Internal field in a long narrow rod

[Mechdude]

Homework Statement

A long narrow solid rod has an atomic density $5 \times 10^{28}m^{-3}$
each atom has a polarizability of $10^{-40}$ . Find the internal field when an axial field of 1 V/m is applied.

Homework Equations

im not sure what formula to use
but here's one:
$$p = E_{loc} \sum_{r} n_j \alpha_j$$
may be the claussius-mossoti equation could be useful,
$$\sum_{r} N_j \alpha_j = 3 \epsilon_0 \frac{ \varepsilon -1}{ \varepsilon + 2}$$

The Attempt at a Solution

i don't know how to start, i need a clue.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[NateD]

The polarization of the rod can be calculated using the Clausius-Mossotti equation: p = E_{loc} \sum_{r} n_j \alpha_j where p is the polarization, E_{loc} is the local electric field, n_j is the atomic density, and alpha_j is the polarizability of each atom. Using the values given in the problem statement, we have:p = 1 V/m \times 5 \times 10^{28} \times 10^{-40} p = 5 \times 10^{-12} C/m^2 The internal field is then equal to the polarization divided by the permittivity of free space: E_{int} = \frac{p}{\epsilon_0} E_{int} = \frac{5 \times 10^{-12}}{8.85 \times 10^{-12}} E_{int} = 0.56 V/m