Plane Wave — Impedance, Fields & Power
For a uniform plane wave, the electric and magnetic fields are locked together by the intrinsic impedance of the medium (377 Ω in free space). This tool gives that wave impedance and converts between the E-field, the H-field and the power density (Poynting vector). Enter the medium (relative permittivity and permeability) and any one field quantity.
Equations & Parameters ▸
\(\eta = \sqrt{\dfrac{\mu_0\mu_r}{\varepsilon_0\varepsilon_r}} = \eta_0\sqrt{\dfrac{\mu_r}{\varepsilon_r}},\quad \eta_0\approx 376.73\ \Omega\)
\(S = \dfrac{E^2}{\eta} = H^2\eta = E\,H,\qquad H = \dfrac{E}{\eta},\qquad v_p = \dfrac{c}{\sqrt{\varepsilon_r\mu_r}}\)
\(S = \dfrac{E^2}{\eta} = H^2\eta = E\,H,\qquad H = \dfrac{E}{\eta},\qquad v_p = \dfrac{c}{\sqrt{\varepsilon_r\mu_r}}\)
| εr, µr | Relative permittivity and permeability of the medium (1 for free space). |
| η | Intrinsic (wave) impedance, ratio of E to H. |
| E, H | Electric field (V/m) and magnetic field (A/m), RMS. |
| S | Power density / time-averaged Poynting vector (W/m²). |
| f | Frequency (optional), for phase velocity and wavelength in the medium. |
References: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Addison-Wesley, 1989. · C. A. Balanis, Advanced Engineering Electromagnetics, 2nd ed., Wiley, 2012.
Inputs
1 = free space
1 = non-magnetic
Pick one to enter
RMS
MHz
For λ, vₚResults
Wave & fields
Wave impedance η—
E-field—
H-field—
Power density S—
Propagation
Phase velocity—
Wavelength—
Diagram