I would know how to calculate C of the funny capacitor, at
least in principle, if the potential of the bottom plate were
specified, for example zero. In that case I would impose
potentials on vertical plates, for example, -50 and +50 V,
and used the Laplace equation to find surface charges
on each vertical plate. Then C=Q/V. The boundary
conditions (potentials on three objects) is given and the
rest is just a matter of number crunching.
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But how can the problem be solved when the lower plate is
floating. That plate will certainly find its own potential, that
is it will adjust to potentials on other plates. But I do not
know to find that potential. Therefore the Laplace equation
has an undefined boundary condition. Is this problem
solvable? Note that plates are in fixed positions with
respect to each other.
Ludwik Kowalski