Electromagnetic Waves Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 8 notes: displacement current, properties of electromagnetic waves, speed of light, and the full electromagnetic spectrum with uses.
Electromagnetic Waves — Class 12 Physics Notes
Chapter Snapshot
Maxwell realised Ampere's law was incomplete and added the displacement current. The corrected equations predicted electromagnetic waves travelling at the speed of light — showing that light is an EM wave. This chapter covers displacement current, the properties of EM waves, their speed, and the electromagnetic spectrum with the uses of each band.
Board relevance: short but reliably examined — usually a displacement-current question or a spectrum question (identify a band, its order, or a use), worth 2–3 marks.
Key Concepts & Definitions
The problem Maxwell solved: Ampere's law (∮B·dl = μ₀I) fails for a charging capacitor. Take two surfaces bounded by the same loop — one cutting the wire (current I passes) and one passing between the capacitor plates (no conduction current). The law gives contradictory answers.
Displacement current — Maxwell's fix. A changing electric field between the plates acts like a current:
Id = ε₀ dΦE/dt
Modified (Ampere–Maxwell) law:
∮B·dl = μ₀(Ic + Id) = μ₀(Ic + ε₀ dΦE/dt)
Inside the capacitor the conduction current is zero but the displacement current exactly equals I, so the law becomes consistent. Key idea: a changing electric field produces a magnetic field (the counterpart of Faraday's "a changing magnetic field produces an electric field"). Together these two effects sustain an EM wave.
Properties of Electromagnetic Waves
- Transverse waves: the electric field E, magnetic field B, and the direction of propagation are mutually perpendicular (E × B gives the direction of travel).
- E and B oscillate in phase, reaching maxima and minima together.
- They require no material medium — they travel through vacuum (unlike sound).
- They travel at the speed of light in vacuum and are produced by accelerating charges.
- They carry energy and momentum and exert radiation pressure.
- They are not deflected by electric or magnetic fields (being uncharged).
Formulas
Quantity Formula
Speed in vacuum c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s
Speed in a medium v = 1/√(με), always < c
Amplitude relation E₀/B₀ = c
Wave relation c = fλ
Energy density u = ½ε₀E² + B²/2μ₀ (equal contributions from E and B)
Displacement current Id = ε₀ dΦE/dt
(μ₀ = 4π × 10⁻⁷ T·m/A, ε₀ = 8.85 × 10⁻¹² C²/N·m².)
The Electromagnetic Spectrum
In order of increasing frequency (decreasing wavelength):
Band Production Main uses
Radio waves Accelerated charges in aerials Radio, TV broadcasting, mobile communication
Microwaves Klystron/magnetron valves Radar, microwave ovens, satellite communication
Infrared Hot bodies and molecules Heating, night-vision, remote controls, physiotherapy
Visible light Atoms and molecules (electron transitions) Vision; the only band our eyes detect (≈ 400–700 nm)
Ultraviolet Special lamps, very hot bodies, the Sun Sterilisation, detecting forgeries, LASIK surgery
X-rays Fast electrons striking a metal target Medical imaging, detecting fractures, industrial flaw detection
Gamma rays Radioactive nuclei / nuclear reactions Cancer treatment (radiotherapy), sterilising equipment
Two things to remember: the ozone layer absorbs harmful UV, protecting life; and infrared is responsible for the greenhouse effect (trapped by CO₂ and water vapour, keeping the Earth warm).
Worked Examples
Example 1 — Speed from constants: Verify c using μ₀ and ε₀.
c = 1/√(μ₀ε₀) = 1/√[(4π × 10⁻⁷)(8.85 × 10⁻¹²)] ≈ 1/√(1.11 × 10⁻¹⁷) ≈ 3 × 10⁸ m/s.
Example 2 — Field amplitude: An EM wave has B₀ = 2 × 10⁻⁸ T. Find E₀.
E₀ = cB₀ = (3 × 10⁸)(2 × 10⁻⁸) = 6 V/m.
Example 3 — Wavelength: Find the wavelength of a 100 MHz FM radio wave.
λ = c/f = (3 × 10⁸)/(100 × 10⁶) = 3 m.
Example 4 — Displacement current: The electric flux between capacitor plates changes at 10⁶ V·m/s. Find Id.
Id = ε₀ dΦE/dt = (8.85 × 10⁻¹²)(10⁶) = 8.85 × 10⁻⁶ A.
Important Question Patterns
1. Displacement current (2–3 marks): define it; why Ampere's law needed correction (the capacitor argument); write the Ampere–Maxwell law.
2. Properties (2 marks): why EM waves are transverse; the mutual perpendicularity of E, B and propagation; that they need no medium.
3. Speed/amplitude (2 marks): c = 1/√(μ₀ε₀); E₀ = cB₀; speed in a medium.
4. Spectrum (2–3 marks): arrange bands in order of wavelength/frequency; identify a band from its use or production method.
5. Applications (2 marks): name the radiation used for a given purpose (X-ray imaging, microwave radar, UV sterilisation, IR remote controls).
⚡ Quick Revision
- Displacement current Id = ε₀ dΦE/dt — Maxwell's fix to Ampere's law; a changing E field produces a B field.
- Ampere–Maxwell: ∮B·dl = μ₀(Ic + ε₀ dΦE/dt).
- EM waves are transverse; E ⟂ B ⟂ direction of travel; in phase; need no medium; carry energy and momentum; undeflected by fields; produced by accelerating charges.
- c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s; in a medium v = 1/√(με) < c; E₀/B₀ = c; c = fλ.
- Spectrum (increasing frequency): radio → microwave → infrared → visible → UV → X-ray → gamma.
- Uses: radio (broadcast), microwave (radar/ovens), IR (heating, remotes), visible (sight), UV (sterilisation), X-ray (imaging), gamma (radiotherapy).
- Ozone absorbs UV; infrared drives the greenhouse effect.
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