Reading the thread on "Exotic Propulsion", this came to mind: It's a variation on the putting two caps with different charges in parallel. I'm sure I'm missing something simple here, but I've got a brain block.
Let's start with a 20 - 365 pF variable capacitor (no leakage) and a 100 volt battery:
Set the capacitor to 20 pF and connect it to the battery.
Q = C*V = 20p*100 = 2000 pC
W = 0.5*C*V² = 0.5*20p*100² = 100,000 pJ
Now disconnect the battery and set the variable cap to 365 pF
V = Q/C = 2000pC/365p = 5.48 volts
W = 0.5*C*V² = 0.5*365p*5.48² = 5481 pJ
Where did the energy go? Did it radiate into space?
Now lets do it the other way around. Charge the 365 pF cap to 100 volts:
Set the capacitor to 365pF and connect it to the battery.
Q = C*V = 365p*100 = 36,500 pC
W = 0.5*C*V² = 0.5*365p*100² = 1,825,000 pJ
Now disconnect the battery and reset the cap to 20pF
V = Q/C = 36,500p/20p = 1825 volts
W = 0.5*C*V² = 0.5*20p*1825² = 33,306,250 pJ
Where did the energy come from?
Let's start with a 20 - 365 pF variable capacitor (no leakage) and a 100 volt battery:
Set the capacitor to 20 pF and connect it to the battery.
Q = C*V = 20p*100 = 2000 pC
W = 0.5*C*V² = 0.5*20p*100² = 100,000 pJ
Now disconnect the battery and set the variable cap to 365 pF
V = Q/C = 2000pC/365p = 5.48 volts
W = 0.5*C*V² = 0.5*365p*5.48² = 5481 pJ
Where did the energy go? Did it radiate into space?
Now lets do it the other way around. Charge the 365 pF cap to 100 volts:
Set the capacitor to 365pF and connect it to the battery.
Q = C*V = 365p*100 = 36,500 pC
W = 0.5*C*V² = 0.5*365p*100² = 1,825,000 pJ
Now disconnect the battery and reset the cap to 20pF
V = Q/C = 36,500p/20p = 1825 volts
W = 0.5*C*V² = 0.5*20p*1825² = 33,306,250 pJ
Where did the energy come from?