Electromagnetic Waves

Plane Wave Propagation

Electric Field (E)
Magnetic Field (B)
Propagation (k)
WebGPU Context Active

Parameters

Amplitude (E₀)2.0 V/m
Wavelength (λ)4.0 m
Wave Properties
Wave Speed (c)
2.998e8 m/s
Frequency (f)
74.9 MHz
Wavenumber (k)
1.57 rad/m
B₀ Amplitude
6.67 nT
Intensity ⟨S⟩
5.3088 mW/m²
Phase at z=0
0.0°
Field Vector at z=0
Ex: 2.00 V/m
By: 2.00 normalized
Real-Time Equations
E⃗(0,t)=2.00cos⁡(0.00) x^\vec{E}(0,t) = 2.00 \cos(0.00) \, \hat{x}
⟨S⟩=12cε0E02=5.3088 mW/m2\langle S \rangle = \frac{1}{2} c \varepsilon_0 E_0^2 = 5.3088\,\text{mW/m}^2
Live Telemetry at z=0

Awaiting Telemetry

Governing Dynamics

Electromagnetic waves consist of coupled oscillating electric (E) and magnetic (B) fields that propagate through space. For a plane wave traveling in the z^\hat{z} direction:

E⃗(z,t)=E⃗0cos⁡(kz−ωt+ϕ)\vec{E}(z,t) = \vec{E}_0 \cos(kz - \omega t + \phi)B⃗(z,t)=1cz^×E⃗(z,t)\vec{B}(z,t) = \frac{1}{c} \hat{z} \times \vec{E}(z,t)

The fields are mutually orthogonal and orthogonal to the direction of propagation:

E⃗⋅B⃗=0\vec{E} \cdot \vec{B} = 0E0=cB0E_0 = c B_0

Wave speed, wavenumber, and angular frequency are related by:

c=1μ0ε0c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}k=2πλ,ω=2πf=ckk = \frac{2\pi}{\lambda}, \quad \omega = 2\pi f = ck