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....
The original questioner was interested to know why the charge at point
B and C have to be numerically equal, as quoted above.
The only person who explicitly contradicted this equality
( as far as I recall ) was John Mallinckrod.
You for example merely modelled the oscillation which could precede
the new steady-state, did you not?
... . If the geometry of
the setup is distorted so the distance between B and C was comparable to or
less than the capacitor gaps which would then have a huge fringe field
volume, and if the geometry of the system significantly broke any left-right
symmetry that the system might possess, then the values of the charges would
not necessarily split up into exactly -Q and +Q on plates B and C but there
would also be some partial charge distributed along the surface of the
conducting connector between them. To solve for the final charge distribution
in this case would entail, in general, solving Laplace's equation over all
space with the requirement the the potential gradient at all metallic
surfaces be locally perpendicular to the surface. This will zero out the
electric field in the interior of the metal.