Electromagnetic Waves

Concept overview

Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields, propagating through vacuum at the speed of light c = 1/√(ε₀μ₀) ≈ 3 × 10⁸ m/s. In an EM wave, E and B are perpendicular to each other and to the direction of propagation; they oscillate in phase with |E|/|B| = c.

Maxwell's addition to Ampere's law introduced the displacement current I_d = ε₀ dΦ_E/dt, which flows between capacitor plates even though no charge crosses the gap. This closure of Ampere's law makes the equations symmetric and predicts the existence of EM waves.

The electromagnetic spectrum spans from long-wavelength radio waves (km to m) through microwaves, infrared, visible (400–700 nm), ultraviolet, X-rays, to short-wavelength gamma rays (< 10 pm). Frequency f, wavelength λ and speed c are related by c = fλ; energy per photon is E = hf.

Energy density in an EM wave is u = ½ε₀E² + B²/(2μ₀) = ε₀E² (since B = E/c). The intensity — power per unit area — is I = uc. Radiation pressure on a perfectly absorbing surface is P = I/c; on a reflecting surface P = 2I/c.

Key formulas & concepts

• Speed of light in vacuum: c = 1/√(ε₀μ₀) ≈ 3 × 10⁸ m/s
• E-B relation in vacuum: |E| / |B| = c
• Photon energy: E = hf = hc/λ
• Energy density: u = ε₀ E² (using B = E/c)
• Intensity: I = ½ε₀ c E₀² (time-averaged)
• Radiation pressure (absorbed): P = I/c
• Radiation pressure (reflected): P = 2I/c
• EM spectrum order: radio < micro < IR < visible < UV < X-ray < γ

Common mistakes to avoid

• Using B = E instead of B = E/c — the two fields have vastly different magnitudes.
• Forgetting that c = fλ holds in vacuum only — in a medium, v = c/n where n is the refractive index.
• Applying non-time-averaged intensity — the ½ factor in I = ½ε₀cE₀² comes from time-averaging E₀² sin²(ωt).
• Confusing radiation pressure on absorbed vs reflected surfaces — reflected gives twice the pressure (momentum reverses).

JEE Main relevance

JEE Main asks 1 EM waves question every paper — usually direct-recall on the spectrum order or a simple photon-energy calculation. High-yield with minimal preparation.

JEE Advanced relevance

Advanced problems combine EM waves with photoelectric effect (energy of incident photons) or with radiation pressure on a moving surface. Displacement current problems inside a charging capacitor are also standard.

Previous-year questions (PYQ)

EM waves PYQs are almost all direct-recall on the spectrum or photon energy. Ten minutes of focused memorisation covers them.