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Home/Electricity & Magnetism/Plane EM Wave (vacuum)

Plane EM Wave (vacuum)

E ⊥ B ⊥ k: sin(kz−ωt) fields, Poynting along z; ω = ck (c = 1).

Wave

2.2
52 px
3.2
36

In vacuum, E and B oscillate in phase with |B| = |E|/c. Here c ≡ 1 in normalized units, so ω = k and the wavefront moves one wavelength per time unit 2π/ω.

Shortcuts

  • •Adjust wavelength to see spatial period
  • •E and B stay in phase in vacuum (c = 1 here)

Measured values

|B|/|E| (1/c)1.000
phase @ mid z (rad)0.000

Live graphs

About this model

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

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.