Problem — EM waves and the structure of the vacuum

Problem

A mechanical wave requires a medium, whereas an EM wave also travels through the vacuum. Explain which elements of Maxwell’s model make propagation in vacuum possible, and from which constants the speed $c$ emerges.

Solution

Maxwell’s mechanism. In the electromagnetic model two laws couple the fields:

• a changing electric field $\vv E$ generates a magnetic field $\vv B$ (Ampère-Maxwell law, via the displacement current);
• a changing magnetic field $\vv B$ generates an electric field $\vv E$ (Faraday-Neumann-Lenz law).

Why the vacuum is enough, and nothing more. The two fields sustain each other: the change in one regenerates the other, in a chain that propagates without needing any material medium. No real charges or currents are needed — the electric and magnetic properties of empty space, that is $\varepsilon_0$ and $\mu_0$, are sufficient.

Speed. Combining the equations gives the propagation speed:

$\ev{c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}\approx 3{,}00\cdot 10^8\ \text{m/s}}$

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Onda elettromagnetica · Equazioni di Maxwell