The Core Idea: Why Can Light Travel Through Empty Space?

Imagine you shake a charge up and down. The electric field around it changes. But a changing electric field — according to Ampere-Maxwell law — creates a magnetic field in the region around it. Now that magnetic field is also changing (since you're still shaking). A changing magnetic field — according to Faraday — creates an electric field in the region beyond it.

So the disturbance travels outward: the changing E creates B further out, which creates a new E further still, which creates a new B even further... The original shaking charge has set off a chain reaction of mutually regenerating fields that races outward at the speed c = 1/√(μ_{0}ε_{0}).

The beautiful insight: You don't need the source (the accelerating charge) to still be shaking for the wave to keep going. Once launched, the wave is completely self-sustaining — it carries itself through empty space using nothing but the relationship between changing E and changing B fields.

Why c = 1/√(μ_{0}ε_{0})? Think of ε_{0} as measuring how "reluctant" empty space is to setting up an electric field (high ε_{0} = space accommodates E fields easily). Think of μ_{0} as measuring how "enthusiastic" space is about B fields. The interplay between these two properties of vacuum sets the pace at which the field disturbance can travel. Maxwell calculated this and got $3 \times 10^{8}$ m/s — the known speed of light. He immediately realised: light IS an electromagnetic wave.

Why are E and B in phase? In a mechanical wave on a string, kinetic energy (velocity) and potential energy (displacement) are 90° out of phase. But for EM waves, the energy stored in E and B fields is related differently — the wave equation couples them such that their maxima coincide. They rise and fall together, maintaining $E_{0}$/$B_{0}$ = c at all times.