the topic "quantum optics". Lagrangian mechanics is also a must for making the "quantum optics" / Dirac legacy, which grounded on Hamiltonian mechanics, fully relativistic. History topics IMO are helpful to make the "quantization procedures" seem less arcane. $\endgroup$ – WetSavannaAnimal Dec 21 '14 at 22:07
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Starting from scratch I would propose an order of topics to study as follows:

  • Kinematics (motion)
  • Dynamics (forces)
  • Rotational kinematics and dynamics
  • Collisions (momentum and impulse)
  • Vibrations and waves
  • Thermodynamics
  • Electricity (DC)
  • Electricity (AC)
  • Magnetic fields and forces
  • Electromagnetic waves
  • Light (optics, photons)
  • Quantum mechanics

Nuclear physics and all about atoms and molecules are good topics to continue with from here. But not necessary to get the hang of electromagnetism.

Get a book like University Physics by Young & Freedman. It is pedagogical gold for an eager physics student.

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