Problem — EM waves without a medium

Problem

A mechanical wave requires a material medium (air, water, a string), whereas an electromagnetic wave also travels in vacuum. Explain which elements of Maxwell’s model make this propagation possible.

Solution

What oscillates in an EM wave. In a mechanical wave, the particles of the medium oscillate. In an electromagnetic wave, on the other hand, it is the fields $\vv E$ and $\vv B$ that oscillate — physical entities defined at every point in space, including vacuum. No vibrating matter is needed.

The self-sustaining chain. Maxwell’s equations show that the two fields generate each other:

• an electric field varying in time generates a magnetic field (the Ampère-Maxwell law, with the displacement-current term $\varepsilon_0\,d\Phi_E/dt$);
• a magnetic field varying in time generates an electric field (the Faraday-Neumann-Lenz law).

A change in $\vv E$ produces a varying $\vv B$, which in turn produces a varying $\vv E$, and so on: the disturbance regenerates itself and propagates without needing material support.

The speed. Combining the equations yields a wave that travels in vacuum at the speed $c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}=3{,}00\cdot 10^8\ \text{m/s}$ which depends only on two vacuum constants, not on the properties of a medium.

No aether. In the nineteenth century an invisible medium, the “aether”, was postulated as the support for light. The Michelson-Morley experiment (1887) searched for it and did not find it: it does not exist. Maxwell’s theory does not need it.

Summary fields $\vv E$ and $\vv B$. Their mutual generation (Ampère-Maxwell + Faraday) makes the propagation self-sustaining: $\ev{\text{no material medium required}}$.

The EM wave is not the vibration of a substance, but of the

Connections

Topics: Electromagnetic waves Concepts: Electromagnetic wave · Maxwell’s equations