# What is the pressure between two electric dipole sheets of finite extent?

I have recently become curious about modeling the repulsion of everyday objects in contact with one another. By repulsion I mean as you attempt to walk through a wall, the pain in your nose suddenly alerts you to the fact that it won't be possible. I've come up with this exercise:

What is the mutual pressure exerted by two dipole sheets of finite extent, each area $A$, separated by a distance $D$? Assume $D \gg$ d where the dipole moment $p = ed$ and $e = 1.6\times10^{-19}$. There are $N$ dipoles per unit area. Make an order of magnitude estimate for $N$ to represent a density one would find in ordinary matter. Make a numerical plot for $10^{-10} < D < 10^{-3}$ meters.

This is a crude electrostatic model of two electrically neutral materials brought close together. The oppositely oriented dipole sheets are generated by the electronic cloud repulsion and deformation as the two interfaces approach. It is meant to serve as a quantitative estimate of the maximum distance at which Coulomb repulsion could possibly stop one body from passing through another. Interface physics is pretty rich, but I wonder how this model does in predicting such pressures.

If anyone has related references please post them, especially any experimental studies.

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This sounds an awful lot like a homework problem... if it is, could you add the homework tag? (Homework questions are fine here, we just want them to be identified as such) And if it isn't a homework problem, I'd suggest rewording it so that it doesn't give that impression. –  David Z Dec 8 '10 at 5:44
This is supposed to be a reaction to my discussion with Pete about net electrostatic force between two lattices. My toy model was a one-atom thick layer of $+$ and $-$ charges arranged in checkerboard pattern (which is quite crude but should still give us some information; you can add more layers though). But this question seems to be even cruder, so it's irrelevant to the above. The reason is that the answer in my model depends on how exactly you align $+$ and $-$ of the two lattices. –  Marek Dec 8 '10 at 11:39
@David, I got my PhD in physics some time ago. I was hoping someone else, perhaps getting ready for an E&M exam, could quickly knock this out so I didn't have to spend an evening on it. I also hoped some solid state theorists out there could comment on modeling two everyday materials brought close together (i.e. why can't I walk through a wall). –  Pete Dec 8 '10 at 15:35