Speed of electromagnetic waves

Applying Faraday’s and Ampère-Maxwell’s equations to a plane wave leads to a clear-cut result: the propagation speed $v$ depends only on the vacuum constants $\varepsilon_0$ and $\mu_0$, not on the frequency nor on the amplitude of the wave.

Speed of an EM wave in vacuum

$\ev{v = \frac{1}{\sqrt{\varepsilon_0\,\mu_0}}}$

Let us substitute the numerical values of the two constants:

$\varepsilon_0 \approx 8{,}85\cdot 10^{-12}\;\text{F/m} \qquad \mu_0 = 4\pi\cdot 10^{-7}\;\text{T·m/A}$

$v = \frac{1}{\sqrt{8{,}85\cdot 10^{-12}\cdot 4\pi\cdot 10^{-7}}} \approx 3\cdot 10^8\;\text{m/s}$

A decisive result

This is exactly the value of the speed of light, known from astronomical measurements since the time of Rømer (around 1676). Maxwell wrote: «We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena».

Two constants measured in the laboratory with balances and coils — experiments that had nothing to do with light — combine and yield the speed of light. This is the clue that leads to the identification: light is an electromagnetic wave.

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Topics: Electromagnetic waves Concepts: Electromagnetic wave Skills: Dimensional analysis

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