Physisorption on metal surfaces provides unique experimental opportunities to establish detailed information about the interaction potential, the induced dipole, and their dependence on the normal distance, z, between the inert adsorbate and the solid surface. These observables involve challenging issues for electron structure theory at distances where electron-

electron interaction gradually changes from nonlocal to local. We show that density functional theory accurately describes the polarization-induced dipole moments measured for H₂ physisorbed on a copper surface. Using a simple dipole model, we conclude that the induced surface dipole is dominated by the charge displacements due to the short-range Pauli repulsion, while the long-range van der Waals attraction only gives a smaller contribution.