Todd Duncan wrote:
> 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?

No, as far as I know. In fact, the no-leaking hypothesis saves the second law, but is quite improbable. A suitable dielectric to imagine is water - with it, the effect would be strong. However it is difficult to imagine that an electric field, however strong it is, can stop a water molecule from leaking. The poles in the water dipole are close to one another and, in a field, the molecule polarizes but still diffuses as a neutral particle. Panofsky speaks of pressure - roughly speaking, this means that the water molecules "press" on the plate. Pressure is without direction, so there will be pressure in the region of the hope as well. Finally, inside the hole, there is no locally-generated field PERPENDICULLAR to the plate.
>
> 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?

The way Panofsky presents the situation suggests that this is a constant-charge capacitor that does not discharge into the liquid - this is a standard model. Still the problem of the energy source is important. It seems that electrostatics ignores an essential class of forces that act in dielectric liquids and are non-conservative. One usually associates "non-conservative" with friction, but generally this is not the case. By definition, non-conservative is any force such that, when you do work against it, dissipates the energy as heat but does not store it within the system. In this sense, a gas pressure is perfectly non-conservative - when you compress a gas isothermally, the energy you spend is dissipated as heat. Vice versa, as
the gas expands and does work (isothermally), it does it AT THE EXPENSE OF HEAT ABSORBED FROM THE SURROUNDINGS. Now it seems that a non-conservative pressure, akin to gas pressure, exists between two opposite charges (or capacitor plates) immersed in a dielectric liquid. If you draw the charges (plates) apart, this pressure does work at the expense of heat absorbed from the surroundings. (Phenomenologically, this is expressed in the fact that the electrostatic force of attraction decreases and you spend much less work to draw the plates apart in the dielectric than in vacuum). If you don't move the plates, as in Panofsky's case, the pressure expresses itself by lifting the liquid inside the capacitor above the surface of the rest of the liquid.

However this lifting is performed AT THE EXPENSE OF HEAT ABSORBED FROM THE SURROUNDINGS. By leaking out and falling, the water releases the accumulated energy (heat).
>
> 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?

In the capillary tube, water is lifted at the expense of the energy of interaction between water and the tube. In the highest position, water is still tightly hold by the wall and cannot leak out.
>
> Analyzing these puzzles always make me realize how little we really
> know! :-)

It is not always a matter of knowing. For instance, unavoidable heat effects have always been both detected and accounted for when an electric field is applied to dielectrics. On the other hand, the above definition of non-conservative force (one that dissipates the work done against it as heat) is also given in textbooks. Then why doesn't one combine the two points and suspect that non-conservative forces might be operative in a dielectric? These days I thought about that and reached the following conclusion. The assumption that non-conservative forces are operative is tantamount to the suggestion
that a new electrostatics is needed - the present one is based on the (sometimes explicit) assumption that ONLY CONSERVATIVE FORCES ARE OPERATIVE. Now imagine a scientist who wants to create a new electrostatics (challenging the second law among other things) and asks for funds.

Pentcho
>
> 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