Fundamental: Why Waves?
Understanding how changing fields sustain each other and why propagation is a physical necessity.
Electromagnetic Waves
In the previous chapter, we assembled the four pillars of Electrodynamics: Maxwell's
Equations.
Now, we explore their most profound mathematical consequence. In source-free regions, changing fields
sustain each other
in a self-propagating loop—an Electromagnetic Wave.
This chapter traces the path from Maxwell's Equations to the Wave Equation, through the
transport of
Energy & Momentum, and finally to the behavior of these fields at the boundaries of
Matter.
1. Wave Fundamentals
The 1D wave equation, sinusoidal waves, and general properties of oscillations.
2. EM Waves in Vacuum
Deriving wave propagation from Maxwell's Equations, transverse nature, and polarization.
3. Energy & Momentum
The Poynting vector, intensity, and the pressure exerted by light.
4. Waves in Matter
Propagation through dielectrics and conductors, and the physics of boundary conditions.