An inductor energy source scan holds inductance fixed at 2 henries and varies the flux source across three rows: flux 2, 4, and 6 webers give inductor energies 1, 4, and 9 joules exactly for the stated toy energy formula. Chapter two's inductor-energy lesson only ever cited one fixed flux source; chapter six later scanned the same quadratic shape for capacitor energy but never for the flux-based term. Real inductor energy storage also has parasitic resistance and finite quality factor that this toy model does not capture.
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.
EL=2LΦ2=44=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.
EL=2LΦ2=416=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.
EL=2LΦ2=436=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.