Class 12 · Chapter 8

Electromagnetic Waves

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Electromagnetic Waves Short Notes

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Condensed revision points for Electromagnetic Waves — for quick recall before exams, not a substitute for the full notes.

1865: Maxwell predicts EM waves theoretically. 1887: Hertz produces/detects them (λ≈6m), confirming the prediction.
J.C. Bose: produced EM waves of λ 5mm–25mm. 1896: Marconi — antenna+earth ≈ capacitor plates, radiates RF waves over km.
1899: Marconi establishes wireless communication across the English Channel (~50 km).

I_d = ε₀(dΦ_E/dt) — a changing electric field acts as a current source for B, exactly like a real current.
Total current I = I_c + I_d. Ampère–Maxwell law: ∮B·dl = μ₀(I_c + ε₀dΦ_E/dt).
In a charging capacitor's gap, I_c = 0 but I_d = I (the same as the conduction current in the wires) — displacement current 'completes the circuit' through the gap.

(I) Gauss (electrostatics): ∮E·dS = q/ε₀. (II) Gauss (magnetism): ∮B·dS = 0 (no monopoles).
(III) Faraday's law: ∮E·dl = −dΦ_B/dt. (IV) Ampère–Maxwell: ∮B·dl = μ₀(I_c + ε₀dΦ_E/dt).
(III) and (IV) mirror each other — changing B drives circulating E, changing E (or current) drives circulating B; this mutual regeneration is what lets the wave propagate.

Induction coil → spherical electrodes with gap (transmitter, ≈LC circuit) → spark at breakdown voltage → oscillatory discharge → radiates EM waves (≈100 MHz).
Receiver: separate loop + spark gap; sparks appear only when receiver's natural frequency matches transmitter's (resonance).

c = 1/√(μ₀ε₀) = 3×10⁸ m/s in vacuum; E/B = c at every instant; E, B in phase, both ⊥ to each other and to propagation direction (transverse).
E = E_m sin(kx−ωt), B = B_m sin(kx−ωt); ω=2πf, k=2π/λ.
Frequency unchanged across media (only speed & λ change). Source: accelerating/oscillating charge. Obey superposition. E is the 'light vector' (dominant for optical effects).

Plane wave along x: E, B depend only on x,t. Gauss's law on a small box (no enclosed charge) ⟹ flux through y,z-faces cancels in pairs.
Remaining x-faces ⟹ Eₓ same on both ⟹ static, can't propagate ⟹ Eₓ=0. Same argument ⟹ Bₓ=0. Both fields confined to the plane ⊥ propagation ⟹ transverse.

S = (1/μ₀)(E×B), points along propagation. I_av = E_mB_m/(2μ₀) = ε₀cE_m²/2 = cB_m²/(2μ₀).
u_E = ½ε₀E² = u_B = B²/2μ₀ at every instant — energy split equally between E and B. u_av(total) = ½ε₀E_m² (each field's average share = ¼ε₀E_m²).

Perfectly absorbing surface: P = S/c. Perfectly reflecting surface: P = 2S/c (momentum reversed, not just absorbed).

By increasing λ: γ-rays (10⁻¹⁴–10⁻¹⁰m) → X-rays (6×10⁻¹²–10⁻⁹m) → UV (6×10⁻¹⁰–3.8×10⁻⁷m) → visible (3.8×10⁻⁷–7.8×10⁻⁷m) → IR (7.8×10⁻⁷–10⁻³m) → microwaves (10⁻³–0.3m) → radio (0.3m–km).
c = fλ always; higher f ⟹ higher photon energy E=hf ⟹ γ/X-rays ionising & dangerous, radio waves harmless.
Visible sub-bands (short→long λ): violet, blue, green, yellow, orange, red.
Radio sub-bands (short→long λ, high→low f): SHF, UHF, VHF, HF, MF, LF, VLF.

γ-rays: radioactive decay (Becquerel/Curie) — nuclear structure studies, medical treatment.
X-rays: high-energy electrons hitting heavy targets (Röntgen) — medical diagnosis, crystal structure, industrial radiography.
UV: ionised gases, sparks, UV lamps (Ritter) — detect adulteration, sterilisation (kills bacteria), signature verification.
Visible: atomic electron transitions, discharge tubes, incandescence (Newton).
IR: electron rearrangement, molecular vibration/rotation, hot bodies (Herschel) — industry, medicine, astronomy, greenhouse effect.
Microwaves: klystron tubes (Hertz) — radar, satellite/telecommunication, molecular structure.
Radio waves: oscillating circuits (Marconi) — radio/TV broadcast.

Ozone layer (stratosphere) absorbs solar UV — protects life from its harmful effects.
Ozone + atmosphere also trap outgoing IR — keeps Earth's surface warm (greenhouse effect). Without this trapping, surface temperature would be much lower.

EM waves transport energy and momentum, but never charge — a very common 'select the false statement' trap.
Frequency never changes when an EM wave crosses into a new medium — only speed and wavelength do; don't apply v=fλ changes to frequency.
Displacement current isn't a flow of charge at all — it's defined purely from the changing electric flux, ε₀dΦ_E/dt, even though it produces a real magnetic field just like a conduction current would.
Energy density of E and B fields are individually equal at every instant (u_E=u_B) — a wave is never 'mostly electric' or 'mostly magnetic'.
Reflecting surface gets exactly double the radiation pressure of an absorbing one for the same intensity — don't forget the factor of 2.
Order of the spectrum by increasing wavelength is γ→X→UV→visible→IR→microwave→radio; many MCQs test this ordering directly or via 'which has the highest frequency/energy' framing.

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