Inductor Energy Source Three-Row Scan - Superconducting Qubits: LC Energy, Toy Josephson Coupling, and Readout Step by Step

Three checked inductor-energy rows make the flux-square relation scanable, mirroring chapter six's capacitor-energy scan for the flux-based term. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Flux row 1 gives inductor energy

Chapter two's inductor-energy lesson only ever cited one fixed flux source. Here flux 2 with inductance 2 produces a checked inductor-energy row.

E_L=\frac{\Phi^{2}}{2L}=\frac{4}{4}=1

Flux row 2 gives inductor energy

Chapter two's inductor-energy lesson only ever cited one fixed flux source. Here flux 4 with inductance 2 produces a checked inductor-energy row.

E_L=\frac{\Phi^{2}}{2L}=\frac{16}{4}=4

Flux row 3 gives inductor energy

Chapter two's inductor-energy lesson only ever cited one fixed flux source. Here flux 6 with inductance 2 produces a checked inductor-energy row.

E_L=\frac{\Phi^{2}}{2L}=\frac{36}{4}=9

Flux changes the inductor energy quadratically, just as charge did for the capacitor

The inductance stays fixed. Each row squares its own flux source before dividing by the same denominator -- the same quadratic shape chapter six already scanned for capacitor energy, now scanned for the flux-based term instead.

\begin{array}{c|c|c}\Phi&\Phi\Phi&E_L\\2&4&1\\4&16&4\\6&36&9\\\end{array}