Companion to the EMFT hub. Pick a section, vary the inputs, see exactly which physics quantity is computed from which formula. All values live-updated from the engine.
Set Ex and Ey amplitudes and the phase δ between them. The tip of E(t) traces an ellipse; the engine classifies it and gives axial ratio + tilt + handedness.
90°
② Phase & group velocity (wave packet)
u(z, t) = cos(2π Δf (t − z/vg)) · cos(2π f0 (t − z/vp)). Carrier (fast) × envelope (slow). In a non-dispersive medium, vp = vg. Set them apart to see the envelope slip behind the carrier.
2.0 ns
③ Reflection & refraction (ray diagram)
Two non-magnetic media, an interface at the horizontal line. Compute the reflected and refracted rays + Fresnel coefficients; show what fraction of the incident power transmits.
30.0°
④ Skin depth δ = √(2 / (ω μ σ))
The skin depth shrinks as 1/√f. Pick a conductor and see the curve. At the marker frequency, the field amplitude drops by 1/e every δ metres.