Plane EM Wave (vacuum)

A uniform plane wave in vacuum is drawn with E along x̂ and B along ŷ, propagating along +ẑ, so E ⊥ B and both are perpendicular to k. Fields use the same sinusoidal phase kz − ωt with ω = ck; in the sim c ≡ 1, so ω = k. ⊗/⊙ glyphs suggest B into/out of the x–z plane; Poynting density is sketched along z.

Who it's for: Introductory E&M after Maxwell waves; contrasts with static Coulomb fields and dipole radiation patterns.

Key terms

  • plane wave
  • Poynting vector
  • transverse electromagnetic
  • wave speed
  • phase velocity

Live graphs

How it works

A transverse electromagnetic plane wave: E is along x̂, B along ŷ, and both are perpendicular to the propagation direction ẑ. Energy flow S ∝ E × B points along +z. This is a traveling field pattern, not the static field of a single charge.

Key equations

E = E₀ sin(kz − ωt) x̂ ,   B = (E₀/c) sin(kz − ωt) ŷ
k = 2π/λ ,   ω = ck ,   c = 1 (sim)
S = (1/μ₀) E × B ∥ ẑ

Frequently asked questions

Why are E and B in phase?
In a simple non-dispersive vacuum plane wave, the Maxwell relations link E and B amplitudes with |B| = |E|/c and the same harmonic phase for sinusoidal solutions.
Is this the same as the dipole radiation simulator?
No: the dipole page shows an angular power pattern in the far field. Here the fields are idealized as uniform in x and y on each z slice — a traveling TEM plane wave.