Calculate the Coulomb potential energy of an electron at a point a distance r from a dipole

Question:

Calculate the Coulomb potential energy of an electron at a point a distance r from a dipole composed of charges Q and – Q separated by a distance l in the arrangement shown in the diagram. Use the fact that l ≪ r to expand the expression 1/(1 + x) into 1 – x + . . . and identify the magnitude of the dipole moment as μ = Ql. Show that the potential energy is proportional to 1/r², as for an ion-dipole interaction. +Q -e r