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Maxwell EM Waves

Electromagnetic wave: E ⊥ B ⊥ k̂ — propagating at speed c

Electromagnetism Polarization Maxwell Equations Light

Polarization:

Frequency 1.0 THz Amplitude E 1.0 Phase δ 0°

λ = 1.00 µm f = 1.0 THz c = 3×10⁸ m/s |S| = — W/m² Polarization: Linear X

📡 Maxwell's Electromagnetic Waves

From Maxwell's four equations, any change in the electric field E generates a magnetic field B, and vice versa. Together they sustain a self-propagating transverse wave in vacuum at speed c = 1/√(ε₀μ₀) ≈ 3×10⁸ m/s.

The wave equations are: ∂²E/∂t² = c²∇²E ∂²B/∂t² = c²∇²B

A plane wave propagating along ẑ: E = E₀ cos(kz − ωt + δ) B = (1/c) ẑ × E

Polarization describes the orientation of E. Linear: fixed plane. Circular: E rotates in a circle as the wave passes (R = right-hand, L = left-hand). Elliptical: phase difference δ ≠ 0° or 90° between Ex and Ey components.

Poynting vector S = (1/μ₀) E × B gives the energy flux density (W/m²), pointing in the direction of wave propagation.