Electromagnetic Waves
What the exam tests
Questions test Maxwell displacement current, the transverse nature of electromagnetic waves, the relation between E and B, speed in vacuum and media, the electromagnetic spectrum, energy density, intensity and momentum.
Core rules
- A changing electric field produces a magnetic field; this displacement current term completes Ampere law and predicts electromagnetic waves.
- EM waves are transverse: E, B and the direction of propagation are mutually perpendicular. E and B oscillate in phase.
- In vacuum c = 1/√(μ0ε0) = 3×10^8 m/s. In a medium v = 1/√(με), and refractive index n = c/v.
- Intensity I = 1/2 ε0cE0^2. Radiation pressure and momentum follow from energy: p = U/c for complete absorption.
- Spectrum in increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays.
- Uses depend on wavelength: radio for communication, microwaves for radar and ovens, IR for remotes, UV for sterilisation, X-rays for imaging, gamma for cancer therapy.
Worked example
An FM station transmits at 100 MHz. Find the wavelength in vacuum. λ = c/f = (3×10^8)/(100×10^6) = 3 m. In a medium with refractive index 1.5, the speed becomes 2×10^8 m/s and the wavelength becomes 2 m, while the frequency stays 100 MHz. Frequency is set by the source and does not change on entering a medium.
Traps
Displacement current is not a flow of electrons; it is due to a changing electric field. E and B are in phase in a plane EM wave, not 90° out of phase. The spectrum order is a common memory trap. Speed decreases in a denser medium, so wavelength decreases but frequency is unchanged. Intensity depends on E0 squared.