Learning Objectives
- Understand Maxwell's equations and displacement current
- Learn the properties of electromagnetic waves
- Study the electromagnetic spectrum and its regions
- Know the applications of different EM waves
- Understand the nature of light as an electromagnetic wave
Key Concepts
Displacement Current and Maxwell's Equations
Maxwell added displacement current (I_d = ε₀ dΦ_E/dt) to Ampere's law to make it consistent.
Modified Ampere's law: ∮B · dl = μ₀(I + I_d) = μ₀(I + ε₀ dΦ_E/dt)
Displacement current flows in the gap between capacitor plates during charging/discharging.
Maxwell's equations unify electricity, magnetism, and optics. They predict electromagnetic waves travelling at speed c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s.
Properties of Electromagnetic Waves
- E and B are perpendicular to each other and to the direction of propagation (transverse waves).
- They travel at speed c = 3 × 10⁸ m/s in vacuum.
- No medium is needed for propagation.
- E and B oscillate in phase: E₀/B₀ = c.
- They carry energy and momentum: Energy density u = ½ε₀E² + B²/(2μ₀).
- Intensity: I = ½cε₀E₀² = E₀B₀/(2μ₀).
- Momentum: p = U/c (energy/speed of light). Radiation pressure = I/c.
- They can be polarised (confirms transverse nature).
Electromagnetic Spectrum
From lowest to highest frequency (longest to shortest wavelength):
- Radio waves (> 0.1 m): Communication, broadcasting. Produced by oscillating circuits.
- Microwaves (0.1 m to 1 mm): Radar, cooking, satellite communication. Produced by klystron, magnetron.
- Infrared (1 mm to 700 nm): Thermal imaging, remote controls, greenhouse effect. Produced by hot bodies.
- Visible light (700 to 400 nm): Vision, photosynthesis. VIBGYOR. Produced by atoms, hot objects.
- Ultraviolet (400 to 1 nm): Sterilisation, vitamin D production, LASIK surgery. Produced by Sun, arc lamps.
- X-rays (1 nm to 0.01 nm): Medical imaging, security scanning, crystallography. Produced by X-ray tubes (deceleration of high-energy electrons).
- Gamma rays (< 0.01 nm): Cancer treatment, nuclear reactions. Produced by radioactive nuclei, nuclear reactions.
All travel at speed c in vacuum. c = fλ.
Summary
Maxwell's equations predict electromagnetic waves, unifying electricity and magnetism. EM waves are transverse, travel at speed c, and need no medium. The EM spectrum spans from radio waves to gamma rays, with different production mechanisms and applications. Light is a small part of this spectrum. EM waves carry energy and momentum.
Important Terms
- Displacement Current: I_d = ε₀ dΦ_E/dt, flows in capacitor gaps
- Maxwell's Equations: Four equations unifying electromagnetism
- Electromagnetic Spectrum: Complete range of EM radiation frequencies
- Radiation Pressure: Pressure exerted by EM waves, P = I/c
- Polarisation: Restriction of E-field oscillation to one plane
Quick Revision
- c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s; c = fλ
- E₀/B₀ = c; E ⊥ B ⊥ direction of propagation
- Spectrum: Radio > Microwave > IR > Visible > UV > X-ray > Gamma
- Displacement current: I_d = ε₀ dΦ_E/dt
- Intensity: I = ½cε₀E₀²
- Momentum of photon: p = E/c = hf/c = h/λ