Re: funny capacitor

["John S. Denker" <jsd@MONMOUTH.COM>]

At 04:21 PM 3/12/01 -0500, Ludwik Kowalski wrote:
> Most physics teachers assume that V in electrostatics does
> refer to a potential difference. By definition V is equal to
> the amount of work per unit charge necessary to bring a
> small probe charge to a conductor from another location.

Use whatever conventions you like, but if you want to make sense of what
I've written you'll have to (at least temporarily) accept the notation I've
been using:  I use delta_V to represent potential differences.  Some of the
things I say about potential differences are not true about absolute
potentials (which I represent by V).

> My personal preference, in the funny capacitor problem,
> is to use the enclosure as a reference location and to
> assign V4=0 to it. I am not trying to impose this convention
> on anybody. I want to know if it is possible to solve our
> problem by assuming that V1, V2 and V3 are differences
> of potentials with respect to a large enclosure.

Sure it's possible.  It's straightforward.  Just turn the crank.  You'll
wind up with a 4x3 matrix giving the four Qi as a function of the three
delta_Vj.

Your questions about the physical significance of C44 will not arise
because there will be no (4,4) element in the C matrix.

You can then throw away the 4th row (or indeed any row) and have a 3x3
matrix that can be inverted to give the three delta_Vk in terms of the
three remaining Qi.

> I have no idea
> what a potential is unless it is a word referring to a difference
> of potentials.

1) If you publish all the differences in potential, you can't prevent some
theorist from running around and adding them up in such a way as to
construct the potential, which is a function that assigns a value to each
point in space (or, in the lumped-circuit approximation, assigns a value to
each of the four nodes).

Given this theoretical potential-function, the physically-observable
potential differences can always be reconstructed by simple subtraction.

2) You also can't prevent said theorist from adding an arbitrary constant
of integration (i.e. a gauge) to this potential-function.  This leaves the
physically-observable potential differences unchanged.

3) I say again you are free to solder the black lead of your voltmeter to
node 4 and leave it there.  However, in my lab I very commonly move both
leads around the circuit in nontrivial ways.  I'm not making this up.

The following story may provide some perspective:

I remember the very first technical thing I learned in college.  I had just
arrived.  Two of the freshmen who had arrived a day earlier were already
trying to build something.  They had scrounged a transistor, but had no
specification sheet for it.  They didn't even know which of the terminals
was which.  The bunch of us tracked down Tak Sing Lo (one of the
upperclassmen) and asked for advice.  He said nothing, but grabbed a pair
of ohmmeter probes in one hand, like chopsticks.  I was somewhat
impressed;  I was just a callow country boy who had never seen chopsticks,
let alone used them.

Tak Sing poked at the transistor with the "chopsticks" five times, wiggled
his finger around the edge, and announced
        "P-N-P.  That (crimp) is base and
       that (crimp crimp) is emitter",
        ... as he crimped the leads to mark which was which.

It was over in less than ten seconds.  Everybody walked away.

I was left standing there, in the corridor by the mailroom, staring into
space, wondering what I had just seen.  Even if you had explained it to me
I wouldn't have understood.  But I promised myself that sooner or later I
was going to master that trick.