The Poynting vector gives the direction and density of electromagnetic power flow:
S = (1/μ₀) E × B [W/m²]
The capacitor and wire scenarios are axisymmetric, so instead of a flattened 3D camera view this renders the true (r, z) half-plane cross-section: the vertical axis is the axial coordinate z, the horizontal axis is the radial distance r from the axis. In this slice, E (axial) is drawn as vertical arrows, B is perpendicular to the slice (azimuthal) so it is drawn the way textbooks draw it — ⊕ for out-of-page, ⊗ for into-page — and S = E×B works out to be purely radial, drawn as horizontal arrows pointing in or out of the axis exactly where the field equations say energy is flowing.
Charging capacitor — the field between the plates grows, so by the Ampère–Maxwell law (displacement current) a circular (azimuthal) B field appears:
∮B·dl = μ₀ε₀ dΦE/dt
Crossing the axial E with the azimuthal B gives S pointing radially inward in the cross-section — the stored field energy visibly streams in from the surrounding space, not along a wire.
Current-carrying wire — the same cross-product trick applied to a resistor is the classic surprise of electrodynamics: the circular B field around the wire (Ampère's law) crossed with the small axial E field (the resistive voltage drop) gives S pointing into the wire's surface. The Joule heat I²R dissipated in the resistor arrives through the field around it, not by flowing down the copper.
Propagating wave — this scenario has no radial structure at all (E, B and S depend only on z and t), so instead of the (r,z) slice it is drawn as a genuine z–t strip chart: E(z) and B(z) plotted as in-plane sinusoids offset above and below the axis, with S(z) = E₀²sin²(kz−ωt) shaded underneath, showing it never goes negative — the energy pulse always marches forward.
- Scenario buttons — switch between the three canonical field geometries.
- Field strength — scales the driving E₀ amplitude in every scenario.
- Animation speed — scales how fast the fields evolve in time.
- Grid density — how many radial/axial sample points the field is drawn at.
All quantities are shown in normalized units (μ₀ = ε₀ = c = 1) so the geometry of the flow, not the SI magnitude, is the point.