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Electromagnetic waves is one of the shortest chapters in Class 12 physics, and one of the most reliable for marks. The questions repeat: put the bands in order, link E and B, write a field equation, and name a use. This post covers each with a worked example and the errors examiners see most.
What is on the syllabus?
The CBSE physics curriculum for 2025-26 lists the basic idea of displacement current, the characteristics and transverse nature of electromagnetic waves (qualitative), and the spectrum from radio waves to gamma rays "including elementary facts about their uses". The JEE (Main) 2026 syllabus and NEET (UG) 2026 syllabus list the same topics plus applications. The CBSE sample question paper for 2025-26 includes a one-mark question comparing the energy and frequency of radio waves and gamma rays and a two-mark question asking for the electric field of a plane wave given its magnetic field. Check your own year's papers too.
What makes a wave electromagnetic?
The NCERT chapter on electromagnetic waves sets out the key facts:
The electric and magnetic fields oscillate at right angles to each other and to the direction of travel, so the wave is transverse.
In vacuum the speed is c = 1/√(μ₀ε₀). In a medium it becomes 1/√(με).
The field amplitudes are linked by B₀ = E₀/c.
No material medium is needed, and the speed in vacuum does not depend on wavelength.
The speed of light in vacuum is now a defined constant, 299,792,458 m/s exactly, per NIST. For problems, 3 × 10⁸ m/s is fine.
The idea goes back to James Clerk Maxwell's 1865 paper, A dynamical theory of the electromagnetic field. Our post on how Maxwell's equations showed light is electromagnetic tells that story, and the one on Hertz and radio waves covers the first laboratory test.
How do you remember the spectrum in order?
From longest wavelength (lowest frequency, lowest photon energy) to shortest, with NCERT's approximate ranges:
Radio: above 0.1 m. Produced by accelerating charges in aerials. Radio, TV, mobile phones.
Microwaves: 0.1 m to 1 mm. Klystrons, magnetrons. Radar, microwave ovens.
Infrared: 1 mm to 700 nm. Hot bodies and molecular vibrations. Remote controls, physical therapy, the greenhouse effect.
Visible: 700 nm to 400 nm. Electrons changing energy levels in atoms.
Ultraviolet: 400 nm to about 1 nm. Very hot bodies and the Sun; mostly absorbed by the ozone layer. Water purifiers, LASIK surgery.
X-rays: about 1 nm to 10⁻³ nm. Electrons hitting a metal target. Medical imaging.
Gamma rays: below about 10⁻³ nm. Radioactive nuclei. Cancer treatment.
NCERT stresses that the boundaries are not sharp and the bands overlap, so an exam will not ask you to defend a boundary to the nanometre.
Worked example 1: find the band
An FM station broadcasts at 100 MHz. What is the wavelength, and which band is it in?
λ = c/f = (3 × 10⁸)/(1.00 × 10⁸) = 3.0 m. That is longer than 0.1 m, so it is a radio wave. NCERT gives the FM band as 88 to 108 MHz, which agrees.
Worked example 2: write the field equation
A plane electromagnetic wave travels along +x in vacuum. Its magnetic field is along z with amplitude B₀ = 400 nT and angular frequency ω = 3.0 × 10⁸ rad/s. Write the electric field.
Amplitude: E₀ = cB₀ = 3 × 10⁸ × 400 × 10⁻⁹ = 120 V/m.
Wave number: k = ω/c = (3.0 × 10⁸)/(3 × 10⁸) = 1.0 rad/m, so λ = 2π/k ≈ 6.28 m (a radio wave).
Direction: the wave travels along E × B. With B along +z and travel along +x, E must be along +y, because ĵ × k̂ = î.
Equation: E_y = 120 sin(1.0x − 3.0 × 10⁸ t) V/m, with B_z = 400 × 10⁻⁹ sin(1.0x − 3.0 × 10⁸ t) T in phase with it.
Common mistakes and how to avoid them
Writing B₀ = cE₀. It is E₀ = cB₀. Check: a magnetic field of a few hundred nanotesla goes with an electric field of about 100 V/m, not a tiny one.
Getting the E direction wrong. Always check E × B points along the direction of travel.
Saying frequency changes in glass. Frequency is set by the source; speed and wavelength change.
Mixing up displacement current with a real flow of charge. It is the term ε₀ dΦ_E/dt, produced by a changing electric field, for example between capacitor plates.
Giving vague uses. "X-rays are used in medicine" earns less than "X-rays are used to image bones".
Fields oscillating in two perpendicular planes are hard to picture from a flat diagram. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read.
A practice routine for this chapter
Day 1: write the seven bands from memory with one source and one use each, then check against NCERT Table 8.1.
Day 2: ten λ = c/f conversions, naming the band each time.
Day 3: five field-equation questions like Example 2, varying the direction of travel.
Day 4: three short answers on displacement current and why the wave is transverse.
Day 5: do the electromagnetic waves questions from the latest CBSE sample paper under time.
Today, write the spectrum in order on a card and add the frequency of your favourite radio station to the right band.
