Schooling · Class 12 · Physics · Electromagnetic Waves · Chapter on a page
CBSE Class 12 · Physics · NCERT Physics Part-I
Electromagnetic Waves: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A time-varying electric field…
- Maxwell introduced displacement…
- Electromagnetic waves are transverse
- In free space, EM waves travel at…
- EM waves carry energy; the average…
- The electromagnetic spectrum spans…
- EM waves also carry momentum; when…
- Formulas and facts
- Displacement current
- Speed of EM waves in vacuum
- Relation between field amplitudes
- Wave equation form
- Energy density
- Intensity
- Radiation pressure
- Worked examples
- Displacement current in a charging…
- Speed of light from constants
- Electric and magnetic field amplitudes
- Watch out for
- Thinking displacement current is a…
- Assuming EM waves need a material…
- Confusing the direction of E or B…
- Using E₀ = B₀ instead of E₀ = c × B₀
- Mixing up frequency and wavelength…
What this chapter is about
This chapter explains how changing electric and magnetic fields create waves that travel through space without needing any medium. You will learn how James Clerk Maxwell predicted these waves by adding a crucial term — the displacement current — to the equations governing electricity and magnetism. This unification showed that light itself is an electromagnetic wave.
Key ideas
- A time-varying electric field produces a magnetic field, and a time-varying magnetic field produces an electric field; together they sustain each other and propagate as an electromagnetic wave.
- Maxwell introduced displacement current, Id = ε₀ × (dΦE/dt), to account for the magnetic field produced by a changing electric flux even when no conduction current flows (for example, between capacitor plates).
- Electromagnetic waves are transverse: the electric field vector E, magnetic field vector B, and the direction of propagation are mutually perpendicular.
- In free space, EM waves travel at speed c = 1/√(μ₀ε₀) ≈ 3.00 × 10⁸ m/s; at every instant, E₀/B₀ = c.
- EM waves carry energy; the average energy density is u = (1/2)ε₀E² + (1/2)(B²/μ₀), and intensity is the energy crossing unit area per unit time.
- The electromagnetic spectrum spans from radio waves (longest wavelength, lowest frequency) through microwaves, infrared, visible, ultraviolet, X-rays to gamma rays (shortest wavelength, highest frequency).
- EM waves also carry momentum; when absorbed by a surface, they exert radiation pressure p = I/c (for total absorption).
Formulas and facts to remember
- Displacement current: Id = ε₀ × (dΦE/dt), where ΦE is electric flux. It has the same unit (ampere) as conduction current.
- Speed of EM waves in vacuum: c = 1/√(μ₀ε₀) ≈ 3.00 × 10⁸ m/s.
- Relation between field amplitudes: E₀ = c × B₀, or at any instant E = c × B.
- Wave equation form: E = E₀ sin(kx − ωt), B = B₀ sin(kx − ωt), with k = 2π/λ and ω = 2πν.
- Energy density: Total average energy density u = ε₀E² (since electric and magnetic contributions are equal in a travelling wave).
- Intensity: I = (1/2) × c × ε₀ × E₀² (average power per unit area).
- Radiation pressure: p = I/c (complete absorption) or p = 2I/c (perfect reflection).
- Spectrum order by increasing frequency: Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma ray.
Common mistakes
- Thinking displacement current is a flow of charges → it is not; it is ε₀ × (dΦE/dt), arising from a changing electric field.
- Assuming EM waves need a material medium to travel → they propagate perfectly through vacuum.
- Confusing the direction of E or B with the direction of wave propagation → E, B and the propagation direction are all mutually perpendicular.
- Using E₀ = B₀ instead of E₀ = c × B₀ → the magnitudes are related by the speed of light, not equality.
- Mixing up frequency and wavelength trends in the spectrum → higher frequency means shorter wavelength.
Quick revision
- Displacement current Id = ε₀ × (dΦE/dt) completes Ampere's law for time-varying fields.
- EM waves are transverse; E ⊥ B ⊥ direction of propagation.
- Speed in vacuum: c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s; field ratio E = cB.
- Spectrum order (low to high frequency): Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma.
- EM waves carry energy (intensity I) and exert radiation pressure I/c on an absorbing surface.