Problem 4.3 According to Eq. 4.1, the induced dipole moment of an atom is pro- portional 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. p = αE. (4.1) The constant of proportionality a is called atomic polarizability. Its value depends on the detailed structure of the atom in question. Table 4.1 lists some

Problem 4.3 According to Eq. 4.1, the induced dipole moment of an atom is pro- portional 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. p = αE. (4.1) The constant of proportionality a is called atomic polarizability. Its value depends on the detailed structure of the atom in question. Table 4.1 lists some