Bound charges of a block (top and bottom surface)

[happyparticle]

You have not used the correct value for the free charge density $\rho$ of the electron layer.
Please include units with the numerical values.

Yes, I saw that, I edited too late.

All right,
$D = \frac{0.02 c/m^3 \cdot 0.002m}{2} = 0.00002 c/m^2$
$E = 705896 v/m$

Finally, I found $\sigma = -0.000014 c/m^2$ for both surface of the block.

 

[TSny]

Yes, I saw that, I edited too late.

All right,
$D = \frac{0.02 c/m^3 \cdot 0.002m}{2} = 0.00002 c/m^2$
$E = 705896 v/m$

Finally, I found $\sigma = -0.000014 c/m^2$ for both surface of the block.

Those answers look correct.

The values that you give for D and E are good for points inside the dielectric except for points within the electron layer. (Of course, we are using an approximation where we are neglecting any fringing of the fields.)

The use of scientific notation and rounding to an appropriate number of significant figures would be nice.

 

[happyparticle]

All right, I have few more questions.
I found E and D using free charges inside the slab. however, since I don't have free charges inside the other part of the dielectric does it means that $\sigma_f = 0$ and $\rho_f = 0$, even if a dielectric has a polarization density.

 

[Gordianus]

Yes. This system has "free" volumen charge only un the central slab

 

[happyparticle]

All right, it took me some time to understand, but thank you both for your help. Things all clearer now.

 

[TSny]

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.