 Charge-induced dipole attraction

A neutral isotropic atom with static electric polarizability $\alpha >0$ in the field of a distant point charge $Q$ has induced dipole $\mathbf{p}=\alpha \mathbf{E}$ and energy $U=-\alpha E^2/2$. Since $E=|Q|/(4\pi {ϵ}_0{r}^2)$,The negative radial force is attractive for either sign of $Q$. Reversing $Q$ reverses the induced dipole but not the energy or leading force. The factor $1/2$ accounts for the work of inducing the dipole; using the permanent-dipole energy $-\mathbf{p}\cdot \mathbf{E}$ without that work would double the answer. The approximation assumes weak fields, a slowly varying field across the atom and negligible electronic overlap.