EM Wave Propagation
E ⟂ B ⟂ direction. Sinusoidal transverse waves traveling at c = 3×10⁸ m/s.
Key Notes
An electromagnetic wave is a self-propagating, transverse oscillation of coupled electric (E) and magnetic (B) fields.
E ⊥ B ⊥ direction of propagation. E × B always points along the propagation direction (Poynting vector).
All EM waves travel at the SAME speed in vacuum: c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s — independent of wavelength, frequency, or amplitude.
E and B are in phase: when E peaks, B peaks at the same point and time.
Ratio of field amplitudes: E₀/B₀ = c. So B is much smaller numerically than E (in SI units), but they carry equal energy density.
In a medium of refractive index n: v = c/n. Frequency f stays fixed (set by the source); wavelength shrinks to λ_medium = λ_vac/n.
EM waves DO NOT need a medium — Maxwell's prediction was confirmed by Hertz's 1887 experiment using spark-gap oscillators.
EM waves carry both energy (Poynting vector) and momentum (radiation pressure).
Formulas
Speed of light in vacuum
Derived directly from Maxwell's equations — no fitting parameters.
Plane-wave fields
Both transverse, in phase, perpendicular to each other and to x (propagation).
Wave-number / frequency
Standard wave-equation relations.
Amplitude ratio
Direct consequence of Faraday's law applied to a plane wave.
Energy density
Electric and magnetic energy densities are equal — total = ε₀E²(t).
Speed in a medium
n = √(μ_r ε_r) ≈ √ε_r for non-magnetic dielectrics.
Important Points
EM waves are TRANSVERSE — that's why they can be polarised. Sound waves (longitudinal) cannot be polarised.
In SI units, E₀/B₀ = c, so for E₀ = 300 V/m, B₀ = 10⁻⁶ T = 1 μT. Magnitudes look unequal but energy contribution is equal.
Frequency is invariant when an EM wave changes medium (source determines it). Wavelength and speed change together so that v = fλ is consistent.
EM waves in vacuum have no charge, no medium — they are pure field disturbances. They were the first 'evidence' of fields being physically real.
Polarisation refers to the direction of E (by convention). The direction of B follows from E × B = propagation direction.
Light slows in a denser medium NOT because photons get tired — it's collective interference with induced atomic dipoles. Group velocity < c, individual photons still travel at c.
EM Wave Propagation notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.