Electromagnetic Waves
What is examined
Electromagnetic Waves tests the displacement current, Maxwell's idea, the transverse nature of EM waves, the relation E₀/B₀ = c, the EM spectrum and its uses, and simple intensity calculations.
Core rules
- A changing electric field produces a displacement current I_d = ε₀ dΦ_E/dt, which produces a magnetic field; this completes the symmetry with Faraday's law.
- EM waves are transverse: E, B and the direction of propagation are mutually perpendicular, with E × B along propagation. E and B are in phase.
- In vacuum E₀/B₀ = c and c = 1/√(μ₀ε₀) ≈ 3×10⁸ m s⁻¹. In a medium v = 1/√(με), refractive index n = c/v, and the vacuum speed is independent of wavelength.
- Intensity: I = ½ε₀cE₀²; momentum and radiation pressure follow from p = U/c.
- Spectrum, increasing frequency: radio, microwave, infrared, visible (400–700 nm), ultraviolet, X-rays, gamma rays. Wavelength order is the reverse.
- Uses: radio for communication, microwave for radar and ovens, IR for remote controls and night vision, UV for sterilisation, X-rays for imaging, gamma for cancer therapy.
Worked example
An EM wave has E₀ = 120 N C⁻¹. Find B₀ and intensity. B₀ = E₀/c = 120/(3×10⁸) = 4.0×10⁻⁷ T. I = ½ε₀cE₀² = ½(8.85×10⁻¹²)(3×10⁸)(120)² ≈ 1.9×10¹ W m⁻². Reasoning: E₀ and B₀ are peak values; use ε₀ in SI and square E₀.
Traps
Thinking displacement current is a flow of electrons; reversing the spectrum order; using rms values in E₀/B₀ = c; and saying E and B are perpendicular but out of phase.