Electricity & Magnetism
Electricity and magnetism begin with a single quantity — charge — and the field it fills space with. Every force, potential, and current in the subject is bookkeeping on that field and how it changes.
A charge sources an electric field, and a field exerts a force on any charge placed in it. Draw the field as lines — dense where it is strong, always leaving + and landing on − — and most of electrostatics becomes a picture you can read.
Two ideas make fields tractable. Potential collapses a vector field to a single scalar you can add up; flux, through Gauss's law, turns a surface integral into the charge enclosed. Symmetry then does the rest.
Store charge on conductors and you get capacitance; let it flow and you get current, resistance, and the circuits that move energy from one place to another.
Moving charge is the bridge to magnetism. A current sets up a magnetic field that circulates around it, and Ampère's law ties the field to the current the same way Gauss's law ties E to charge.
The two fields are not independent. A changing magnetic flux drives an electric field around a loop — Faraday's law of induction — which is how every generator, transformer, and inductor works.
Maxwell added the missing symmetry — a changing electric field is itself a source of magnetic field — and the four equations closed on themselves. A field could now sustain a field, with no charges in sight.
That self-sustaining ripple is light. Electromagnetic waves carry energy and momentum, come in every wavelength, and — through reflection and refraction — hand the subject over to optics.