Electromagnetic Waves
Source lecture(s): SC134 Lec14
Intuition
Oscillating electric and magnetic fields sustain each other in vacuum, propagating at the speed of light.
Formal Definition
Self-sustaining solutions to Maxwell's equations in free space with no charges or currents.
Mathematical Formulation
Wave equation from Maxwell: \(\nabla^2 E = \mu_0\varepsilon_0 \partial^2 E/\partial t^2\) Speed: \(c = 1/\sqrt{\mu_0\varepsilon_0} \approx 3.00\times10^8\,\text{m/s}\) Energy density: \(u = \frac{1}{2}\varepsilon_0 E^2 + \frac{1}{2\mu_0}B^2\)
Derivation
Take curl of Faraday's law, substitute Ampere-Maxwell, use \(\nabla\cdot E = 0\) in vacuum.
Worked Example
Radio waves, visible light, X-rays are all EM waves with different frequencies.
Common Mistakes
- Confusing phase between \(E\) and \(B\) (they are in phase in vacuum).
- Using SI units without \(\mu_0\varepsilon_0\).
Related Concepts
Quiz
Q1. What is the ratio \(E/B\) in an EM wave in vacuum?
Answer
\(c\).