# Bound charges of a block (top and bottom surface)

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For dielectrics that are linear, isotropic, and homogeneous, we have ##\vec P = \epsilon_0 \chi_e \vec E## where ##\chi_e## is a constant related to the relative permittivity, ##\epsilon_r##: ##\chi_e = \epsilon_r - 1##.

For these dielectrics, it is not hard to derive a useful relation between the bound charge density ##\rho_{b}## and free charge density ##\rho_f## that holds for any point inside the dielectric.

##\large \rho_b = - \frac{\chi_e }{\epsilon_r}\rho_f \,\,\,\,\,## (This type of relation does not hold for the the surface charge densities ##\sigma_b## and ##\sigma_f##.)

You can use this to get the bound volume charge density ##\rho_b## inside the electron layer. Then you can check that the total bound charge of the dielectric is zero, as it must be.