Jack and I were discussing this yesterday, and some questions came up that I need to understand better in order to form an opinion on this puzzle:

1) Experimentally, if you punch a hole in the plate as described, does the dielectric liquid in fact leak out through the hole? In general there will be an electric force (due to fringe fields) pulling the dielectric back into the capacitor, so the liquid can only leak out if there is a force on it strong enough to counteract this tendency to stay inside the capacitor, right? Has it been confirmed that this leaking actually occurs?

2) In order to maintain the voltage difference across the capacitor, there must be a power source (battery or whatever). So assuming that the liquid does leak out, is there a way to show that the energy necessary to do so does not come from whatever power source is maintaining the voltage across the capacitor?

3) How does this puzzle relate to similar puzzles that could be raised for fluid in a capillary tube? For example, an ordinary thin tube immersed in a container of liquid creates a situation where the fluid level inside the tube is higher than the level in the container outside the tube. Why can't you create a perpetual motion machine by just poking a hole in the side of the tube to let liquid leak out and fall back down into the container of liquid, then getting pulled back up the tube in a continuous cycle? I'm pretty certain this won't work, but is the reasoning for why it won't work similar to the dielectric example?

Analyzing these puzzles always make me realize how little we really know! :-)

- Todd

On Tuesday, April 30, 2002, at 06:46 AM, Pentcho Valev wrote:
> I have found a very simple example that everybody can understand but
> that at the same time can resolve a fundamental problem. One should only
> see fig. 6-7 on p. 112 in W. Panofsky, M. Phillips, Classical
> Electricity and Magnetism, 2nd ed., Addison-Wesley, 1962 (or fig. 6-7 on
> p. 102 in the 1st ed.). As a pair of (vertical) capacitor plates
> partially dip
> into a dielectric liquid, the liquid inside the capacitor is shown to
> rise
> high above the surface of the liquid that is outside the capacitor. Four
> hypotheses seem relevant:
>
> 1. Panofsky gives a wrong picture - the effect does not exist.
>
> 2. If we punch a hole in the plate, below the surface of the liquid
> inside the
> capacitor but above the surface of the liquid outside the capacitor, no
> liquid
> will leak out through the hole.
>
> 3. The liquid will leak out in violation of the first law.
>
> 4. The liquid will leak out in violation of the second law.
>
> I think the 4th hypothesis is correct.
>
> Best regards,
> Pentcho