According to Eq. 4.1, the induced dipole moment of an atom is proportional to the external field. This is a “rule of thumb,” not a fundamental law, and it is easy to concoct exceptions––in theory. Suppose, for example, the charge density of the electron cloud were proportional to the distance from the center, out to a radius R. To what power of E would p be proportional in that case? Find the condition on p(r) such that Eq. 4.1 will hold in the weak-field limit.