We are obviously talking about two different problems.
Very clearly so.
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I was answering the question originally posed by
brian which was
Consider a vanishingly thin lamina of the kind beloved by space
time enthusiasts, opposed by another similar lamina, both having
the same volume and density as the spheres which Bernard
considered, and separated by a gap of similar size as the
laminate thickness.
Is the attractive force stronger, or the same, as two spheres
seperated by a similar distance?
as clarified by my assumptions
1. The lamina are disks
2. "Vanishingly thin" => thickness of disk << radius of disk
3. "two spheres [separated] by a similar distance"
=> the two spheres are essentially in contact.
with which you agreed. (Note: It isn't necessary, of course, for
the lamina to be disks, but they must be very thin with respect to
*both* laminar directions.)
The answer is that the force between the two lamina is *far*
smaller than that between the spheres. Indeed, it is proportional
to the separation itself. (This is ultimately because the
thickness of the lamina decreases with the separation as
required by the problem statement.
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You answered a different question which (1) removed the
requirement that the laminar thickness be connected to the
separation and (2) ignored the requested comparison to the force
between the spheres.
Your answer to this different (and, in my opinion less interesting
problem) is that the force is independent of the separation as
long as that separation remains small compared to the laminar
dimensions, an answer I completely agree with. Furthermore, if
you go on to compare that force to the force between nearly
contacting spheres of the same volume and density, you will find
that it is, as I said, far smaller for precisely the reason I gave
in my second message.