Interestingly enough, I was just in private discussion with Ludwik about the
same concerns Carl had; I've alway felt uncomfortable lecturing about the
standard textbook equal charge statements. Here are some of my thoughts on
the topic and some responses to what else has just been written:
1) First a minor comment. I disagree with a statement David made. He
wrote: "If the charges on plates B and C of the interior plates were not -Q
and +Q respectively then there would be an electric field in the region
between the capacitors . . ."
If we look at an ideal case where the two capacitors are well approximated
by two infinite parallel plate capacitors far apart and connected by a very
thin wire. We can model the static charge distribution as 4 sheets of
charge and the field in between the two plates is zero, even if the
interior charges are +- 1.1 Q.
2) I rather like John's response. Let's assume we are not dealing with an
extreme geometry case; but rather a case where the textbook rule applies to
very good approximation. I think the rule hinges on two points. One must
argue that all field lines originating on plate A terminate on plate B.
(This is what gets violated in extreme geometry cases). For situations
like (1) above this isn't too hard to justify, because in a single capacitor
one has already talked about this in the usual "what is a capacitor
discussion". Secondly, you need to invoke Gauss' Law, put surfaces around
each of plates A and B; the field line flux is the same (in magnitude, there
is a sign difference of course), therefore the magnitudes of the net charge
on plates A and B are the same.
Similar discussion applies at plates C and D.
3) Most textbooks I've looked at (Calculus level introductory texts) have
abysmal explanations that amount to non-justification of the equal charge
rule. A cursory look has shown me that most books have illogical and bogus
statements that don't imply the rule, and in fact amount to just asserting
that it is the case. I.e. they make it seem that it is "patently obvious"
without true justification. Often they talk about the inner plates being
one conductor that is overall neutral and invoke conservation of charge;
this doesn't do IT as Carl's original thought of the inner plates having a
plus/minus 1.1Q charge doesn't violate conservation of charge. One or two
books I've looked at, at least refer to all the field lines on plate A
terminating on B; but don't make the further crucial step of invoking Gauss'
Law. They are missing a golden opportunity to use Gauss' Law in a profound
way (and necessary way) to justify the equal charge law.
4) Thanks to Carl for bringing this up, he's braver than I.