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Re: series capacitors: more in sorrow than in anger.



Brian Whatcott (among other things) wrote:
....
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?

At the risk of being accused of a public show of sniping I must mention that
this is not correct. Although my post did mention some of the details that
must occur for the charge re-equilibration process to proceed, the point of
it was to show how and why the second law makes the system minimize its
macroscopic electrostatic potential energy in equilibrium. I *did* discuss a
case for which the charges at B and C were not (oppositely) equal to either
each other or to the charges on the other cap plates at A and D. This was
an explicit consideration of an extreme geometry case similar to that which
John Mallinckrodt considered and to which Carl Mungan asked about. I wrote:

... . 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.

BTW, my explanatory framework has no difficulty let alone an "overwhelming
difficulty in explaining the reasonable case of two caps of different C
value, precharged to the same voltage". The reason that I did not happen to
consider such a precharged case was that it was not a concern of the
original questioner.

I'll forgo any further public sniping here since John Mallinckrodt did such
a fine job of it in his previous post.

David Bowman
dbowman@gtc.georgetown.ky.us