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Re: [Phys-L] circular definition of "success" .... was: standard DC circuits



On 12/04/2013 04:14 AM, Jeffrey Schnick wrote:
By charge separation, I understood Bruce to mean that there is a
certain tiny amount of positive charge on the positive terminal of
the battery and the same amount of negative charge on the negative
terminal. This charge creates the electric field that is
characterized by the constant electric potential difference between
the terminals. To maintain that constant electric potential
difference, the battery has to maintain that charge distribution. The
total amount of charge that has flowed through the battery to date
does not seem to be relevant to the question of charge separation.

The fact that we have to guess what is meant by "charge" and
"charge separation" is a sign that almost nobody thinks very
clearly about this business. Most of our terminology for
"standard DC circuits" was developed for the usual engineering
situation where Kirchhoff's laws apply. If/when we decide to
delve into the microscopic steering charges, we have to do a
*lot* more work. This includes introducing new concepts, defining
new terminology, and (!) redefining old terminology.

Between two stools one sits in the ashes. There is no way to
explore the extra detail without doing a lot of extra work ...
which is where this sub-thread began.

Than on 12/04/2013 05:11 AM, Chuck Britton wrote:
But - that ‘tiny amount of charge’ varies widely depending upon the
geometry of the terminal itself rather than the ‘voltage’ of the
battery. A lower voltage battery may well show a greater amount
charge separation than might a higher voltage battery with a
different terminal geometry. (If I’m following this correctly)

Exactly.

To say the same thing in different words: If you show me a battery
with a certain amount of charge on the positive terminal, I can
show you another battery with the same voltage and half as much
terminal-charge, plus another with twice as much. With a little
more complexity I can produce zero terminal-charge -- or the "wrong"
sign of charge.

It is therefore not OK to mention charge and voltage on the same
footing when defining what a battery does. The zeroth-order defining
property of an ideal battery is constant voltage. Mentioning charge
is just silly.

We're talking about the third sentence of chapter 19, featured in
the [ *KEY IDEAS* ] section:

«A battery maintains a charge separation and a potential difference.»

At first I thought this was just a typo, but since then there have been
concerted efforts to defend the «A battery maintains a charge separation»
claim. Also note that throughout chapter 19 students are required to
draw diagrams based on the assumption that the local charge density is
proportional to the local voltage.

There is some inconsistency, because 18 pages after the previous claim
we find a different statement:

[ *ROLE OF A BATTERY* ]
[ ]
[ A battery maintains a potential difference across the battery. This po- ]
[ tential difference is numerically equal to the battery's emf. ]

That's just fine, as a zeroth-order model. No mention of charge. (Or
maybe the bogus idea of charge proportional to voltage is so consolidated
by this point that it goes without saying.)

========================

To come at this from the point of view of basic physics: The idea of
capacitance is reeeeally fundamental to circuit physics. This includes
self-capacitance and mutual capacitance.

To assume charge proportional to voltage is tantamount to assuming that
the capacitance matrix is the identity matrix, i.e. everything has the
same self-capacitance and nothing has any mutual capacitance(s). This
is just silly.