It's easier to get the numbers than to explain the
process. This supports an idea we've discussed
before: Conscious attentive thought is serial,
but the other 99.9999% of thought is highly parallel,
subconscious, and not open to introspection.
Any attempt to retell what happened as a nice sequential
story involves a certain amount of fictionalization.
In that spirit, here's how it would have gone down
*if* I had used a logical sequential process:
1) Recognize it as the sort of problem that can be
solved by superposition.
2) Recognize the importance of symmetry.
3) Do the easy sub-problem: +2 C on one plate
along with -2C on the other plate. I call this
two units of /gorge/. This is a plain old
capacitor. The solution is well known.
4) Do a completely different sub-problem: Start
with an object consisting of two plates with
/zero/ gorge. Treat this as a /single/ object.
Apply -1 C of real honest-to-goodness charge
(not gorge) to this object. This is a plain
old charged object. The solution is obvious
by symmetry
5) Superpose the two sub-problems. We now have
2 units of gorge and -1 units of charge.
6) Check the work. In particular, verify that the
two inner faces still have equal-and-opposite
charges. This is consistent with the requirement
to ignore fringing fields, together with the basic
equations of electrostatics. Any field line that
originates from one inner face must terminate on
the other inner face, because there is nowhere
else for it to go. This alone is enough to
guarantee uniqueness of the solution.
==========================
There are a lot of situations where it really helps
to be able to think clearly about the distinction
between /gorge/ on a capacitor and plain old net
/charge/ on a capacitor. Ditto for batteries.
For details, see: http://www.av8n.com/physics/electrophorus.htm#sec-gorge