= Solution
For two equal spheres of radius $R$, the effective radius in the <Derjaguin approximation> is $R_{\rm eff}=R/2$. The nonretarded attractive <van der Waals potential> is
$$
U(h)=-\frac{A R_{\rm eff}}{6h}=-\frac{AR}{12h}.
$$
Differentiating with respect to the surface gap gives
$$
\boxed{F(h)=-\frac{AR}{12h^2}
=-\frac{(4.0\times10^{-19})(10^{-9})}{12(2\times10^{-9})^2}
=-8.3\times10^{-12}\ \mathrm N.}
$$
Thus the requested approximation gives \b[an attraction of about $8.3$ pN]. Here $h/R=2$, whereas the <Derjaguin approximation> requires $h\ll R$. This is the formal estimate requested by the hint, not a quantitatively reliable near-contact approximation for the printed dimensions.
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