Free surface charge density (not bound density)

1. The problem statement, all variables and given/known data

a parallel plate capacitor has 2 plates separated by a dielectric of rel. permittivity 5.0 are separated by 0.20mm and have area of 5.0 cm2.

Potential difference between the plates is 500V.



I need to be able to calculate the free surface charge density.









2. Relevant equations

I'm assuming D_out = D_in



From boundary conditions D₁ ┴ = D₂ ┴

and D₂ ┴ - D₁ ┴ = σf



Could someone just confirm what the boundary conditions are so I can say that the free surface charge density is zero or not!





3. The attempt at a solution



I have D_out = D_in = ε₀E_in + P

so from calculations

P = 4.43x10^-9 - (8.85x10^-12 x 100)

P = 3.54x10^-9 Cm^-2



Could I just say;

D₁ ┴ = D₂ ┴ so there is zero free surface charge density!