= Near-contact van der Waals attraction of spheres
{title2=$U(h)\simeq-A_Ha/(12h)$}
For two equal spheres of radius $a$ separated by a surface gap $h\ll a$, a positive <Hamaker constant> $A_H$ gives the nonretarded <Van der Waals force> approximation $U=-A_Ha/(12h)$ and $F=-dU/dh=-A_Ha/(12h^2)$. The <Derjaguin approximation> derives the geometry factor from the planar interaction energy per area $W=-A_H/(12\pi h^2)$ and effective radius $a/2$. A sphere and plane instead have effective radius $a$, doubling the force at the same gap. Molecular repulsion, roughness and retardation limit these continuum formulas.
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