Question

What is an electromagnetic wave? On which factors does its velocity in vacuum depend?

Hint:

In vacuum, all electromagnetic waves (radio, light, X-rays, etc.) travel with the same velocity \( c = 3 \times 10^8 \, \text{m/s} \).

Answer 1

Step 1: Electromagnetic waves are produced by the acceleration of electric charges. When charges accelerate, they create time-varying electric and magnetic fields that are mutually perpendicular and propagate through space.
Step 2: These varying electric and magnetic fields sustain each other as they move through space. The changing electric field generates a magnetic field, and the changing magnetic field induces an electric field, allowing the wave to propagate even in vacuum without the need for any medium.
Step 3: The speed of electromagnetic waves (speed of light) in vacuum is derived from Maxwell’s equations and is given by: \[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \, \text{m/s}, \] where \( \mu_0 \) is the permeability of free space, and \( \varepsilon_0 \) is the permittivity of free space.
Hence, the velocity of electromagnetic waves depends solely on these two fundamental constants \( \mu_0 \) and \( \varepsilon_0 \), highlighting the intrinsic properties of free space.