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Openai/68713b82-90e0-8006-8973-ea152bf13a2c
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===== Letβs model the total capacitance and charge storage. ===== ====== Letβs treat the gold shell like a spherical conductor, and the internal gold wires as extensions. ====== A sphere in vacuum: C=4ΟΞ΅0RC = 4 \pi \varepsilon_0 RC=4ΟΞ΅0βR Letβs say R = 1 cm = 0.01 m C=4Οβ 8.85Γ10β12β 0.01=1.11Γ10β12βFC = 4 \pi \cdot 8.85 \times 10^{-12} \cdot 0.01 = 1.11 \times 10^{-12} \, \text{F}C=4Οβ 8.85Γ10β12β 0.01=1.11Γ10β12F But with dense internal wiring, surface area goes way up. Letβs assume 10,000x the surface area: Ceffβ104β C=1.1Γ10β8βFC_{\text{eff}} \approx 10^4 \cdot C = 1.1 \times 10^{-8} \, \text{F}Ceffββ104β C=1.1Γ10β8F ====== Say over time you trap 101210^{12}1012 electrons inside: ====== Q=nβ e=1012β 1.6Γ10β19=1.6Γ10β7βCQ = n \cdot e = 10^{12} \cdot 1.6 \times 10^{-19} = 1.6 \times 10^{-7} \, CQ=nβ e=1012β 1.6Γ10β19=1.6Γ10β7C ====== V=QC=1.6Γ10β71.1Γ10β8β14.5βVV = \frac{Q}{C} = \frac{1.6 \times 10^{-7}}{1.1 \times 10^{-8}} \approx 14.5 \, \text{V}V=CQβ=1.1Γ10β81.6Γ10β7ββ14.5V ====== Now if you keep accumulating more electrons: * At 101310^{13}1013 electrons β 145 V. * At 101410^{14}1014 electrons β 1,450 V. * This is very feasible in vacuum with strong internal capacity. So over time β especially with: * Vibration-induced electron motion (through internal mesh), * Photon input energizing electrons, * Electron retention inside, β The system charges itself gradually without air breakdown, and holds potentially kilovolt-range voltages.
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