Re: How many volts ?

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

On Tue, 25 Mar 1997, W. Barlow Newbolt wrote:
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> I think that John has the solution right for the difference in potential 
> for two plates which may be considered infinite. That is, those charges 
> were charge densities. ...  What happens if the plates are not infinite? 
> I think this is at least part of Ludwik's objection.

No, charges were not densities, they were given in nC. And the plates were
not infinite. The final distance between the plates, however, was rather
small (1 cm) for squares or circles of one square meter. The shape was not
specified in the first formulation; it was specified later as circular.

Soon after Donald E. Simanek wrote:
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> The problem had several quirks. One was the distractor, the comment about
> the capacitance, calculated from the parallel-plate capacitor formula, a
> result not necessary to solving the problem. 

Yes; this presents a problem. Suppose we accept that dV=62 volts. How do
we calculate C when |Q1|=-10 nC and |Q2|=+100 nC? Which Q should we use
in C=Q/dV?

> I think John's solution, and answer are correct, and insightful, using
> Gauss' superposition principle.

But, if I undertood him properly, he took it for granted that final charge 
distributions must be uniform, at least approximately. How much would you
bet, Don, on the outcome of an experiment? I know where to borrow a very
good electrostatic voltmeter (20 pF and 3 to 300 volts). You win if the
result is between 52 and 82 volts, I win otherwise. We would have to agree
on the method. How many people would like to participate in betting? This 
is not a formal offer. Referring to Barlow:

> > 2. What happens to the potential difference between the plates as they 
> >    are moved together. After all, they were infinitely far apart 
> >    originally. I presume that the total potential would go down since 
> >    they attract each other and work will be done by the field.

Don continues:
> That's another distractor, in my understanding of this problem, for the
> potential of any charge configuration is the (work done)/charge in
> assembling it from charges initially infinitely separated. it doesn't
> matter how the assembly is carried out. You might as well start with the
> plates in place and put the given charges on them. 

You can do this "in a gedanken experiment" but in reality giving a known
amount of charge to a plate must be done separately for each plate, most
easilly using an auxiliary plate and a source of known voltage. 

> .. The potential will change as the plates are moved together, of course, 
> but that fact is, I think, irrelevant to this problem, since it merely spoke 
> of charges placed on the plates, not on their changes in potential. Only the 
> *final* potential was wanted. 

That is correct.

> It's really a very neat problem which forces one to keep one's wits intact, 
> understand concepts, avoid irrelevant disctractions, and pick up on subtle 
> clues. ... I give high marks to whoever invented and worded this clever 
> problem. ...

Thanks for the compliment. I plan to place this problem, and great messages 
it generated, as an entry on my home page. Will let phys-L know about this in 
a separate posting. I hope it is not the end of the thread; several questions
remain unanswered.
                              Ludwik Kowalski