The bound charge density and free charge density are 12 and 6 units respectively. Calculate the susceptibility

To calculate the susceptibility, we use the definition of bound charge density in terms of polarization (P) and susceptibility (chi), alongside the relationship with electric field (E). When in vacuum or air, the electric displacement field (D), the electric field (E), and the polarization (P) are related as follows:

[D = varepsilon_0 E + P]

The polarization (P) can also be expressed as:

[P = chi varepsilon_0 E]

The bound charge density (rho_b) is related to the polarization by the equation:

[nabla cdot P = -rho_b]

For a uniform polarization, (rho_b) can simply be equated to the volume density of bound charges, which is given as 12 units in the question.

However, the information provided doesn’t directly relate to how we usually calculate susceptibility. Susceptibility (chi) is a measure of how much a material will become polarized in an external electric field, affecting its polarization (P), but the relationship to bound charge density (rho_b) and free charge density requires additional context about the electric field (E) or the medium’s permittivity.

Given only the bound charge density (12 units) and free charge density (6 units), and without information about the electric field (E) or the material’s permittivity (varepsilon), the