Poynting Vector 2D: Field Cross-Section & Energy Flow

Electromagnetic energy does not travel where intuition expects it to. This 2D simulator renders the Poynting vector S = (1/μ₀)E×B as a true axisymmetric cross-section: a charging parallel-plate capacitor and a current-carrying resistor are both drawn in the (r, z) half-plane, with the perpendicular B field shown using the classic ⊕/⊗ dot-and-cross notation instead of a flattened 3D arrow field. A propagating plane wave, which has no radial structure at all, switches to a z–t strip-chart view of the same E, B and S formulas. Every frame recomputes E, B and S from the real field equations — Ampère–Maxwell's law for the displacement current, Ampère's law for the wire, and the wave equation for the propagating fields — with numeric readouts at a fixed probe point so you can see cause and effect in real numbers, not just arrows.