Re: series capacitors: more in sorrow than in anger.

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

brian whatcott writes:

> Carl Mungan asked this:
>
> Suppose I connect two capacitors in series across a battery. Label the four
> capacitor plates from left to right as A, B, C, and D. Okay, suppose A is
> connected to the positive terminal of the battery, so out goes charge +Q to
> it, and compensating charge off D, leaving -Q on it. My question is: why
> does the charge on B and C have to be -Q and +Q, respectively?

Yes, but Carl went on to clarify his question saying:

> If the isolated circuit consisting of plates B and C and the wire between
> them is initially uncharged, then the sum of the charges presumably has to
> remain zero. But why couldn't I get -1.1Q and +1.1Q on these two plates,
> say? Why *exactly* -/+Q? Is it always exact: what if plates A and B have
> different shapes? Or what if I imagine distorting the wire between plates B
> and C, so that B and C are both portions of some larger object, say the two
> ends of a solid rectangular block, or even a sphere? Surely at some point
> the answer will no longer be -/+Q. At what point - in other words, what
> assumptions go into the usual derivation? I've looked in several textbooks
> and it's presented as though -/+Q is patently obvious. Carl

Making it plain to anyone who read his message to the end that he 
was interested in the *reason* for the result; in what its limits 
of applicability, if any, are; and *not at all* in what happens if 
the capacitors are initially charged.  Frankly, I wouldn't be at 
all surprised to find that Carl, having landed a position as a 
professor of physics in a university physics department, knows how 
to solve simple introductory physics problems like the one you 
posed.

brian goes on to write:

> ...
> The original questioner was interested to know why the charge at point
> B and C have to be numerically equal, as quoted above.

Again, no.  Please take the time and have the courtesy to read his 
post in its entirety.

Quoting David Bowman, brian goes on:

> ...
>
> > What difficulty?
>
> The difficulty of erroneously assigning equal charge on connected plates of
> series caps.

Since the net charge on the connected plates was irrelevant to 
Carl's central question, he explicitly made the simplifying 
assumption that it was zero.  Read his post.

brian goes on:

> ...
>
> I may have mentioned recently that I do NOT subscribe to the
> orthodox ( I deliberately do not say "old-fashioned") view
> that there are "natural laws" that scientists discover;
>  I find it much more productive to suppose that there are man-made models -
> any of which may be more or less suitable to any particular case.
>  This has the particular virtue that when physicists comfortably think they
> are dealing on a 'more-fundamental' level, I can as easily see the flaws in
> their models as in any other man made elaboration.

Very interesting.

Continuing to quote David Bowman, brian writes:

> ...
> > Let u = [mu] = 10^(-6)
> > Q_1 = 30 uC (Q_A = -30 uC, Q_B = +30 uC), Q_2 = 60 uC (Q_C = +60 uC,
> > Q_D = -60 uC)
>
> So you can now easily admit a case where Qb is not numerically equal to Qc
>  This was the crux of Carl's question, was it not?

No, quite clearly it was not.

> ...
>
>  It was Cockroft and Walton who defined this arrangement for a 
> voltage multiplier in the earliest accelerator experiments.
>   They were physicists as I recall.
>     But  I don't suppose their names are known to teachers hereabouts.

Why on earth would you suppose such an absurdity?

> (On careful deliberation, I have deleted the putative reason I offered 
> for this. I hope you will accept this as a tribute to your private coaching
> in how to prevent public shows of sniping)

And I must apologize for *this* public show of sniping.  I guess I 
get a little exercised by remorseless public shows of nonsense.

John
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