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.

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.

Other simulators in this category — or see all 56.

View category →

NewSchool

DC Motor & Generator

Coil in B: motor V = IR + kω, generator E = kω into a load — same k, two modes.

Launch Simulator

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Gradient-B Drift

B_z(x,y) with weak gradient; orbit from q(E+v×B) at local B — gyration + drift.

Launch Simulator

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Magnetic Mirror (Bottle)

Axial B(z) pinch; μ adiabatic invariant, v∥ from −μ ∂B/∂z — Van Allen / mirror sketch.

Launch Simulator

NewSchool

Dipole Radiation Pattern

Time-averaged power ∝ sin² θ in the plane containing the dipole axis (far-field cartoon).

Launch Simulator

NewSchool

Half-Wave Dipole Antenna Pattern

Far-field E-plane pattern of a thin λ/2 wire: power ∝ [cos(½π cos θ)/sin θ]², directivity D ≈ 1.64 (~2.15 dBi); optional sin² θ overlay vs a short dipole.

Launch Simulator

NewSchool

Rotating Dipole E-field

±q orbit in the plane: Coulomb superposition arrows — near-field sketch before full radiation.

Launch Simulator

Plane EM Wave (vacuum)

Live graphs

How it works

Key equations

Frequently asked questions

More from Electricity & Magnetism

DC Motor & Generator

Gradient-B Drift

Magnetic Mirror (Bottle)

Dipole Radiation Pattern

Half-Wave Dipole Antenna Pattern

Rotating Dipole E-field

Plane EM Wave (vacuum)

Live graphs

How it works

Key equations

Frequently asked questions