Top: a plane wave traveling in +z with E in x, H in y, propagation k in z. Drag the time and E-H phase sliders to see how the two components move relative to each other. Bottom: a static-field modeler (point charge, dipole, infinite wire) — click anywhere to probe the field value.
Ex(z, t) = E0 cos(ωt − kz). Hy(z, t) = (E0/η) cos(ωt − kz − φEH). S = E × H in +z direction.
Static field
Click anywhere on the field plot to read off the field value at that point.
Vector calculus playground
Central-difference derivatives with h = 0.05. The colored background is the chosen operator (red = +, blue = −); arrows are F.
Custom field + line integral
Type expressions using x, y, z (for the field) and t (for the curve). Then click ∫ F·dr. Nerdamer evaluates symbolically; the integral is computed by trapezoidal rule with N = 401 samples.
① Plane wave Ex(z) and Hy(z) at current time
E and H are 90° apart in space (E in x, H in y, k in z). They share a phase (or differ by φEH you set).
Maxwell's equations (free space, plane wave)
∇ × E = −∂B/∂t ⟹ ∂Ex/∂z = −μ₀ ∂Hy/∂t
② Time-domain oscillogram at one z (Ex(t) and Hy(t))
At a fixed z, watch how the E and H sinusoids move relative to each other as you change φEH.
Ex(z,t) Hy(z,t) Poynting Sz = Ex·Hy
③ Static field modeler (vector field plot)
Click on the plot to probe the field at any (x, y).
④ Vector calculus operators ∇·F, ∇×F, ∇f
Pick a 2-D vector field, see divergence (red + / blue −) and curl (background tint) computed at every point via central-difference derivatives. All four Maxwell equations in free space reduce to div E = 0, div B = 0, curl E = −∂B/∂t, curl B = μ₀ε₀ ∂E/∂t.
Maxwell on the plane wave E = E₀ cos(ωt − kz) x̂, B = (E₀/c) cos(ωt − kz) ŷ
⑤ Line integral ∫C F · dr (user-defined F and curve)
Result of the most recent line integral (default: F = (−y, x, 0) around the unit circle; the answer is 2π by Green's theorem since curl F = 2 ẑ).
⑥ Boundary conditions (Fresnel equations at an interface)
Interface at z = 0 between two non-magnetic media. Pick the materials and the angle of incidence; get reflection / transmission amplitudes, power coefficients, Brewster angle (TM), and critical angle.
30.0°
⑦ Poynting vector S = E × H & time-average <S>
Type the 6 field components (or use the plane-wave preset). Instantaneous S and |S| are shown, plus the time-average for a sinusoidal plane wave.