Circle-in-Square — Coil (Algebra) & Field (Geometry)

The square coil represents algebraic structure (quantized turns, fixed boundaries). The circular flow shows the geometric field that arises from current. Adjust the current and overlays to see how equations frame motion and motion gives equations meaning.

Visualization

Square = algebra Circle = geometry
Field tracers Square coil Field arrows
Tip: higher current → stronger, tighter circular motion. Pause to inspect arrows precisely.

Controls & Theory

1.00
240
0.965
Radius scale:
1/r
Arrow density:
coarse→fine with I
Show equations (algebra framing geometry)
Maxwell (curl form):
∇ × E = −∂B/∂t    ,    ∇ × B = μ₀ε₀ ∂E/∂t

Loop intuition (centered, illustrative):
|B(r)| ≈ k · I / r    with   k ≈ μ₀/2π (heuristic for circular flow)

Tangential direction êθ gives geometry; magnitude |B| gives algebra.