In this problem you are to find how the van der Waals force between a polar and a nonpolar molecule depends on the distance between the molecules. Let the dipole moment of the polar molecule be in the x direction and the nonpolar molecule be a distance x away.

(a) How does the electric field due to an electric dipole depend on distance x ?

(b) Use the fact that the potential energy of an electric dipole of moment p in an electric field E is U = -p · E, and that the induced dipole moment of the nonpolar molecule is proportional to E to find how the potential energy of interaction of the two molecules depends on separation distance.

(c) Using Fx = - dU/dx find the x dependence of the force between the two molecules.