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
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.
More from Electricity & Magnetism
Other simulators in this category — or see all 42.
DC Motor & Generator
Coil in B: motor V = IR + kω, generator E = kω into a load — same k, two modes.
Gradient-B Drift
B_z(x,y) with weak gradient; orbit from q(E+v×B) at local B — gyration + drift.
Magnetic Mirror (Bottle)
Axial B(z) pinch; μ adiabatic invariant, v∥ from −μ ∂B/∂z — Van Allen / mirror sketch.
Dipole Radiation Pattern
Time-averaged power ∝ sin² θ in the plane containing the dipole axis (far-field cartoon).
Bode Diagram (RC low-pass)
|H| in dB and phase vs log f; f_c = 1/(2πRC) marked — first-order pole intuition.
Skin Effect
δ = √(2/(ωμσ)): AC current density vs depth in a conductor (1D exponential).