Maxwell's EM Wave Propagation

True 3D vector field visualization of an electromagnetic wave derived from Maxwell's equations. Displays mutually perpendicular transverse Electric field E vectors (Cyan), Magnetic field B vectors (Rose), and the longitudinal Poynting energy propagation vector S = 1/μ₀(E × B).

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Wave Frequency (ω) 1.2

Angular frequency of the electromagnetic oscillation

Field Amplitude (E₀) 1

Peak electric and magnetic field amplitude

Mathematical Formulation

65 chars medium

Analytical Equation

\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}, \quad \mathbf{S} = \frac{1}{\mu_0}(\mathbf{E} \times \mathbf{B})

Compact Formula

E(z,t) = E_0 sin(kz - wt) j_hat; B(z,t) = B_0 sin(kz - wt) k_hat;

Renderer Logic

// Transverse EM Wave Fields
const eField = Math.sin(xPos * k - t * 3.5) * (70 * waveAmp);
const bField = Math.sin(xPos * k - t * 3.5) * (70 * waveAmp);
// Poynting vector S along propagation axis

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#electrodynamics #maxwell-equations #em-wave #poynting-vector #physics-study #vector-fields

Author: Electrodynamics Core Target: 60 FPS

Maxwell's EM Wave Propagation

Live Parameters

Mathematical Formulation

Mathematical Tags

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