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3) I think that a cubical cloud is mathematically easier. Try to derive
the force formula for a cloud of radius L. The left segment of your
sphere will become a meniscus lens whose volume would not be
a linear function of x. I will accept your claim "cubes are less
tractable than spheres" after I see your derivations. Perhaps you
have a good shortcut that is OK for an introductory course.
4) There was a typing error in the formula for Emax; it is obvious
that the denominator should have been L^2 and not L.
Regards, Ludwik