Poynting Vector⚠ unverified
Physics / Electromagnetics · Compute the magnitude of the Poynting vector
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| E | E | V/m | 1.0 | Electric field magnitude |
| H | H | A/m | 1.0 | Magnetic field strength |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | S | W/m**2 | Power flux density, in watts per square metre (W/m**2) |
The science & history
Understanding the Parameters
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$E$, $H$ — in a plane wave in free space, $E/H = \eta_0 \approx 377\,\Omega$ (Wave Impedance), so $S = E^{2}/\eta_0 = \eta_0 H^{2}$.
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$S$ — energy per unit time per unit area carried by the field; direction $\mathbf{E}\times\mathbf{H}$.
Derivation (Approaching a Proof)
From Poynting’s theorem (energy conservation in Maxwell’s equations), the energy flux density is $\mathbf{S} = \mathbf{E}\times\mathbf{H}$ (SI). For $|\mathbf{E}\times\mathbf{H}| = EH\sin\phi$ with $\phi = 90^{\circ}$, $S = EH$.
History
John Henry Poynting (1884) identified $\mathbf{E}\times\mathbf{H}$ as the EM energy-flow vector; it is standard in antenna and RF power analysis.
Related Concepts: Wave Impedance, Radiation Resistance, Energy Electric Field, Energy Magnetic Field
Notes: Registry calculator poynting-vector (unverified). Scalar $EH$ form (perpendicular fields).