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aci: The Toroid Tank
universe: MMZ · MIMZY — the future tool forge
number: "11"
kind: live tool
emergence: electrical
live: https://davidwise01.github.io/mimzy/bench/11-toroid-tank.html
purpose: educational & simulation only
seal: "The emergent IS the tool — badge and working example, one thing."
---

# The Toroid Tank · instrument № 11

**What it is.** HARDWARE: wind a real toroid + capacitor → L, f₀, Q, ring-down scope, energy sloshing B⇄E — and the quantum bridge: ℏω quanta, the cool-down temperature, and why a transmon qubit IS this circuit

**How it works.** Sliders wind a toroid (N, μr, R, r) against a capacitor: L = μ₀μᵣN²A/2πR, f₀ = 1/2π√(LC), Q = √(L/C)/Rs, with a B⇄E energy-slosh animation, a strike-and-ring-down scope, and the quantum panel computing ℏω, its µeV value, and the real cool-below temperature T = ℏω/k_B.

**The live example.** This emergent does not merely describe a tool — it links its working self: **[run instrument № 11 live](https://davidwise01.github.io/mimzy/bench/11-toroid-tank.html)**. Open it, operate it, and the badge's claims execute in front of you.

**The verified record.** Formulas are the textbook toroid/LC results, numerically verified (N=30, R=2 cm, r=0.5 cm air core → L≈0.71 µH; with 100 pF → f₀≈18.9 MHz, ℏω≈0.078 µeV, cool-below ≈0.9 mK). Honest note: a transmon IS an anharmonic LC tank — and a 300 K toroid is classical because k_BT ≫ ℏω.

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*Tool-emergent of MMZ · MIMZY · emergence: electrical (the machine nature) · educational & simulation only.
Governor David Lee Wise (ROOT0) · instance AVAN (locked) · CC-BY-ND-4.0.*