I can't follow your pace Horace, let's stick to the first and second versions of fig. 1 we were discussing shall we, at least until the controversy is solved. The issue is general anyway, either only potential differences matter, whatever the case at hand, or not.
>> (*) I first mentioned Gauss's law/theorem a few days ago, you may >> remember I applied it to a judiciously chosen small box, > > And I asked you "what box" to which you did not reply, unless I > missed it. I did not see a definition of the box. I had given it though, here it is again: "a small box whose side walls are perpendicular to the metal surface and whose other two walls are parallel to it, one of area A right outside the metal, and the other of area A' anywhere inside it" As I said apply Gauss's law to the surface of that box, and you'll find the law relating a conductor's surface charge density (in C/m2) with the field strength (in V/m) just outside it: sigma = epsilon * E (1) I mean it, do that derivation, this is the only way you'll believe it. >> (note again that the capacitor charge equation q=C*Delta_V alone >> should have sufficed > > That Q is merely an *incremental* Q, not an absolute charge on the > plate surface. Could this be the source of your misconception? Then the end of the controversy is near, as that q _is_ indeed the absolute (or net) charge, which if negative translates directly into the number of excess electrons, i.e. what you are after! Well, what you're really after is the excess electron density in units per m2, so starting from equation (1) above will be more handy. Gauss's law is the key I tell you. Michel ----- Original Message ----- From: "Horace Heffner" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Tuesday, August 14, 2007 7:33 PM Subject: Re: [Vo]:Re: Only potential differences matter > > On Aug 14, 2007, at 3:55 AM, Michel Jullian wrote: > > >> >> What you are still missing Horace is that the two plates, provided >> they are closer together than their lateral extent, act as their >> own Faraday cage so their surface charges really only depend on >> their difference of potential, irrespective of their potential >> relative to nearby external objects including the external Faraday >> cage (whose use is desirable anyway as previously discussed). > > > What you are missing Michel is the discussion that started this whole > thing, the original discussion about the massive morphological > effects of small electrostatic fields *parallel to the plates* in the > Szpak cell experiments. It was a mysterious effect. I hypothesized > these morphological surface effects were due to changes in ion > concentration and electron fugacity, and from the amazingly small E > fields that must have remained at the electrodes from the 6 kV > applied across the cell. I suggested that such a small change in > fields could be affecting cold fusion experiments all over the world > due to differing atmospheric conditions at differing times and > places. Let's be more specific (below). > > > > >> This follows as I said from Gauss's law (also mentioned by John, >> appropriately). I sent you a link earlier, here it is again: >> >> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html > > > > Here is the important figure with regards to our discussion. > > > V1 V2 > (Ground)=(++HV--)===I I==============(Ground) > I I > V3 I GGGIGGG > I===(+LV-)=====I G GgG G > .....I..............I...G GgG G............................. > I I G GgG G > I I XG GgG G > + ==oXG GgG Go > + oXG GgG Go > + oXG GgG Go > + oXG GgG Go > + oXG GgG Go > + oXG GgG Go > + XG GgG G > + G GgG G > + GGGGGGG > GGGGGGG > > Key: > =I - Rubber HV insulated test lead > (--HV) - High voltage low current DC power supply > (LV) - Floating low voltage electrolysis DC power supply > G - Surface of thick strong electrolyte-proof insulator > + - Electrolysis anode, slightly less negative than > cathode wire. > X - CR-39 slab > g - Ground potential electrode for the high voltage field. > o - Cathode wire cross section > .. - Electrolyte level > > Figure 1 - High electron fugacity experiment > > > Your position is the electron fugacity in the cathode supplied by V1 > is dependent only on the potential difference V1-V2, and not the > absolute potential of the cathode coil as I defined absolute > potential. Your position is any potential can be added to both V1 > and V2 and the electron fugacity in the cathode will be the same - > especially on the surface opposed to the anode plate. > > My position is that the fugacity of the cathode supplied by V1 will > differ depending on the absolute potential of that cathode as I > defined absolute potential. In other words, an electron deficit in > the cathode produces low electron fugacity. You say not. This is our > central issue and central disagreement. Other issues are academic. > > The fugacity of the electrons is critical because it affects the > quantum state of some of the population. > > I further say you can not apply the difference idea without limits > because a conductor stripped of conduction band electrons can not > have high electron fugacity. A sufficiently negative plate (using > potential within the gauge I defined) can not have high electron > surface fugacity regardless how positive the plate adjacent to it may > be. That is an extreme case, but it demonstrates the fact you can > not pedantically apply the principles you suggest out of context, > especially the principle: > > http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html#c2 > > which is based on *incremental* charge changes on the plate surfaces. > > I also say Gauss's law has limited relevance with regards to electron > fugacity in this case, and to your position, because it ignores the > effects of any external field on the electrode within the envelope, > and also because you've ignored the effects on the cathode coil (or > plate if need be) other than the surface area opposed to the HV > anode. It also was the objective to have potential (not field > measurement) be useful for design and measurement of experimental > values. > > > > >> >> excerpt:"It is an important tool since it permits the assessment of >> the amount of enclosed charge by mapping the field on a surface >> outside the charge distribution." >> >> Once you will have come to terms with this powerful law and its >> implication which I already mentioned(*) that a conductor's surface >> charge density is uniquely determined by the field right above that >> surface, then this controversy will be solved, at last :-) >> >> Michel >> >> (*) I first mentioned Gauss's law/theorem a few days ago, you may >> remember I applied it to a judiciously chosen small box, > > And I asked you "what box" to which you did not reply, unless I > missed it. I did not see a definition of the box. > > >> I suggest you dig that post out (search for "Gauss"). In my >> derivation I had forgotten a permittivity factor I realize, sorry >> about that, surface charge density sigma is in fact permittivity >> epsilon (or epsilon0 if dielectric is vacuum or air) times the >> field strength E (=delta_V/d in the case of two parallel plates), >> and its sign is determined by the field direction (negative if the >> field is towards the plate, which is the case for the most negative >> of the two plates). Capacitor equations follow from the above, see: >> >> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html#c2 >> >> (note again that the capacitor charge equation q=C*Delta_V alone >> should have sufficed > > That Q is merely an *incremental* Q, not an absolute charge on the > plate surface. > >> to convince you, surely you realize that what you have been >> preaching at length contradicts this simple elementary equation, >> isn't this a bit foolish?) > > Needling will not change the facts, whatever they may be. 8^) > > Horace Heffner > http://www.mtaonline.net/~hheffner/ > > >
