Is There a Perpetual Motion Machine Hidden in the Capacitor Paradox?

[Meir Achuz]

So basically you have increased the capacitance by increasing the plate area.It is true that if you take a large and a small capacitor and charge them to the same voltage then the large one will store more energy.With this paradox we can have different situations:
1.BATTERY PERMANENTLY CONNECTED.In this case V will equalise when the capacitance is varied but Q will vary.If C is increased, more charge will flow from the battery and the energy stored will increase.
2.CAPACITOR CHARGED AND BATTERY DISCONNECTED.In this case Q will be constant but V will vary.If C is increased, V will decrease and the energy stored will decrease.
In my post above I was referring to situation two and although both situations give opposite results the paradox still exists.

I got to this thread late, but just noticed your "paradox".
This is treated in most EM textbooks. A battery connected to keep the capacitor at constant voltage does twice as much work as the negative energy difference at constant Q. This work done by the battery effectively changes the sign. The arithmetic is -1+2=+1.

 

[Dadface]

Perhaps I'm not understanding. What, specifically, is the paradox?

I got to this thread late, but just noticed your "paradox".
This is treated in most EM textbooks. A battery connected to keep the capacitor at constant voltage does twice as much work as the negative energy difference at constant Q. This work done by the battery effectively changes the sign. The arithmetic is -1+2=+1.

I think we are at cross purposes here and it is necessary to read throught the whole thread.The paradox is about the changes that would apparently be observed by different observers if the capacitor was moving at relativistic speeds.In my posts I was mainly pointing out that that the equal volume changes in the two capacitor orientations referred to earlier in the thread do not result in equal capacitance changes.

 

[Dale]

Perhaps I'm not understanding. What, specifically, is the paradox?

I agree with you. There is no real paradox here. Just a typical "apparent paradox" from not using the laws of physics and then being surprised that the result is non-physical.