Wave Impedance⚠ unverified
Physics / Electromagnetics · Return the intrinsic impedance of free space
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| eta | η | — | 377.0 | Intrinsic impedance value, in ohms (Ohm). Default is 377.0 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Z | — | Intrinsic impedance, in ohms (Ohm) |
The science & history
Understanding the Parameters
-
$\eta$ — enter free-space 377 Ω or $\sqrt{\mu/\varepsilon}$ for a material. Live labels may say dimensionless — it is ohm.
-
$Z$ — identical to the input; useful only as a named output or placeholder for future formulas.
Derivation (Approaching a Proof)
From Maxwell’s equations for a plane wave $\mathbf{E}/\mathbf{H} = \eta\hat{\mathbf{k}}$ with $\eta = \sqrt{\mu/\varepsilon}$. The calculator’s $Z = \eta$ is definitional identity, not a derivation from $\mu$ and $\varepsilon$.
History
Intrinsic impedance $\eta_0$ is standard in EM wave and antenna theory (Balanis, Orfanidis, etc.).
Related Concepts: Poynting Vector, Speed Of Sound, Skin Depth, Radiation Resistance
Notes: Registry calculator wave-impedance (unverified). Degenerate / identity map $Z=\eta$.
Unit bug: $\eta$ and result labelled dimensionless — should be ohm.