Fields & Forces
Electromagnetism is the second of the four fundamental forces — and the one that governs almost everything in everyday engineering. Unlike gravity, electric and magnetic fields can be visualised directly: field lines, equipotential surfaces, flux density, and induced currents all have intuitive geometric interpretations. Our simulations exploit this.
∇·E = ρ/ε₀ (Gauss — electric)
∇·B = 0 (Gauss — magnetic, no
monopoles)
∇×E = −∂B/∂t (Faraday)
∇×B = μ₀J + μ₀ε₀ ∂E/∂t (Ampère-Maxwell)
These four equations completely describe all classical
electromagnetic phenomena. The ∂E/∂t term (Maxwell's correction) is
what predicts electromagnetic waves.
Waves & Propagation
Optics & Quantum Effects
Why FDTD for EM waves? The Yee grid interleaves electric and magnetic field components in space and time — E and B are staggered by half a cell. This gives second-order accuracy in both space and time with no matrix inversion, making it ideal for real-time browser simulation. The key constraint is the CFL stability condition: c·Δt < Δx/√2.
Algorithms at a Glance
Suggested Learning Paths
- Electric Field & Potential — Coulomb's law
- Faraday Induction — generators and transformers
- RLC Resonance — tuned circuits
- Double-Slit — wave-particle duality
- Mirrors & Lenses — geometrical optics
- EM Wave Propagation (FDTD) — Maxwell in discrete form
- Antenna Radiation Pattern — far-field analysis
- AM & FM Modulation — analogue communications
- Digital Signal Filter — DSP theory and z-plane design
- Magnetic Field Lines — Biot-Savart and solenoids