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Physics 3% exam weight

EM Waves

Part of the NEET UG study roadmap. Physics topic phy-022 of Physics.

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EM Waves

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your NEET attempt.

Electromagnetic (EM) waves are transverse waves produced by accelerating charges, made of mutually perpendicular, in-phase electric (E) and magnetic (B) fields that travel in vacuum at c = 3 × 10⁸ m/s. The propagation direction is given by the Poynting vector S = (1/μ₀)(E × B).

  • Speed in vacuum: c = 1/√(μ₀ε₀), where μ₀ = 4π × 10⁻⁷ T·m/A and ε₀ = 8.854 × 10⁻¹² C²/(N·m²).
  • Amplitude relation: E₀ = cB₀, so B₀ is far smaller than E₀ in SI units.
  • Spectrum order (↑λ, ↓ν): γ-rays → X-rays → UV → visible → IR → microwaves → radio.

NEET pointer: Expect one conceptual MCQ — usually spectrum ordering, wavelength range of visible light (400–750 nm), or the displacement current term.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Origin and Maxwell’s prediction

A stationary charge produces only a static E-field; a steady current produces only a static B-field. Only an accelerating charge generates a self-sustaining disturbance where a changing E-field produces a B-field and vice versa. Maxwell captured this reciprocity through the displacement current term (ε₀ dΦ_E/dt) added to Ampère’s law — without it, his equations would forbid wave solutions.

Structure of a plane EM wave

In a plane wave travelling along +x, the fields take the form: E = E₀ sin(kx − ωt) ŷ, B = B₀ sin(kx − ωt) ẑ.

The three vectors E, B and the propagation direction form a right-handed system, so the direction is E × B, not E · B. E and B oscillate in phase — they reach zero and maximum together.

Energy and intensity

The wave carries energy density u = ½ε₀E² + B²/(2μ₀). The average intensity (energy flux) is I = ½ ε₀ c E₀², and the momentum delivered on absorption is p = U/c.

The electromagnetic spectrum

RegionApprox. λTypical source / use
γ-rays< 10⁻¹² mRadioactive nuclei
X-rays10⁻¹⁰–10⁻⁸ mMedical imaging
UV10⁻⁸–4 × 10⁻⁷ mSun, sterilisation
Visible4 × 10⁻⁷–7.5 × 10⁻⁷ mOptics, human vision
Infrared7.5 × 10⁻⁷–10⁻³ mThermal radiation
Microwaves10⁻³–10⁻¹ mRadar, ovens
Radio> 10⁻¹ mCommunication

Exam trap: “A steady current radiates EM waves.” False — acceleration is essential. Also, microwaves sit between IR and radio, never near UV.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge cases and subtleties

In a dielectric medium the wave slows to v = c/n, where n is the refractive index, while the frequency stays fixed — wavelength shrinks to λ/n. The in-phase E–B relation still holds, but the amplitude ratio becomes E₀ = vB₀, not cB₀. In a conductor the fields penetrate only to the skin depth δ = √(2/(ωμσ)), beyond which the wave is exponentially attenuated.

Connection to modern physics

Quantum-mechanically, an EM wave of frequency ν is a stream of photons with energy E = hν and momentum p = h/λ. This duality is why a single Young-style double-slit experiment cannot decide whether light is a wave or a particle — both frameworks coexist. The Compton shift Δλ = (h/mc)(1 − cos θ) for scattered X-rays is direct evidence of photon momentum.

Common mistakes

  1. Writing E · B for the propagation direction — propagation is E × B.
  2. Saying radio waves have higher frequency than X-rays — the order is reversed.
  3. Believing Maxwell’s equations are only for static fields — the displacement current is what makes the wave equation ∂²E/∂x² = μ₀ε₀ ∂²E/∂t² fall out.
  4. Confusing phase velocity with signal velocity in a dispersive medium.

Worked micro-example

A radio antenna broadcasts at 100 MHz. The wavelength is λ = c/ν = (3 × 10⁸)/(10⁸) = 3 m, placing it firmly in the VHF band. If the radiated E-field amplitude is 0.1 V/m, then B₀ = E₀/c = (0.1)/(3 × 10⁸) ≈ 3.33 × 10⁻¹⁰ T.

Practice prompts

  1. Show, starting from Faraday’s and Ampère–Maxwell laws, that E(x, t) = E₀ sin(kx − ωt) satisfies a wave equation with speed 1/√(μ₀ε₀).
  2. Arrange the following in order of decreasing photon energy: microwaves, green light, X-rays, UV. Justify using E = hν.

NEET strategy: This chapter rarely crosses one question, so spend ~30 minutes mastering spectrum ordering, the c = 1/√(μ₀ε₀) relation, and the displacement current idea. Skip lengthy derivations — focus on the five boxed formulas and the spectrum table.

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